**Perovskite Quantum Dot Light-Emitting Diodes**

**Perovskite Quantum Dot Light-Emitting Diodes**

DOI: 10.5772/intechopen.68275

Zhifeng Shi, Xinjian Li and Chongxin Shan Zhifeng Shi, Xinjian Li and Chongxin Shan Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68275

#### **Abstract**

Recently, lead halide perovskite quantum dots (QDs) have attracted much attention because of their excellent properties of high color purity, tunable emission wavelength covering the whole visible region, and ultrahigh photoluminescence (PL) quantum yield. They are expected to be promising candidates for the next-generation cost-effective lighting and display sources. Here, we introduced the recent development in the direct solutionprocessed synthesis and ion exchange-based reactions, leading to organic/inorganic hybrid halide perovskites (CH3 NH3 PbX3 ; X = Cl, Br, I) and all-inorganic lead halide perovskites (CsPbX3 ; X = Cl, Br, I), and studied their optical properties related to exciton-related emission and quantum confinement effect. Finally, we reviewed the recent progresses on the perovskite light-emitting diodes (LEDs) based on CH<sup>3</sup> NH3 PbX3 and CsPbX3 quantum dots and provided a critical outlook into the existing and future challenges.

**Keywords:** perovskite, CH3 NH3 PbX3 , cesium lead halide, light-emitting diodes

#### **1. Introduction**

Motivated by the remarkable color tunability and relatively high photoluminescence (PL) quantum yield of colloidal quantum dots (QDs), the concepts of QD-based light-emitting diodes (LEDs) have been proposed and developed for a few years, and multicolor LEDs were successfully fabricated either for PL or electroluminescence (EL) mechanism [1–6]. It has been recognized that using QD-based LEDs as the backlighting system of liquid crystal display can greatly expand the color gamut of display and present vibrant colored images [7]. Although the conventional CdSe-based QD system has been commercially used, it suffers from the lack of surface control during process and low-cost preparation technique [8]. Moreover, development of high-performance CdSe QD-based LEDs strongly relies on the precise core/shell design, involving the band engineering and surface ligands. In this circumstance, colloidal lead halide perovskite QDs began to attract a great scientific attention. The appealing properties

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

of this new class of materials that might enable advances in electroluminescent devices are their outstanding optical properties including the narrow emission band (<20 nm), a wide wavelength tunability (400–800 nm), and a high PL quantum yield, which make them suitable for high-performance, low-cost, and lightweight LED applications [9–11]. Beyond LEDs, they were also explored as interesting materials for low-threshold lasing [12], photodetectors [13], and solar cells [14]. And, many studies on these fields have been reported recently. In the following, two typical synthesized methods for the novel perovskite QDs system were introduced in detail, and their optical properties related to the exciton-related emission and quantum confinement effect were investigated. Finally, we reviewed the previously reported device structures on perovskite QD LEDs and provided a critical outlook into the existing and future challenges.

#### **2. Crystal structure features**

Lead halide perovskite QDs have a crystal structure of ABX3 , in which A and B are the monovalent and divalent cations, respectively, and X is a monovalent halide anion (Cl, Br, I). The typical crystal structure of lead halide perovskites was illustrated in **Figure 1a**. B cation is coordinated to six halide ions in an octahedral configuration, and the octahedra are corner-sharing, with the A cation located in between those octahedra. In addition, the lead halide perovskite QDs can fall into two categories depending on the chemical component of A cation, organic-inorganic hybrid, and all-inorganic perovskites. Methylammonium (MA) lead trihalide perovskites have so far been the most intensively explored in optoelectronics, and they have the chemical composition of MAPbX*m*Y3−*m*. This perovskite is a hybrid inorganic-organic direct-bandgap semiconductor. Also, the perovskites based on colloidal CsPbX3 QDs are extensively investigated in recent years. As is well known, MAPbX3 or CsPbX3 QDs can crystalline in orthorhombic, tetragonal, and cubic polymorphs according to the environment temperature and total system energy. And, experimental results have confirmed that MAPbX<sup>3</sup> or CsPbX3 QDs possess different crystal structures at different temperatures or with different halide ions [15]. For the

**Figure 1.** Illustration of the perovskite crystal structure.

two types of perovskite QDs, their optical and electronic properties are tunable by varying the composition of constituted halide ions and a smaller degree of the cations. Also, the size of perovskite QDs plays an important role on their optical properties due to quantum confinement effect [16].

#### **3. Chemical synthesis of perovskite QDs**

#### **3.1. Synthesis of MAPbX3 QDs**

of this new class of materials that might enable advances in electroluminescent devices are their outstanding optical properties including the narrow emission band (<20 nm), a wide wavelength tunability (400–800 nm), and a high PL quantum yield, which make them suitable for high-performance, low-cost, and lightweight LED applications [9–11]. Beyond LEDs, they were also explored as interesting materials for low-threshold lasing [12], photodetectors [13], and solar cells [14]. And, many studies on these fields have been reported recently. In the following, two typical synthesized methods for the novel perovskite QDs system were introduced in detail, and their optical properties related to the exciton-related emission and quantum confinement effect were investigated. Finally, we reviewed the previously reported device structures on perovskite QD LEDs and provided a critical outlook into the existing and future challenges.

lent and divalent cations, respectively, and X is a monovalent halide anion (Cl, Br, I). The typical crystal structure of lead halide perovskites was illustrated in **Figure 1a**. B cation is coordinated to six halide ions in an octahedral configuration, and the octahedra are corner-sharing, with the A cation located in between those octahedra. In addition, the lead halide perovskite QDs can fall into two categories depending on the chemical component of A cation, organic-inorganic hybrid, and all-inorganic perovskites. Methylammonium (MA) lead trihalide perovskites have so far been the most intensively explored in optoelectronics, and they have the chemical composition of MAPbX*m*Y3−*m*. This perovskite is a hybrid inorganic-organic direct-bandgap semi-

or CsPbX3

tetragonal, and cubic polymorphs according to the environment temperature and total system

ferent crystal structures at different temperatures or with different halide ions [15]. For the

, in which A and B are the monova-

QDs are extensively investigated

QDs possess dif-

QDs can crystalline in orthorhombic,

or CsPbX3

**2. Crystal structure features**

48 Quantum-dot Based Light-emitting Diodes

Lead halide perovskite QDs have a crystal structure of ABX3

conductor. Also, the perovskites based on colloidal CsPbX3

energy. And, experimental results have confirmed that MAPbX<sup>3</sup>

in recent years. As is well known, MAPbX3

**Figure 1.** Illustration of the perovskite crystal structure.

Perez-Prieto and coworkers pioneered the wet chemistry colloidal synthesis of free-standing hybrid perovskite QDs (MAPbBr3 in their case) [17]. A simple one-step approach was employed in their experiment. The PbBr2 was reacted directly with a mixture of ammonium bromide with short methyl chain and longer alkyl chains. In the middle part of the crystal, the MA cations were embedded, which would connect the neighboring [PbBr<sup>6</sup> ] − octahedra. And, the outer space will be occupied by the longer alkyl ammonium cations; as a result, the growth of MAPbBr3 nanocrystals (NCs) is terminated. Therefore, one could assume that the longer alkyl ammonium cations in the outer space played the role of capping ligands of the perovskite NCs, which may be the reason that the MAPbBr3 NCs could be dispersible in many solvents. That is to say that the role of these ligands is to provide a self-termination of the crystallization, leading to the formation of discrete nanoparticles in solution. In their case, the resulting MAPbBr3 QDs could be stable for concentrated solutions as well as in solid states for 3 months. The corresponding microstructure of the synthesized products was shown in **Figure 2a**, in which a mixture of nanodots (~10 nm) and nanoplatelets (~40 nm) could be distinguished. **Figure 2b** and **c** shows the absorption and PL spectra of these highly crystalline MAPbBr3 QDs, and a high-purity green emission at about 530 nm can be found. The corresponding PL quantum efficiency was about 20%.

By optimizing the molar ratio of octylammonium bromide:MA bromide:PbBr2 (8:12:5) in a typical reprecipitation method while maintaining the 1-octadecene:PbBr2 molar ratio of 62.6:1.0, this research group promoted the quantum efficiency of MAPbBr<sup>3</sup> QDs to 83% [18], demonstrating a promising potential for use in luminescent devices, such as LEDs and laser diodes. Owing to the fact that surface states in QDs would support the desired passivation treatment, Perez-Prieto and colleagues improved the organic capping of the MAPbBr3 QDs; as a result, intensely luminescent and easily dispersible MAPbBr3 QDs were produced, as shown in **Figure 2d**. As for the origin of the surface states, Li et al. recognized that the richness of halogen at the surface of QDs ought to be responsible for surface states [19]. On the one hand, abundant Br atoms at the surface will connect with cations, inhibiting the trapping of excited carriers and then high PL quantum efficiency. This process can be named as self-passivation effect, which is similar to the intentional passivation behaviors of traditional QDs with halogen ions. On the other hand, riched Br on surface should be binded with MA to form PbBr*<sup>x</sup>* analogs, which possesses a relatively large bandgap of 4.0 eV. Therefore, quasi-core-shell structure of MAPbBr3 /Br was formed. This superior characterization is similar as the shelling of ZnS around CdSe QDs core, photoexcitated carriers would be confined, and a high PL quantum efficiency could be expected. For a further confirmation, Zhong and coworkers performed the energy-dispersive spectroscopy measurements for synthesized MAPbBr3 QDs [20]. They found a Br/Pb ratio of 3:5 for QDs with an average diameter of 3.3 nm, matching with the observation in Li's report. Also, the X-ray photoelectron spectroscopy results for MAPbBr3 QDs support their argument above, and the smaller the diameter of QDs, the larger the ratio of Br/Pb.

Subsequently, this simple synthetic method was adopted in other groups, and an increasing number of papers have been published in this field. For example, Luo and coworkers used either octylammonium bromide or octadecylammonium bromide to produce perovskite QDs by using the reprecipitation method, with the size of QDs of 3.9 and 6.5 nm, respectively [21]. In their case, the size control of QDs was due to the different ligand-binding kinetics, and the high solubility of longer hydrophobic chain ligands could facilitate the increase of QD size. Zou et al. developed a ligand-assisted reprecipitation strategy to fabricate highly luminescent and color-tunable colloidal MAPbBr3 QDs with the absolute quantum efficiency up to 70% at room temperature (RT) and low excitation fluencies. In their work, the reprecipitation method was a simple way for preparing organic nanocrystals or polymer dots simultaneously through the solvent mixing [22]. As shown in **Figure 3a**, they employed the same principle and simply mix a solution of MAPbX3 precursors in good solvent (*N*-dimethylformamide (DMF)) into a vigorously stirred poor solvent (toluene, hexane, etc.) to form the organometal halide perovskites. Simultaneously, the long-chain organic ligands, such as n-octylamine and

**Figure 2.** (a) Transmission electron microscope image of MAPbBr3 QDs with a mixture of nanodots and nanoplatelets. (b) UV-visible absorption and (c) PL spectra of the MAPbBr3 QDs. (d) Image of the toluene dispersion of MAPbBr3 QDs under UV-laser pointer excitation.

oleic acid (OA), were introduced into a mixture to control the crystallization of precursors into colloidal QDs. So, it can be assumed that n-octylamine controlled the kinetics of crystallization and further contributed to the size control of MAPbX3 QDs, whereas OA suppressed the aggregation effects and ensures their colloidal stability. **Figure 3b** shows the typical transmission electron microscopy image of MAPbBr3 QDs, which were quasi-spherical and had an average diameter of 3.3 nm with a size deviation of ±0.7 nm. In addition, the simple ligand-assisted reprecipitation approach can be easily extended to fabricate colloidal MAPbX3 QDs through halide substitutions. By mixing of PbX2 slats in the precursors, a series of QDs with tunable compositions and emission wavelengths were prepared. **Figure 3c** shows the PL spectra and optical images of these samples under sunlight and an UV lamp (365 nm).

#### **3.2. Synthesis of CsPbX3 QDs**

coworkers performed the energy-dispersive spectroscopy measurements for synthesized

3.3 nm, matching with the observation in Li's report. Also, the X-ray photoelectron spectros-

Subsequently, this simple synthetic method was adopted in other groups, and an increasing number of papers have been published in this field. For example, Luo and coworkers used either octylammonium bromide or octadecylammonium bromide to produce perovskite QDs by using the reprecipitation method, with the size of QDs of 3.9 and 6.5 nm, respectively [21]. In their case, the size control of QDs was due to the different ligand-binding kinetics, and the high solubility of longer hydrophobic chain ligands could facilitate the increase of QD size. Zou et al. developed a ligand-assisted reprecipitation strategy to fabricate highly lumines-

70% at room temperature (RT) and low excitation fluencies. In their work, the reprecipitation method was a simple way for preparing organic nanocrystals or polymer dots simultaneously through the solvent mixing [22]. As shown in **Figure 3a**, they employed the same principle

(DMF)) into a vigorously stirred poor solvent (toluene, hexane, etc.) to form the organometal halide perovskites. Simultaneously, the long-chain organic ligands, such as n-octylamine and

QDs [20]. They found a Br/Pb ratio of 3:5 for QDs with an average diameter of

QDs support their argument above, and the smaller the diameter

QDs with the absolute quantum efficiency up to

precursors in good solvent (*N*-dimethylformamide

QDs with a mixture of nanodots and nanoplatelets.

QDs

QDs. (d) Image of the toluene dispersion of MAPbBr3

MAPbBr3

copy results for MAPbBr3

50 Quantum-dot Based Light-emitting Diodes

of QDs, the larger the ratio of Br/Pb.

cent and color-tunable colloidal MAPbBr3

and simply mix a solution of MAPbX3

**Figure 2.** (a) Transmission electron microscope image of MAPbBr3

(b) UV-visible absorption and (c) PL spectra of the MAPbBr3

under UV-laser pointer excitation.

Colloidal synthesis routes of all-inorganic CsPbX3 QDs have also been developed, and such novel QD systems have been receiving increasingly significant attention, which is assumably due to the reason that CsPbX3 QDs possess higher stability than that of organic-inorganic hybrid MAPbX3 QDs. Following the traditional hot-injection approach which is commonly used for the synthesis of metal chalcogenide QDs, Kovalenko and coworkers firstly synthesized the monodisperse CsPbX3 QDs with a high degree of compositional bandgap engineering [23]. In their report, the Cs precursors were injected into the lead halide precursors, which contained the hot, high boiling point solvents. OA and oleylamine were mixed to dissolve the lead halide sources and to stabilize the QDs. By using the in situ PL measurements, they observed an interesting phenomenon that the reaction process after the Cs precursor injection was very quick. Within several seconds, the synthesis of the majority of CsPbX<sup>3</sup> QDs was realized. For the above synthesis method with a very rapid process, the unit size of CsPbX3 QDs depends strongly on

**Figure 3.** (a) Schematic illustration of the reaction system and process of ligand-assisted reprecipitation method. (b) Transmission electron microscope images of the produced MAPbBr3 QDs. (c) PL emission spectra of the MAPbX3 QDs and the corresponding optical images of colloidal MAPbBr3 QDs solutions under ambient light and a 365 nm UV lamp.

the reaction temperature, and the size of the QDs decreases by decreasing the reaction temperature. In their study, the CsPbX3 QDs were produced with tunable size from 4 to 15 nm. Note that CsPbX3 QDs crystallized in the cubic phase in their case rather than the tetragonal or orthorhombic phases at high temperature, as shown in **Figure 4a** and **b**. More importantly, the emission wavelength or photon energy of the resulting CsPbX3 QDs was tunable over the entire visible spectral region (410–700 nm) by varying the ratios of the precursor salts (PbCl2 /PbBr2 , PbBr2 /PbI2 ). As shown in **Figure 4c** and **d**, the obtained CsPbX3 QDs exhibit continuously tunable PL emission with a narrow linewidth of 12–42 nm and also a superior PL quantum yield up to 90%. Such an excellent optical performance is interesting, considering the facile synthesis route which involves neither core-shell structure nor surface modifications. Later on, by means of a droplet-based microfluidic platform, allowing for online absorption/PL measurements, the same research group investigated the formation mechanisms of such perovskite QDs.

In addition to the hot-injection technique, RT reprecipitation methods have also been proposed and developed for the controllable synthesis of CsPbX3 QD system. For instance, Huang et al. reported the emulsion-based synthesis of perovskite nanocrystals involving many morphologies at RT [20]. Li et al. reported that the CsPbX3 QDs can be synthesized at RT, which was similar to the ligand-assisted reprecipitation method used for MAPbX3 QD system [19].

**Figure 4.** Monodisperse CsPbX3 QDs and their structural characterization. (a) Schematic of the cubic perovskite lattice and (b) typical microstructure image of CsPbX3 QDs. (c) Colloidal CsPbX3 QDs exhibiting composition-tunable bandgap energies covering the entire visible region with narrow and bright emission (colloidal solutions in toluene under UV lamp).

#### **4. Synthesis of perovskite QDs through halide ion exchange reaction**

#### **4.1. Synthesis of MAPbX3 QDs**

A post-preparative halide ion exchange on perovskite QDs provides an additional means to modify their composition and thus the optical characterizations while preserving their size and morphology. Jang et al. reported the reversible halide exchange reaction of organometal trihalide perovskite colloidal QDs for full-range bandgap tuning [24]. **Figure 5a** shows a schematic of the reversible halide exchange reaction of MAPbX3 QDs with MAX, where X = Cl, Br, and I. The MAPbX3 can be converted to any composition ones using MAX in isopropyl solution at RT. In their case, the synthesis of composition-tuned MAPbBr3−*<sup>x</sup>* Cl*<sup>x</sup>* and MAPbBr3−*<sup>x</sup>* I *x* was carried out by the Br exchange reaction of MAPbBr3 . As the starting material, MAPbBr3 QDs were synthesized using a mixture of 1:1 MABr:PbBr2 dissolved in octylamine and (octadecene) ODE. Octylamine serves as the capping ligands for the QDs. Then, MAPbBr3 QDs were added into a MACl- or MAI-dissolved isopropyl solution affording MAPbBr3−*<sup>x</sup>* Cl*<sup>x</sup>* and MAPbBr3−*<sup>x</sup>* I *x* , respectively. As shown in **Figure 5b**, the composition of the mixed halide perovskite QDs can be easily distinguished by their colors. **Figure 5c** shows the UV-visible diffuse reflectance spectrum of all produced samples (10 μm thick films on silicon substrates). The composition tuning of these samples enabled the bandgap to display absorption over a wide range of 400–850 nm, corresponding to the photon energy of 1.5–3.1 eV. The corresponding PL spectra of these samples were also measured and put together on a normalized scale for a comparison. Note that the emission intensity of MAPbBr3−*<sup>x</sup>* Cl*<sup>x</sup>* and MAPbBr3−*<sup>x</sup>* I *x* significantly decreases with increasing *x*, matching with other reports either for perovskite QDs or films. The anion-exchange method is also possible in the solid phase, as demonstrated by Yang and coworkers [25]. Following a solution-phase growth of MAPbBr3 nanorod arrays, they were subsequently converted to MAPbI3 with similar morphology via a low-temperature annealing at ~140°C in MAI vapor. Such an approach was further confirmed to be feasible by constructing heterostructured LEDs, with MAPbBr<sup>3</sup> nanorods exhibiting a green EL emission at 533 nm and MAPbI<sup>3</sup> nanorods emitting a red emission at 782 nm.

the reaction temperature, and the size of the QDs decreases by decreasing the reaction tem-

orthorhombic phases at high temperature, as shown in **Figure 4a** and **b**. More importantly, the

able PL emission with a narrow linewidth of 12–42 nm and also a superior PL quantum yield up to 90%. Such an excellent optical performance is interesting, considering the facile synthesis route which involves neither core-shell structure nor surface modifications. Later on, by means of a droplet-based microfluidic platform, allowing for online absorption/PL measurements, the

In addition to the hot-injection technique, RT reprecipitation methods have also been pro-

et al. reported the emulsion-based synthesis of perovskite nanocrystals involving many mor-

**4. Synthesis of perovskite QDs through halide ion exchange reaction**

A post-preparative halide ion exchange on perovskite QDs provides an additional means to modify their composition and thus the optical characterizations while preserving their size and morphology. Jang et al. reported the reversible halide exchange reaction of organometal trihalide perovskite colloidal QDs for full-range bandgap tuning [24]. **Figure 5a** shows a schematic of the

QDs. (c) Colloidal CsPbX3

energies covering the entire visible region with narrow and bright emission (colloidal solutions in toluene under UV lamp).

can be converted to any composition ones using MAX in isopropyl solution at RT. In

Cl*<sup>x</sup>*

QDs and their structural characterization. (a) Schematic of the cubic perovskite lattice

visible spectral region (410–700 nm) by varying the ratios of the precursor salts (PbCl2

same research group investigated the formation mechanisms of such perovskite QDs.

QDs were produced with tunable size from 4 to 15 nm.

QDs was tunable over the entire

QDs exhibit continuously tun-

QD system. For instance, Huang

QD system [19].

QDs can be synthesized at RT, which

QDs exhibiting composition-tunable bandgap

QDs with MAX, where X = Cl, Br, and I. The

I *x*

was carried out by

and MAPbBr3−*<sup>x</sup>*

/PbBr2 ,

QDs crystallized in the cubic phase in their case rather than the tetragonal or

perature. In their study, the CsPbX3

52 Quantum-dot Based Light-emitting Diodes

emission wavelength or photon energy of the resulting CsPbX3

posed and developed for the controllable synthesis of CsPbX3

phologies at RT [20]. Li et al. reported that the CsPbX3

 **QDs**

reversible halide exchange reaction of MAPbX3

their case, the synthesis of composition-tuned MAPbBr3−*<sup>x</sup>*

). As shown in **Figure 4c** and **d**, the obtained CsPbX3

was similar to the ligand-assisted reprecipitation method used for MAPbX3

Note that CsPbX3

/PbI2

**4.1. Synthesis of MAPbX3**

**Figure 4.** Monodisperse CsPbX3

and (b) typical microstructure image of CsPbX3

MAPbX3

PbBr2

**Figure 5.** (a) Schematic of anion-exchange reactions for MAPbX3 QD synthesis. (b) Photographs of mixed-halide MAPbBr3−*<sup>x</sup>* Cl*<sup>x</sup>* and MAPbBr3−*<sup>x</sup>* I*x* QDs under room light. (c) UV-visible absorption and RT PL spectra of MAPbBr3−*<sup>x</sup>* Cl*<sup>x</sup>* and MAPbBr3−*<sup>x</sup>* I*x* QDs.

#### **4.2. Synthesis of CsPbX3 QDs**

As for the synthesis of CsPbX3 QDs by halide ion exchange, Kovalenko and coworkers and Manna and coworkers have almost simultaneously reported this method for CsPbX3 (X = Cl, Br, I) QD systems [26, 27], tuning their emission wavelength over the spectra range of 410–700 nm, as shown in **Figure 6a** and **b**. In their cases, five kinds of halide ion sources were investigated for ion exchange reaction, oleyammonium/octadecylammonium/tetrabutylammonium halides, organometallic Grignard reagents, and PbX2 salts. An interesting observation was that the anion-exchange reaction between different halide ions is very fast, and the halide ions could achieve exchange reaction within seconds. A blueshift trend includes I<sup>−</sup> to Br<sup>−</sup> and Br<sup>−</sup> to Cl<sup>−</sup> routes, and, similarly, a redshift trend includes Cl<sup>−</sup> to Br<sup>−</sup> and Br<sup>−</sup> to I<sup>−</sup> routes, respectively. An important fact should be pointed out that a little size variation for CsPbX<sup>3</sup> QDs can be distinguished after the anion-exchange reaction, but the shape of the produced QDs was identical to their original appearance (parent QDs). Also, there was no change on the crystal structure of the produced QDs. Additionally, the ion exchange reaction process did not induce the undesired formation of any remarkable lattice and/or surface defects. As a result, the optical properties of anion-exchanged CsPbX3 QDs are remarkable, including the linewidth and PL quantum yield, and comparable with those directly synthesized through the hot-injection method introduced above.

**Figure 6.** (a) Schematic representation of possible anion-exchange reactions within the crystal structure of CsPbX3 crystal lattice, with indication of suitable reagents. (b) Different routes and precursors for CsPbX<sup>3</sup> (X = Cl, Br, I) ion exchange.

## **5. Optical properties of perovskite QDs**

#### **5.1. Exciton-related emission of perovskite QDs**

Perovskite QDs exhibit remarkable optical properties, such as the high emission purity, large quantum yield, as well as tunable emission wavelength by varying the constituent elements, size, or dimensions. In the initial stage, most of the researches focused on the synthesis of the perovskite QDs and also their integration into device applications. But, it would be more interesting in our opinion if the optical properties of perovskite QDs or films made out of perovskite QDs could be investigated in detail. Despite the reported advances on perovskite-based optoelectronics, a deeper understanding of perovskites photophysical properties must be achieved if these materials are to make a technological impact. For example, as a key parameter controlling the recombination dynamics of photogenerated charges, the localization of exciton or free carrier needs to be specified. It means that the identification of dominant recombination mechanisms in perovskites will help interpret the seemingly counterintuitive facts that perovskites can act as both extraordinary photovoltaic materials and superior optical gain mediums for LED and lasers. In general, photovoltaic materials require efficient separation of photocarriers, and emissive materials require high recombination rates [28]. If the obtained exciton-binding energy of the perovskites is comparable to the thermal energy at RT (~26 meV), excited states will tend to dissociate into free carriers rather than recombination radiatively. The photoexcitation of perovskites can lead to the formation of free carriers and excitons, which then recombine to emit photons corresponding to the bandgap of perovskites. Although the question over the dominant species is still under investigation, it is generally accepted that free carriers are prevalent in perovskite films. Even et al. claimed that free carriers are photoexcited at RT, where Wannier-Mott excitons are dominant at low temperatures [29]. As for perovskite QDs, several groups have used temperaturedependent PL measurements to study the competition between exciton and free carriers. In Shi's study, temperature-dependent PL measurements were carried out to understand the optical transition mechanisms of the CsPbBr3 QDs [30]. As shown in **Figure 7a**, with the decrease of the temperature, only one emission peak can be solved, indicating the absence of structural phase transition. And, the strong excitonic emission behavior was verified by performing the power-dependent PL measurements. As shown in **Figure 7b**, a power law dependence with *β* = 1.31 confirms the excitonic characteristics of the spontaneous emission. Moreover, by plotting the emission intensity of CsPbBr<sup>3</sup> QDs *versus* temperature, thermally activated nonradiative recombination process was observed, as shown in **Figure 7c**. Excitonbinding energy of the CsPbBr3 QDs was further achieved by the following equation:

$$I(T) = \frac{I\_o}{1 + A \exp\left(-\frac{E\_o}{KT}\right)}\tag{1}$$

where K is the Boltzmann constant, T is the temperature, I<sup>0</sup> is the emission intensity at 0 K and A is a proportional constant. From the fitting, a value of 43.7 ± 4.9 meV for *E*B was extracted. The data are much higher than the thermal energy at RT and ensure exciton survival well above RT. Therefore, they argued that the observed PL performance originates from the exciton-related emission. However, many studies attributed the PL spectra at RT to free carrier recombination. For example, D'Innocenzo et al. stated that excitons generated by low-density excitation were almost fully ionized at RT when the exciton-binding energy is moderately larger than the thermal energy at RT [31]. As shown in **Figure 7d**, the exciton-phonon interaction in carrier recombination process for CsPbBr3 QDs was also investigated in Shi's report by studying the linewidth broadening behavior of CsPbBr3 QDs. The value of optical phonon energy of 36.3 ± 1.8 meV was derived.

#### **5.2. Quantum confinement effect in perovskite QDs**

**4.2. Synthesis of CsPbX3**

As for the synthesis of CsPbX3

54 Quantum-dot Based Light-emitting Diodes

 **QDs**

organometallic Grignard reagents, and PbX2

properties of anion-exchanged CsPbX3

method introduced above.

routes, and, similarly, a redshift trend includes Cl<sup>−</sup>

**5. Optical properties of perovskite QDs**

**5.1. Exciton-related emission of perovskite QDs**

and coworkers have almost simultaneously reported this method for CsPbX3

achieve exchange reaction within seconds. A blueshift trend includes I<sup>−</sup>

important fact should be pointed out that a little size variation for CsPbX<sup>3</sup>

systems [26, 27], tuning their emission wavelength over the spectra range of 410–700 nm, as shown in **Figure 6a** and **b**. In their cases, five kinds of halide ion sources were investigated for ion exchange reaction, oleyammonium/octadecylammonium/tetrabutylammonium halides,

anion-exchange reaction between different halide ions is very fast, and the halide ions could

guished after the anion-exchange reaction, but the shape of the produced QDs was identical to their original appearance (parent QDs). Also, there was no change on the crystal structure of the produced QDs. Additionally, the ion exchange reaction process did not induce the undesired formation of any remarkable lattice and/or surface defects. As a result, the optical

quantum yield, and comparable with those directly synthesized through the hot-injection

Perovskite QDs exhibit remarkable optical properties, such as the high emission purity, large quantum yield, as well as tunable emission wavelength by varying the constituent elements, size, or dimensions. In the initial stage, most of the researches focused on the synthesis of the perovskite QDs and also their integration into device applications. But, it would be more interesting in our opinion if the optical properties of perovskite QDs or films made out of perovskite QDs could be investigated in detail. Despite the reported advances

**Figure 6.** (a) Schematic representation of possible anion-exchange reactions within the crystal structure of CsPbX3

lattice, with indication of suitable reagents. (b) Different routes and precursors for CsPbX<sup>3</sup>

to Br<sup>−</sup>

QDs by halide ion exchange, Kovalenko and coworkers and Manna

and Br<sup>−</sup>

salts. An interesting observation was that the

to I<sup>−</sup>

QDs are remarkable, including the linewidth and PL

to Br<sup>−</sup>

(X = Cl, Br, I) QD

and Br<sup>−</sup>

QDs can be distin-

routes, respectively. An

to Cl<sup>−</sup>

crystal

(X = Cl, Br, I) ion exchange.

As we mentioned above, the optical properties of perovskite QDs depend not only on the constituent halide ions but also on their size or diameter. As we all know, quantum confinement effect has been widely studied in conventional semiconductor nanomaterials. Also, the

**Figure 7.** (a) Temperature-dependent PL spectra of the CsPbBr3 QDs taken from 10 to 300 K. (b) The relationship between the integrated PL intensity and the excitation power of the CsPbBr3 QDs at 300 and 120 K. (c) Integrated PL intensity and (d) linewidth of the CsPbBr3 QDs as a function of reciprocal temperature from 10 to 300 K.

latest development in the size-controlled synthesis of perovskite QDs has enabled detailed investigations of quantum confinement effect in QDs. Friend and coworkers observed sizedependent photon emission from MAPbBr3 QDs embedded in an organic matrix [16], where the QD size and their PL peak could be tuned by varying the concentration of the precursors. In their case, a MAPbBr3 precursor solution (MABr and PbBr2 dissolved in *N*,*N*dimethylformamide) and 4,4-bis(*N*-carbazolyl)-1,1-biphenyl (CBP) matrix solution were prepared and mixed to achieve various weight ratios between CBP and the perovskite precursor. They firstly determined the average size of perovskite QDs by using X-ray diffraction, as shown in **Figure 8a**. As the concentration of perovskite QDs decreased, a reduced peak intensity accompanied by peak broadening was observed for (1 0 0) and (2 0 0) diffraction peaks, indicating a reduction of the size of nanocrystallites. Accordingly, the PL peak gradually shifted to higher energy decreasing the particle size, as shown in **Figure 8b**. They also summarized the changing trend by fitting with the equation of *E*PL = 2.39 + 12/*d*<sup>2</sup> eV (**Figure 8c**), in which *d* is the particle size in nanometer. This suggested that the PL blueshift is a manifestation of quantum confinement of excitons in the perovskite nanocrystals. **Figure 8d** shows the corresponding absorbance data of the produced MAPbBr3 QDs with different sizes, and a monotonic shift of the absorption edge toward the higher energies matched the above observation in PL spectra.

Quantum confinement effects have also been observed in all-inorganic CsPbBr<sup>3</sup> QDs. Kovalenko and coworkers reported the size-dependent PL emission from square-shaped CsPbBr3 QDs [23], in which the PL emission peak gradually blueshifted from 512 to 460 nm as the diameter of QDs decreased from 11.8 to 3.8 nm, as shown in **Figure 9a**. **Figure 9b** shows the experimental and theoretical size dependence of the bandgap of CsPbBr3 QDs in their case. In addition, tunable PL from CsPbBr3 nanocrystals by varying the number of layers has also been reported, and the corresponding bandgap energy increases with the decreasing the number of layers. Alivisatos and coworkers reported the synthesis of quantum-confined highly fluorescent CsPbBr<sup>3</sup> nanoplatelets [32]. Their observations show that the thickness of CsPbBr3 nanoplatelets can be tuned from 1 to 5 unit cells by changing the reaction temperature, with the monolayer platelets emitting at 400 nm, whereas the bulk-like crystals emitted at 520 nm.

latest development in the size-controlled synthesis of perovskite QDs has enabled detailed investigations of quantum confinement effect in QDs. Friend and coworkers observed size-

QDs as a function of reciprocal temperature from 10 to 300 K.

where the QD size and their PL peak could be tuned by varying the concentration of the

dimethylformamide) and 4,4-bis(*N*-carbazolyl)-1,1-biphenyl (CBP) matrix solution were prepared and mixed to achieve various weight ratios between CBP and the perovskite precursor. They firstly determined the average size of perovskite QDs by using X-ray diffraction, as shown in **Figure 8a**. As the concentration of perovskite QDs decreased, a reduced peak intensity accompanied by peak broadening was observed for (1 0 0) and (2 0 0) diffraction peaks, indicating a reduction of the size of nanocrystallites. Accordingly, the PL peak gradually shifted to higher energy decreasing the particle size, as shown in **Figure 8b**. They also

summarized the changing trend by fitting with the equation of *E*PL = 2.39 + 12/*d*<sup>2</sup>

precursor solution (MABr and PbBr2

QDs embedded in an organic matrix [16],

QDs taken from 10 to 300 K. (b) The relationship between

QDs at 300 and 120 K. (c) Integrated PL intensity and

dissolved in *N*,*N*-

eV (**Figure 8c**),

dependent photon emission from MAPbBr3

**Figure 7.** (a) Temperature-dependent PL spectra of the CsPbBr3

the integrated PL intensity and the excitation power of the CsPbBr3

precursors. In their case, a MAPbBr3

(d) linewidth of the CsPbBr3

56 Quantum-dot Based Light-emitting Diodes

**Figure 8.** (a) X-ray diffraction patterns and (b) PL spectra of CBP:MAPbBr<sup>3</sup> with various weight ratios. (c) Energy of PL emission peak as a function of average perovskite nanocrystal size. (d) Absorbance data of the produced samples.

**Figure 9.** (a) Quantum size effects in the absorption and emission spectra of 5–12 nm CsPbBr<sup>3</sup> QDs. (b) Experimental *versus* theoretical (effective mass approximation (EMA)) size dependence of the bandgap energy.

#### **6. Perovskite QD LEDs**

#### **6.1. Structure of perovskite QDs LEDs**

As we mentioned above, perovskite QDs have been shown to possess high PL quantum yield, high emission purity, and tunable emission wavelength that make them suitable for highperformance, low-cost, and lightweight LEDs. Perovskite materials were incorporated into LEDs functioning at liquid nitrogen temperature back in the 1990s, and RT-working bright LEDs were fabricated by solution processing of hybrid perovskites by Tan et al. [33]. In their device, a solution-processed MAPbI3−*<sup>x</sup>* Cl*<sup>x</sup>* perovskite layer was sandwiched between TiO2 and poly(9,9-dioctylfluorene) (F8) layers for effective radiative recombination of electrons and holes in the perovskite layer. Also, using MAPbBr3 -emissive layer, an architecture of ITO/PEDOT:PSS/MAPbBr<sup>3</sup> /F8/Ca/Ag was fabricated, producing a luminance of 364 cd/m<sup>2</sup> at a current density of 123 mA/cm2 . Because of the significantly higher quantum efficiency of perovskite QDs than that of perovskite bulk films, superior device performance for perovskite QD LEDs could be expected [34]. A typical perovskite QD LED consists of an intrinsic active layer in a double-heterojunction structure. As shown in **Figure 10**, an n-type electron transport layer and a p-type hole transport layer are usually used to construct a typical perovskite QD LED. Under forward bias, the injection of charge carriers into a thin luminescent layer leads to radiative recombination and provides light emission in all directions. Efficient LEDs use electrodes that readily inject carriers into the active region and prevent charges from passing through the device and quenching at contacts. Since the work of Tan et al. in 2014 [33], various perovskite QD LEDs using different perovskite active layers and electron/hole transport layers have been reported.

#### **6.2. LEDs based on perovskite QDs**

**6. Perovskite QD LEDs**

58 Quantum-dot Based Light-emitting Diodes

**6.1. Structure of perovskite QDs LEDs**

As we mentioned above, perovskite QDs have been shown to possess high PL quantum yield, high emission purity, and tunable emission wavelength that make them suitable for highperformance, low-cost, and lightweight LEDs. Perovskite materials were incorporated into

QDs. (b) Experimental

**Figure 9.** (a) Quantum size effects in the absorption and emission spectra of 5–12 nm CsPbBr<sup>3</sup>

*versus* theoretical (effective mass approximation (EMA)) size dependence of the bandgap energy.

Song and coworkers firstly reported the perovskite QD LEDs with tunable emission wavelength based on CsPbBr3 QDs [4]. For the device structure of ITO/PEDOT:PSS/PVK/QDs/TPBi/ LiF/Al (shown in **Figure 11a**), the luminescence of blue, green, and orange LEDs reached 742, 946, and 528 cd/m2 , with external quantum efficiency of 0.07, 0.12, and 0.09%, respectively. In addition, the produced LEDs possess narrow linewidths, indicating their potential applications in displays. However, non-optimized devices exhibited poor emission efficiency. Generally, in order to improve the device performance, three important factors should be considered: carrier

**Figure 10.** General device structure of perovskite QD LEDs. ETL, electron transport layer; HTL, hole transport layer.

injection efficiency, radiative recombination efficiency, and injection balance. For an improved carrier injection efficiency, a thin perfluorinated ionomer film was introduced between the hole transport layer and CsPbBr3 QDs active layer in Zhang's study [35]. In their case, the hole injection efficiency was enhanced greatly, which favored a high brightness. Besides, the usage of carrier transport layers with a high conductivity could ensure a high carrier injection efficiency, resulting in an improved external quantum efficiency.

In order to promote the carrier radiative recombination efficiency, the undesired lattice and surface/interface defects should be excluded. Sun's research group found an interesting phenomenon that the introduction of CsPb2 Br5 QDs attached on CsPbBr<sup>3</sup> QDs could improve the emission lifetime by decreasing nonradiative energy transfer to the trap states via controlling the trap density [36]. As a result, a high external quantum efficiency of about 2.21% was achieved, and a maximum luminance of 3853 cd/m2 was obtained. **Figure 12a** shows the X-ray diffraction patterns of the synthesized perovskite QD products. The peak located at 30.36° is assigned to (2 0 2) diffraction of CsPbBr<sup>3</sup> , whereas the peak at 30.69° is identified from CsPb<sup>2</sup> Br5 . And, the impurities of CsPb2 Br5 phase were emerged in the low-temperature (70°C) solutionprocessed CsPbBr3 products. The generation of the secondary phase CsPb2 Br5 in the product can be ascribed to the following process: PbBr2 + CsPbBr3 → CsPb2 Br5 . **Figure 12b** displays the schematic diagrams of the corresponding crystal structures of the CsPbBr3 and CsPb2 Br5 QDs. They further fabricated the LED device by constructing the heterostructure shown in

**Figure 11.** (a) Structure of the perovskite LED device. (b) Energy band alignment of the device. (c–e) Blue, green, and orange LEDs with abbreviations of NUST.

**Figure 12c** and achieved a high-purity green emission at about 527 nm. The inset of **Figure 12d** shows the corresponding photograph of a device with an active area of 2 × 2 mm2 . In fact, contradiction exists about carrier radiative recombination efficiency and injection efficiency. For example, to keep a high quantum yield, surface passivation is usually necessary, while long-chain ligands will reduce the conductivity of QDs. In this regard, Pan and coworkers applied a short ligand, di-dodecyl dimethyl ammonium bromide, to passivate CsPbBr3 QDs and facilitate the carrier transport ability [37]. Consequently, a promoted PL quantum yield of about 71% was achieved, and a higher external quantum efficiency of ~3.0% was obtained.

injection efficiency, radiative recombination efficiency, and injection balance. For an improved carrier injection efficiency, a thin perfluorinated ionomer film was introduced between the hole

tion efficiency was enhanced greatly, which favored a high brightness. Besides, the usage of carrier transport layers with a high conductivity could ensure a high carrier injection efficiency,

In order to promote the carrier radiative recombination efficiency, the undesired lattice and surface/interface defects should be excluded. Sun's research group found an interesting phe-

emission lifetime by decreasing nonradiative energy transfer to the trap states via controlling the trap density [36]. As a result, a high external quantum efficiency of about 2.21% was

diffraction patterns of the synthesized perovskite QD products. The peak located at 30.36° is

products. The generation of the secondary phase CsPb2

QDs. They further fabricated the LED device by constructing the heterostructure shown in

**Figure 11.** (a) Structure of the perovskite LED device. (b) Energy band alignment of the device. (c–e) Blue, green, and

Br5

QDs active layer in Zhang's study [35]. In their case, the hole injec-

QDs could improve the

Br5 .

Br5

in the product

and CsPb2

. **Figure 12b** displays

was obtained. **Figure 12a** shows the X-ray

Br5

Br5

, whereas the peak at 30.69° is identified from CsPb<sup>2</sup>

phase were emerged in the low-temperature (70°C) solution-

QDs attached on CsPbBr<sup>3</sup>

transport layer and CsPbBr3

60 Quantum-dot Based Light-emitting Diodes

resulting in an improved external quantum efficiency.

achieved, and a maximum luminance of 3853 cd/m2

Br5

can be ascribed to the following process: PbBr2 + CsPbBr3 → CsPb2

the schematic diagrams of the corresponding crystal structures of the CsPbBr3

nomenon that the introduction of CsPb2

assigned to (2 0 2) diffraction of CsPbBr<sup>3</sup>

And, the impurities of CsPb2

orange LEDs with abbreviations of NUST.

processed CsPbBr3

As discussed above, the carrier injection efficiency, radiative recombination efficiency, and injection balance are important factors for the device performances of perovskite QD LEDs. In fact, the QDs applied in previous reports were not well purified due to the continuous growth with classical purification strategies. Recently, Zeng's group developed a handy surface purification method that can achieve recyclable treatment on QDs using hexane-/ethyl acetate-mixed solvent [38]. Thus, a balance of carrier injection efficiency and surface passivation effect can be constructed, as illustrated in **Figure 13a**. After two purifications, the QDs

**Figure 12.** (a) X-ray diffraction patterns of CsPbBr<sup>3</sup> QDs and precipitates of products. (b) The schematic diagrams of the corresponding crystal structures of the CsPbBr3 and CsPb2 Br5 QDs. (c) Device structure of the studied perovskite LEDs. (d) EL spectra at different driving voltages. The inset shows the photograph of a device with an active area of 2 × 2 mm<sup>2</sup> .

obtained still possess a good stability (shown in **Figure 13b**). But, the PL quantum yield shows no obvious decrease (**Figure 13c**), indicating a good surface passivation. Therefore, we could expect that good dispersivity ensures an excellent film formation ability and pure surface that leads to efficient carrier transport. So, the efficiency of carrier injection was greatly enhanced (shown in **Figure 13d**). In virtue of the above advantages discussed, the luminance (**Figure 13e**) and current efficiency (**Figure 13f**) of the resulting LEDs based on CsPbBr<sup>3</sup> QDs are greatly improved compared to previous studies, and more importantly, the studied LED achieves a record external quantum efficiency of 6.27% (**Figure 13g**).

**Figure 13.** (a) Schematic illustration of the control of ligand density of CsPbBr3 QD surfaces. (b) Photographs of CsPbBr3 QD inks without (upper) and with (below) UV light excitation after two cycles of treatments. (c) PL quantum yield of CsPbBr3 QDs with different purifying cycles. (d) Current density-voltage, (e) luminance-voltage, (f) current efficiencycurrent density, and (g) external quantum efficiency-luminance characteristics of the perovskite QD LEDs.

Although the device performance of perovskite QD LEDs was promoted greatly in a short time, operation stability has always been criticized for such devices in a continuous current mode, which are the main obstacles hindering the reliable device operation and their future application. In previous reports, conventional carrier injection conducting polymer or small molecules, such as PEDOT:PSS, PCBM, and 1,3,5-tris(2-*N*-phenylbenzimidazolyl) benzene, have been frequently employed as the carrier injectors in perovskite LEDs [25, 33, 35, 36], but their inherent chemical instability inevitably degrades the device performance; thus, a high-efficiency light emission cannot be sustained over a long running time. More recently, Shi et al. present a strategy that addresses simultaneously the emission efficiency and stability issues facing current perovskite LEDs' compromise [30]. Wide bandgap semiconductors, n-MgZnO and p-MgNiO, were employed as the electron and hole injectors to construct CsPbBr<sup>3</sup> QD LEDs. The resulting diode demonstrates a high luminance (3809 cd/m2 ) and external quantum efficiency (2.39%), as well as a significantly improved stability compared with reference and other previously reported devices constructed with organic carrier injectors. **Figure 14a** illustrates the emission intensity of the diode *versus* running time, and one can see that the EL intensity has almost not changed over 30 min. A long-term operation stability measurement demonstrated that the device could operate continuously for 10 h with an emission decay of below 20%, greatly superior to other previously reported devices constructed with organic electron and/or hole transport layers. It is believed that the device concept proposed in their study will provide valuable information for the future design and development of high-efficiency and air-stable perovskite QD LEDs.

obtained still possess a good stability (shown in **Figure 13b**). But, the PL quantum yield shows no obvious decrease (**Figure 13c**), indicating a good surface passivation. Therefore, we could expect that good dispersivity ensures an excellent film formation ability and pure surface that leads to efficient carrier transport. So, the efficiency of carrier injection was greatly enhanced (shown in **Figure 13d**). In virtue of the above advantages discussed, the luminance (**Figure 13e**)

improved compared to previous studies, and more importantly, the studied LED achieves a

QDs are greatly

QD surfaces. (b) Photographs of CsPbBr3

and current efficiency (**Figure 13f**) of the resulting LEDs based on CsPbBr<sup>3</sup>

record external quantum efficiency of 6.27% (**Figure 13g**).

62 Quantum-dot Based Light-emitting Diodes

**Figure 13.** (a) Schematic illustration of the control of ligand density of CsPbBr3

CsPbBr3

QD inks without (upper) and with (below) UV light excitation after two cycles of treatments. (c) PL quantum yield of

current density, and (g) external quantum efficiency-luminance characteristics of the perovskite QD LEDs.

QDs with different purifying cycles. (d) Current density-voltage, (e) luminance-voltage, (f) current efficiency-

**Figure 14.** (a) Time dependence (30 min) of the emission intensity of the prepared LEDs at 8.0 V. (b) Emission intensity of the studied LEDs and three reference LEDs as a function of running time under a bias of 10.0 V. The insets show the corresponding photographs of the LEDs after different running periods. (c) Evolution of the emission spectra of the prepared LEDs after different running periods.

#### **7. Summary**

In summary, recent developments in perovskite QDs add a new class of members to the family of colloidal QDs. In spite of a short development of only 2 years, perovskite QDs have shown great potential in application in cost-effective LED fields. However, compared with traditional metal chalcogenide QDs, novel synthesis approaches are needed to tailor the surface ligands and enhance the stability of perovskite QDs. At present, the perovskite LEDs based on both organic-inorganic hybrid and inorganic QDs show relatively poor performances, and, therefore, new device structures are required to make a step change in the emission efficiency and operation stability of LEDs. Despite these challenges, we believe that the newly emerging perovskite QDs have a bright future, and the previous studies will provide valuable information for the future design and development of high-performance perovskite QD LEDs.

#### **Author details**

Zhifeng Shi\*, Xinjian Li and Chongxin Shan

\*Address all correspondence to: shizf@zzu.edu.cn

Department of Physics and Engineering, Zhengzhou University, Zhengzhou, China

#### **References**


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**7. Summary**

64 Quantum-dot Based Light-emitting Diodes

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**Author details**

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Zhifeng Shi\*, Xinjian Li and Chongxin Shan

\*Address all correspondence to: shizf@zzu.edu.cn

In summary, recent developments in perovskite QDs add a new class of members to the family of colloidal QDs. In spite of a short development of only 2 years, perovskite QDs have shown great potential in application in cost-effective LED fields. However, compared with traditional metal chalcogenide QDs, novel synthesis approaches are needed to tailor the surface ligands and enhance the stability of perovskite QDs. At present, the perovskite LEDs based on both organic-inorganic hybrid and inorganic QDs show relatively poor performances, and, therefore, new device structures are required to make a step change in the emission efficiency and operation stability of LEDs. Despite these challenges, we believe that the newly emerging perovskite QDs have a bright future, and the previous studies will provide valuable information for the future design and development of high-performance

Department of Physics and Engineering, Zhengzhou University, Zhengzhou, China

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**Provisional chapter**

#### **CdS(Se) and PbS(Se) Quantum Dots with High Room Temperature Quantum Efficiency in the Fluorine-Phosphate Glasses Temperature Quantum Efficiency in the Fluorine-Phosphate Glasses**

**CdS(Se) and PbS(Se) Quantum Dots with High Room** 

DOI: 10.5772/intechopen.68459

Elena Kolobkova and Nikolay Nikonorov Elena Kolobkova and Nikolay Nikonorov Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.68459

#### **Abstract**

In this study, the luminescent properties of the CdS(Se) quantum dots (QDs) with the mean size of 2–4 nm, the (PbS)n/(PbSe)n molecular clusters (MCs) and PbS(Se) quantum dots (QDs) with the mean size of 2–5 nm embedded in the fluorine-phosphate glass are investigated. The dependence of the photo luminescence absolute quantum yield (PL AQY) on the sizes of the CdS(Se) QDs are studied. It is found that the PL AQY of the CdSe QDs increases monotonically to its maximum height and then falls down. The PL AQY of the CdS(Se) QDs can reach 50–65%. Luminescence of (PbS)n/(PbSe)n MCs embedded in fluorine-phosphate matrix and excited by UV radiation is obtained in the visible spectral region and its absolute quantum yield was up to 10%. The PbSe QDs have broadband photoluminescence with quantum efficiency about five times more than MCs (~50%) in the spectral range of 1–1.7 µm. Glasses doped with PbS(Se) QDs provide potential application as infrared fluorophores, which are both efficient and possess short life times. The glass matrix protects the QDs from external influence and their optical properties remain unchanged for a long time.

**Keywords:** quantum dots, molecular clusters, fluorine-phosphate glass, luminescence, absolute quantum yield

#### **1. Introduction**

#### **1.1. Why fluorine-phosphate glasses?**

Glass-crystalline materials (or glassceramics) are composite materials, usually consisting of a glassy matrix (glass phase) and nano-sized dielectric or semiconductor crystals or metallic

particles distributed in it. Glassceramics are formed by the growth of crystalline phase inside of a glass matrix. The growth of crystalline phase occurs as a result of the crystallization of amorphous phase during heat treatment. Glasses doped with CdS, CdSe, CdTe, PbS, PbSe nanocrystals are typical representatives of the nano-glassceramics or nanocomposite materials and usually used as a nonlinear optical media [1, 2]. Traditionally silicate glassy matrix has been used for QDs formation. These glasses are characterized by high synthesis temperature (1300–1500°C), long-time (tens of hours) and high temperature (500–700°C) of heat treatment [3–7].

In this study, we used a fluorine-phosphate (FP) glass featuring with a number of advantages compared to conventional silicate glasses, including low temperature synthesis and heat treatment, formation of quantum dots in the wide range of concentrations, short time of heat treatment and higher spatial distribution homogeneity. Two-stage heat treatment was afforded to get quantum dots (QDs) with narrow size distribution. The CdS and CdSe QDs dispersed in a fluorine-phosphate glasses are attracting much attention as nonlinear optical materials [1], but information about luminescent properties is not available.

In this communication, we present the results of our research designed for synthesis and characterization of yellow-red and IR emitting semiconductor quantum dots embedded in the fluorine-phosphate glass. The composites are fabricated by two-staged heat treatment and stabilization of synthesized II–VI and IV–VI semiconductor QDs into glass matrices. **Figure 1** demonstrates initial glasses and glasses after heat treatment.

#### **1.2. Why phosphors for visible spectral region based on CdSe and CdS quantum dots?**

QDs are a type of nanomaterials with good fluorescent properties. The size-dependent emission is probably the most attractive property of semiconductor nanocrystals. Among them, CdS and CdSe QDs are one of the most promising materials because QDs have bright luminescence in the visible range of the optical spectrum. For example, CdSe QDs have shown potential as superior biological labels [8–10], laser sources [11, 12] and tunnel diodes [13, 14].

**Figure 1.** Photo Initial glasses doped with CdS (1), CdSe (2), PbS (3) and PbSe (4) and glasses after heat treatment doped with CdSe QDs (with different sizes) (5) and PbSe (6).

Compared with conventional fluorescent dyes, CdS(Se) QDs have a wide continuously distributed excitation spectra, not only with symmetrical distributed narrow emission spectra, but also many other excellent properties such as adjustable color, excellent photochemical stability and high threshold of light bleaching [15].

particles distributed in it. Glassceramics are formed by the growth of crystalline phase inside of a glass matrix. The growth of crystalline phase occurs as a result of the crystallization of amorphous phase during heat treatment. Glasses doped with CdS, CdSe, CdTe, PbS, PbSe nanocrystals are typical representatives of the nano-glassceramics or nanocomposite materials and usually used as a nonlinear optical media [1, 2]. Traditionally silicate glassy matrix has been used for QDs formation. These glasses are characterized by high synthesis temperature (1300–1500°C), long-time (tens of hours) and high temperature (500–700°C) of heat

In this study, we used a fluorine-phosphate (FP) glass featuring with a number of advantages compared to conventional silicate glasses, including low temperature synthesis and heat treatment, formation of quantum dots in the wide range of concentrations, short time of heat treatment and higher spatial distribution homogeneity. Two-stage heat treatment was afforded to get quantum dots (QDs) with narrow size distribution. The CdS and CdSe QDs dispersed in a fluorine-phosphate glasses are attracting much attention as nonlinear optical

In this communication, we present the results of our research designed for synthesis and characterization of yellow-red and IR emitting semiconductor quantum dots embedded in the fluorine-phosphate glass. The composites are fabricated by two-staged heat treatment and stabilization of synthesized II–VI and IV–VI semiconductor QDs into glass matrices. **Figure 1**

**1.2. Why phosphors for visible spectral region based on CdSe and CdS quantum dots?**

QDs are a type of nanomaterials with good fluorescent properties. The size-dependent emission is probably the most attractive property of semiconductor nanocrystals. Among them, CdS and CdSe QDs are one of the most promising materials because QDs have bright luminescence in the visible range of the optical spectrum. For example, CdSe QDs have shown potential as superior biological labels [8–10], laser sources [11, 12] and tunnel

**Figure 1.** Photo Initial glasses doped with CdS (1), CdSe (2), PbS (3) and PbSe (4) and glasses after heat treatment doped

materials [1], but information about luminescent properties is not available.

demonstrates initial glasses and glasses after heat treatment.

treatment [3–7].

70 Quantum-dot Based Light-emitting Diodes

diodes [13, 14].

with CdSe QDs (with different sizes) (5) and PbSe (6).

However, colloidal synthesized bare quantum dots, including CdSe(S) QDs, usually have surface defects and cause to reduction in absolute photoluminescence (PL) quantum yield. The best PL absolute quantum yield (AQY) (quantum efficiency) reported for the as-prepared nanocrystals at room temperature is around 20% in the wavelength range of 520–600 nm and about a few percent or lower in the spectrum range above 600 nm. Also, in the spectrum range below 520 nm, it is a few percent or lower of total absolute quantum yield [13, 15]. In general, a low PL AQY is due to the surface states located in the bandgap of the nanocrystals. These surface states act as trapping states for the photogenerated charges. The origin of the surface trapping states is dangling bonds of the surface atoms [3, 16, 17]. Therefore, it is essential to control the QDs surfaces to reduce the surface defects by passivating the surface of QDs [18, 19].

The core/shell structures solve optical problems, such as low PL AQY and improve the stability of QDs. As was shown, the room temperature quantum efficiency of the band-edge luminescence of CdSe QDs could be improved to 40–60% by surface passivation with inorganic (ZnS) or organic (alkylamines) shells [18]. Due to the non-radiative processes, a reduction in the PL emission intensity was observed by annealing of the prepared samples in different environments (oxygen, hydrogen, and air).

Due to the failure of orange-red emitting materials in general, efforts were directed to synthesize colloidal CdS/CdSe QDs that can emit light with wavelengths that range from orange (600 nm) to red (650 nm). Nevertheless, both stability and reproducibility of the PL AQY are not predictable. With some inorganic and organic surface functionalization, the PL QY of synthesized colloidal CdSe nanocrystals is boosted more than 50% in the range of 520–650 nm. However, the emission efficiency for the orange-red color window is still low. Especially for red emission (around 650 nm), the PL QY of the nanocrystals in solution was nearly zero [15].

#### **1.3. Why optical transparent glasses doped with CdS and CdSe quantum dots?**

Semiconductor CdS and CdSe nanoparticles dispersed in a silicate glass matrix are attracting much attention [3–5]. The possibility of QDs formation in the optical glasses creates significant benefits for their application. Currently, optical transparent glasses doped with nanocrystals are of great interest for the modern element base of photonics. In these materials, the best properties of nanocrystals and glasses technology (possibilities of pressing and molding, spattering, pulling optical fibers, using ion exchange technology) are easily combined. In addition, the glass matrix protects the QDs from external influence.

In the QDs doped silicate glasses, the PL spectra consist of two bands: a less intense highenergy band and a lower energy broader band. The first band occurs at a wavelength 10–20 nm higher than the absorption edge of QDs and is due to direct electron-hole recombination. This weak peak shifts to the higher wavelength with increasing particle size. The second band is due to surface defects and occurs at 800–900 nm spectral region. PL AQY is less than 30% for CdS(Se) QDs in the silicate glasses and decreases as the size of QD increases [4].

#### **1.4. Optical composite materials with PbS and PbSe quantum dots as tunable near-IR phosphors**

Semiconductor PbS and PbSe quantum dots have been widely investigated because of their unique optical and electronic properties. PbS and PbSe are a typical narrow bandgap (*Eg* = 0.41 eV, *Eg* = 0.29 eV) semiconductors with the Bohr's exciton radii 20 nm (for PbS) and 46 nm (for PbSe). Their large Bohr radius provides strong quantum confinement effect that can be easily realized in a wide range of QD size [20, 21].

Optical composite materials with PbS and PbSe QD are widely used in optical and photonic applications. For example, PbS(Se) QDs have potential applications in near-infrared photodetectors, photovoltaics and as saturable absorbers [22, 23]. In contrast to rare-earth ions-doped optical materials, lead chalcogenide quantum dot-doped glasses can provide tunable near-IR luminescence (about 1–2 µm) with high absolute quantum yield (≥60%) by controlling the size and distribution of QDs [22–24]. Despite a lot of efforts spent to find a novel gain medium which can almost cover the whole optical communication window, it is essential to tailor the emission of QDs embedded in a glass matrix in a wide bandwidth of the optical communication network. Therefore, PbS and PbSe QDs are promising gain media for covering the whole optical communication window [24–28]. Several advances of controlled chemical synthesis of the materials have provided the ways to grow QDs and manipulate their size, shape and composition using different methodologies [29].

PbSe and PbS QDs with a band gap in the mid-infrared are interesting infrared phosphors materials. In the visible spectral range organic dyes usually present large PL AQY value than quantum dots, but infrared organic dyes have very low PL AQY suffer from poor photostability. On the other hand, the rare-earth ions can be used as the efficient infrared phosphors but they have small absorption cross sections and microsecond lifetimes. Infrared phosphors of PbS(Se), that are both efficient and possess short lifetimes, may find unique applications in the near-IR spectral range where biological tissues are relatively transparent, or as fluorescent materials in the fiber communication range of 1.3–1.5 microns.

Variation of temperature and duration heat treatment (HT) of the glasses doped with Pb, S or Se make possible to change sizes of PbS(Se) QDs in a wide range (2–15 nm). The choice of these parameters enhances the formation of nucleation centers (NCs) in the glass and leads to good size control and small size dispersions. The growth processes of lead chalcogenide QDs is based mainly on the phase decomposition from the over-saturated solid solution. Twostage heat treatment of the glass afforded QDs with narrow size distribution.

Lead chalcogenide QDs have been synthesized in silicate glasses, fluorine-phosphate glasses and germanosilicate glasses [7, 30–32]. Among these glasses, fluorine-phosphate glasses have the largest solubility of lead chalcogenide compounds [32].

It is evident that during the process of formation and growth, these structures pass through the phase when their sizes are less than 1.0 nm and they do not possess semiconductor properties. This phase corresponds to the existence of lead chalcogenide compounds in a form of molecular clusters (MCs) [36]. The optical properties of MCs are considerably different from the properties of QDs.

In this study, we used a fluorine-phosphate glass (FPG) doped with high concentration of CdS, CdSe, PbSe and PbS QDs. FPGs are featured with a number of advantages compared to conventional silicate and borosilicate glasses. FPGs characterize low temperature synthesis, possibility for a wide range adjustment of the formed quantum dots concentration, low temperature and time of heat treatment and higher spatial distribution homogeneity of the QDs. We represent the luminescent properties of the fluorine-phosphate glasses doped with CdS, CdSe, PbSe and PbS QDs.

#### **2. Preparation procedure**

In the QDs doped silicate glasses, the PL spectra consist of two bands: a less intense highenergy band and a lower energy broader band. The first band occurs at a wavelength 10–20 nm higher than the absorption edge of QDs and is due to direct electron-hole recombination. This weak peak shifts to the higher wavelength with increasing particle size. The second band is due to surface defects and occurs at 800–900 nm spectral region. PL AQY is less than 30% for CdS(Se) QDs in the silicate glasses and decreases as the size of QD

**1.4. Optical composite materials with PbS and PbSe quantum dots as tunable near-IR** 

Semiconductor PbS and PbSe quantum dots have been widely investigated because of their unique optical and electronic properties. PbS and PbSe are a typical narrow bandgap (*Eg*

Optical composite materials with PbS and PbSe QD are widely used in optical and photonic applications. For example, PbS(Se) QDs have potential applications in near-infrared photodetectors, photovoltaics and as saturable absorbers [22, 23]. In contrast to rare-earth ions-doped optical materials, lead chalcogenide quantum dot-doped glasses can provide tunable near-IR luminescence (about 1–2 µm) with high absolute quantum yield (≥60%) by controlling the size and distribution of QDs [22–24]. Despite a lot of efforts spent to find a novel gain medium which can almost cover the whole optical communication window, it is essential to tailor the emission of QDs embedded in a glass matrix in a wide bandwidth of the optical communication network. Therefore, PbS and PbSe QDs are promising gain media for covering the whole optical communication window [24–28]. Several advances of controlled chemical synthesis of the materials have provided the ways to grow QDs and manipulate their size, shape and

PbSe and PbS QDs with a band gap in the mid-infrared are interesting infrared phosphors materials. In the visible spectral range organic dyes usually present large PL AQY value than quantum dots, but infrared organic dyes have very low PL AQY suffer from poor photostability. On the other hand, the rare-earth ions can be used as the efficient infrared phosphors but they have small absorption cross sections and microsecond lifetimes. Infrared phosphors of PbS(Se), that are both efficient and possess short lifetimes, may find unique applications in the near-IR spectral range where biological tissues are relatively transparent, or as fluorescent

Variation of temperature and duration heat treatment (HT) of the glasses doped with Pb, S or Se make possible to change sizes of PbS(Se) QDs in a wide range (2–15 nm). The choice of these parameters enhances the formation of nucleation centers (NCs) in the glass and leads to good size control and small size dispersions. The growth processes of lead chalcogenide QDs is based mainly on the phase decomposition from the over-saturated solid solution. Two-

 = 0.29 eV) semiconductors with the Bohr's exciton radii 20 nm (for PbS) and 46 nm (for PbSe). Their large Bohr radius provides strong quantum confinement effect that can be easily

= 0.41

increases [4].

72 Quantum-dot Based Light-emitting Diodes

**phosphors**

realized in a wide range of QD size [20, 21].

composition using different methodologies [29].

materials in the fiber communication range of 1.3–1.5 microns.

stage heat treatment of the glass afforded QDs with narrow size distribution.

eV, *Eg*

In order to investigate the effect of the QDs sizes on the PL properties, the fluorine-phosphate (FP) glasses 0.25Na<sup>2</sup> O-0.5P<sup>2</sup> O5 -0.05ZnF<sup>2</sup> -0.1Ga<sup>2</sup> O3 -0.05AlF3 -0.05NaF (mol%) doped with CdS, CdSe or PbSe (PbF<sup>2</sup> +ZnS) and PbS (PbF<sup>2</sup> +ZnSe) were synthesized The glass synthesis was conducted in an electric furnace at 1050°C in the Ar-atmosphere using the closed glassy carbon crucibles. This method allows for maintaining the high concentrations of volatile components (such as Se, Se ore F) and avoiding the interaction with atmospheric air, thus preventing the fluorine-oxygen substitution reaction. After quenching, the glasses were annealed at 320°C for 1 h to release thermal stress and to form MCs. Then glasses were cut into pieces of 10 × 10 mm and were optically polished. Planar polished samples 0.4–1.0 mm thick were prepared for further investigation. Samples were heat treated using a muffle furnace (Nabertherm) with program temperature control to induce formation of CdS(Se) and PbS(Se) QDs at a temperature above glass transition temperature (*Tg* ).

### **3. Luminescent properties of quantum dots in the fluorine-phosphate glasses**

#### **3.1. Fluorine-phosphate glasses doped with CdSe quantum dots**

The emission properties of semiconductor nanocrystals can be evaluated by three key parameters, which are the brightness, the emission color and the stability of the emission.

Samples of the glass-containing CdSe QDs were prepared by heat treatment of 0.25Na<sup>2</sup> O-0.5P<sup>2</sup> O5 -0.05ZnF<sup>2</sup> -0.1Ga<sup>2</sup> O3 -0.02PbF<sup>2</sup> -0.08AlF3 glass doped with 0.6 mol% CdSe. The glass transition temperature measured with STA 449 F1 Jupiter (Netzsch) differential scanning calorimeter (DSC) was found to be 400 ± 3°C (**Figure 2**). DSC curve of the glass doped with CdS and CdSe was identical. High crystallization pick in 430–460 temperature range confirms high concentration CdSe(CdS) QDs in the glass. Hence, on the base of DSC data, we have determined the regimes of heat treatment of the starting glasses which are necessary for the nanocrystalline phase production: temperature *T* = 410°C, time 20–60 min.

The optical density spectra of the studied FP glass samples were recorded using a doublebeam spectrophotometer Lambda 650 (Perkin Elmer) in the 1.5–5 eV spectral region with 0.1 nm resolution. Absorption spectra demonstrate that due to quantum size effect, the band gap of CdSe QDs increases from 2.2 to 3.0 eV, as the size of the nanocrystals decreases from 4.0 to 2.0 nm.

The emission color of the PL of the nanocrystals shifts continuously from red (centered at 730 nm) to orange (centered at 630 nm) as size of QDs decrease (**Figure 3**). QDs sizes were defined using data [34, 35].

In the PL spectra, the broad band with a large Stokes shift is dominant, and the band-edge PL is negligibly weak (**Figure 3**). The emission spectrum of samples is dominated by "deep trap" emission, strongly red shifted from the band edge (**Figures 3** and **4**). For registration of the emission spectra was used an EPP2000-UVN-SR (Stellar Net) fiber spectrometer. The luminescence was excited by semiconductor lasers (λ= 405 nm). **Figure 5** illustrates a luminescence shift from yellow to red with the increasing size of QDs.

**Figure 6** demonstrates the excitation energy dependence of PL AQY magnitudes for glasses doped with CdSe QDs. The QDs concentration in the glasses 2 and 3 is equal (**Figure 3**), but AQY of the QD with size 3 nm is two times higher. The emission color of the PL of the QDs with size 3 nm is red with λmax = 700 nm. Absolute quantum yield measurements were carried out inside the integrated sphere with Photonic Multichannel Analyzer (PMA-12, Hamamatsu) at room temperature. The measurement error for the absolute quantum yield was ±1%.

**Figure 2.** Thermal curve of the starting FP glass doped with Cd, Se and S measured with differential scanning calorimeter.

CdS(Se) and PbS(Se) Quantum Dots with High Room Temperature Quantum Efficiency... http://dx.doi.org/10.5772/intechopen.68459 75

Samples of the glass-containing CdSe QDs were prepared by heat treatment of 0.25Na<sup>2</sup>

transition temperature measured with STA 449 F1 Jupiter (Netzsch) differential scanning calorimeter (DSC) was found to be 400 ± 3°C (**Figure 2**). DSC curve of the glass doped with CdS and CdSe was identical. High crystallization pick in 430–460 temperature range confirms high concentration CdSe(CdS) QDs in the glass. Hence, on the base of DSC data, we have determined the regimes of heat treatment of the starting glasses which are necessary for the

The optical density spectra of the studied FP glass samples were recorded using a doublebeam spectrophotometer Lambda 650 (Perkin Elmer) in the 1.5–5 eV spectral region with 0.1 nm resolution. Absorption spectra demonstrate that due to quantum size effect, the band gap of CdSe QDs increases from 2.2 to 3.0 eV, as the size of the nanocrystals decreases from

The emission color of the PL of the nanocrystals shifts continuously from red (centered at 730 nm) to orange (centered at 630 nm) as size of QDs decrease (**Figure 3**). QDs sizes were defined

In the PL spectra, the broad band with a large Stokes shift is dominant, and the band-edge PL is negligibly weak (**Figure 3**). The emission spectrum of samples is dominated by "deep trap" emission, strongly red shifted from the band edge (**Figures 3** and **4**). For registration of the emission spectra was used an EPP2000-UVN-SR (Stellar Net) fiber spectrometer. The luminescence was excited by semiconductor lasers (λ= 405 nm). **Figure 5** illustrates a luminescence

**Figure 6** demonstrates the excitation energy dependence of PL AQY magnitudes for glasses doped with CdSe QDs. The QDs concentration in the glasses 2 and 3 is equal (**Figure 3**), but AQY of the QD with size 3 nm is two times higher. The emission color of the PL of the QDs with size 3 nm is red with λmax = 700 nm. Absolute quantum yield measurements were carried out inside the integrated sphere with Photonic Multichannel Analyzer (PMA-12, Hamamatsu) at room temperature. The measurement error for the absolute quantum yield

**Figure 2.** Thermal curve of the starting FP glass doped with Cd, Se and S measured with differential scanning calorimeter.


0.5P<sup>2</sup> O5

4.0 to 2.0 nm.

was ±1%.

using data [34, 35].


74 Quantum-dot Based Light-emitting Diodes


O3

shift from yellow to red with the increasing size of QDs.


nanocrystalline phase production: temperature *T* = 410°C, time 20–60 min.

O-

**Figure 3.** Absorption and luminescence spectra of the FP glass doped with CdSe QDs with sizes of 2.0 nm (1), 3.0 nm (2) and 4.0 nm (3). The excitation energy is 3.06 eV.

**Figure 4.** Dependence of the Stokes shift on the QDs size. Inset: Luminescence FP glasses doped with CdSe QDs with different sizes.

**Figure 5.** Photography of the luminescence of the glasses doped with CdSe QDs with sizes 2–4 nm.

**Figure 6.** Dependence of the PL AQY for FP glasses doped with CdSe QDs with sizes 2.0 nm (1), 3.0 nm (2) and 4.0 nm (3) on the excitation energy.

The PL AQY magnitudes for glasses doped with CdSe QDs demonstrate a nonlinear dependence on the size (**Figure 7**). The PL AQY of the QDs increases monotonically from 4% to a maximum and then falls down to 30% (**Figure 4**). For convenience, the position with the maximum PL AQY is called the bright point as in Ref. [15]. The bright point for CdSe QDs in FP glass was observed for QDs with size 3.0 nm.

**Figure 7.** Dependence of the PL AQY on the PL peak position of the CdSe QDs.

The typical full width at half-maximum (FWHM) of the PL peak of the CdSe QDs ensemble at room temperature in FP glass, around 300–600 meV, is noticeably broader than that observed for colloidal QDs (30–70 meV) [15]. FWHM magnitudes decrease as QDs sizes increase (**Figure 8**).

#### **3.2. Fluorine-phosphate glasses doped with CdS quantum dots**

The PL AQY magnitudes for glasses doped with CdSe QDs demonstrate a nonlinear dependence on the size (**Figure 7**). The PL AQY of the QDs increases monotonically from 4% to a maximum and then falls down to 30% (**Figure 4**). For convenience, the position with the maximum PL AQY is called the bright point as in Ref. [15]. The bright point for CdSe QDs in

**Figure 6.** Dependence of the PL AQY for FP glasses doped with CdSe QDs with sizes 2.0 nm (1), 3.0 nm (2) and 4.0 nm

FP glass was observed for QDs with size 3.0 nm.

(3) on the excitation energy.

76 Quantum-dot Based Light-emitting Diodes

**Figure 7.** Dependence of the PL AQY on the PL peak position of the CdSe QDs.

As a result of quantum confinement effects, the absorption bands of the colloidal semiconductors CdS QDs shift to the higher energy region compared with the band-gap energy of 2.5 eV in a CdS bulk crystal [15]. Heat treatment leads to this effect in the glasses. It was shown [36] that heat treatment has a significant impact on properties of glasses doped with CdS QDs. With increasing of the heat-treatment duration, the absorption band shifts to a lower energy side. These results indicate the formation and growth of the CdS QDs. Based on the theory of the quantum size effect in spherical QDs [37], the mean radii of prepared CdS QDs are estimated to be 2.3 and 3.5 nm. The observation of the clear absorption peaks indicates that the size-distribution width of the CdS QDs is rather small (**Figure 9**).

**Figure 9** clearly shows effect of the heat treatment on the absorption and emission spectra of FP glasses doped with CdS QDs with sizes 2.3 and 3.5 nm. In PL spectra, the broad PL band with a large Stokes shift (1.2 eV) is dominant, and the band-edge PL is negligibly weak. The emission spectrum of samples is dominated by "deep trap" emission, strongly red shifted from the band edge.

**Figure 9** demonstrates size dependence of the PL AQY magnitudes for glasses doped with CdS QDs with sizes 2.3, 3.5 and 1.5 nm.

The PL AQY magnitudes for glasses doped with CdS QDs with sizes 2.3–3.5 nm demonstrate weak dependence on the size (**Figure 10**). The PL AQY of the CdS QDs increases to 65% for QDs with size 2.3 nm and then slowly fells down to 60% for QDs with size 3.5 nm. In a whole range of the QDs sizes (1.8–3.5 nm) PL AQY magnitudes does not fall below 30%.

**Figure 8.** Dependence of the PL FWHM magnitudes for glasses doped with CdSe QDs with different sizes.

**Figure 9.** Absorption and luminescence spectra of the FP glasses doped with CdS QDs with sizes of 2.3 nm (1) and 3.5 nm (2). The excitation energy is 3.06 eV. Inset: Luminescence of the FP glasses doped with CdS QDs.

**Figure 10.** Dependence of PL AQY magnitudes for glasses doped with CdS QDs with sizes 2.3 nm (1), 3.5 nm (2) and 1.8 nm (3), respectively, on the excitation wavelength.

#### **3.3. Stability of CdS and CdSe quantum dots in the fluorine-phosphate glasses**

The PL properties of the CdS and CdSe nanocrystals prepared in the FP glasses, including the PL QY, the peak position and the PL FWHM, did not show any detectable change upon aging in air for several years.

It is known that under the various external factors (fluorescent lighting, laser and UV exposure in an oxygen environment) the CdS(Se) QDs sizes decrease [15] due to the formation of the layer in which sulfur or selenium substitute for oxygen. This process is named photo-oxidation. Photo-oxidation destroys the luminescent centers and reduces PL AQY magnitudes of the colloidal QDs.

A stability of nanocrystals in the FPG were defined by an impulse wave laser photo-oxidation experiment at UV (355 nm), visible (532 nm) wavelengths and after interrelation with Hg lamp during 3 h.

**Figure 11** shows the result of the experiment on the FP glass samples doped with CdSe QDs in a diameter of 4.5 nm. The laser power density was 15 mJ and durations of the interaction laser change was from 0 to 15 min.

Before and after irradiation, the absorption spectra of the four samples were identical. This result demonstrates that the photo-oxidation of the nanocrystals in the glass is negligible.

A related photo-oxidation experiment was done on CdSe and CdS nanocrystals. The optical densities of the three samples were within 10% of each other below 375 nm. The CdS sample showed an absorption peak at 418 nm and for the CdSe sample, it is at 420 and 450 nm. A 240 W Hg lamp illuminated the three samples simultaneously for 3 h at a large enough distance from the lamp to prevent significant heating. As above, the CdS and CdSe nanocrystals did not show the blue shifting of their absorption maximums and a general loss of optical density at all wavelengths of absorption. The magnitudes of quantum yields were within the error of measurement for all tested glasses before and after the UV radiation.

Our qualitative results demonstrate the enhanced photostability of the QDs synthesized in the FP glasses. We measured the absorption spectra and the quantum yields of FP glasses doped with QDs before and after irradiation during 12 months. No changes in absorption spectra and in quantum yield were detected. This combination of photostability and high quantum yield makes these materials very attractive for use in optoelectronic devices like LEDs.

**3.3. Stability of CdS and CdSe quantum dots in the fluorine-phosphate glasses**

in air for several years.

nm (3), respectively, on the excitation wavelength.

78 Quantum-dot Based Light-emitting Diodes

The PL properties of the CdS and CdSe nanocrystals prepared in the FP glasses, including the PL QY, the peak position and the PL FWHM, did not show any detectable change upon aging

**Figure 10.** Dependence of PL AQY magnitudes for glasses doped with CdS QDs with sizes 2.3 nm (1), 3.5 nm (2) and 1.8

**Figure 9.** Absorption and luminescence spectra of the FP glasses doped with CdS QDs with sizes of 2.3 nm (1) and 3.5 nm

(2). The excitation energy is 3.06 eV. Inset: Luminescence of the FP glasses doped with CdS QDs.

It is known that under the various external factors (fluorescent lighting, laser and UV exposure in an oxygen environment) the CdS(Se) QDs sizes decrease [15] due to the formation of

**Figure 11.** Absorption spectra of FP glasses doped with CdSe QDs with size of 4.5 nm after laser irradiation at power density 15 mJ during 0 min (1), 5 min (2), 10 min (3) and 15 min (4) at *λ*exc = 355 nm. The diameter of the laser beam is 4 mm.

Absolute quantum yield allows to estimate the efficiency of converting UV light in the visible range and emphasizes the importance of this parameter for industrial applications of glasses doped with CdS(Se) QDs as luminescence down-shifting material or phosphor.

#### **3.4. A fluorine-phosphate glass doped with CdS(Se) as a new type of red phosphor**

The blue LED InGaN used as a basic component of the white LED emits with the spectra maximum at 450 nm. YAG:Ce3+ powder is a conventional phosphor with the spectral maximum at 570 nm and shifts the LED color temperature range toward the "warmer" white light. However, this composition gives the so-called "cold" white light, because their radiation does not cover the overall visible range. This "cold" white light is not always comfortable for eyes. Thus if one wants to get the composition of the emitters with "warm" white light, it is necessary to introduce an additional phosphor—some new component, introducing into the spectrum the red component with broad band luminescence and the maximum at 600–750 nm. Prospective for this task are, for instance, materials doped with manganese ions. However, this type of LEDs has a significant disadvantage—the absorption cross-section by manganese ions in the spectral range of 400–600 nm is negligible.

One can solve this problem with the use of other phosphor activators—CdS(Se) QDs with the maximum of the emission band at 650–700 nm, which introduces into the blue LED emission of the red component. As a result, the mixing of blue, green and red light takes place. In our work we have tried to solve the mentioned problems by means of the FP glasses doped with CdS(Se) QDs.

**Figure 12** shows the CIE chromaticity coordinates of the FP(CdSe) glass heat treated at *T* = 405°C for 30 and 60 min and **Figure 13** illustrates CIE chromaticity coordinates of the FP(CdS) glass heat treated at *T* = 415°C for10, 30 and 40 min. It is shown the increasing of the heat-treatment duration shifts the chromaticity coordinates from the yellow area (x = 410, y = 370) to the area of the diagram that corresponds to the red color (x = 440, y = 380).

**Figure 12.** CIE chromaticity coordinates of the FP(CdSe) glass heat treated at *T* = 405°C during 30 min (a) and 60 min (b).

CdS(Se) and PbS(Se) Quantum Dots with High Room Temperature Quantum Efficiency... http://dx.doi.org/10.5772/intechopen.68459 81

Absolute quantum yield allows to estimate the efficiency of converting UV light in the visible range and emphasizes the importance of this parameter for industrial applications of glasses

The blue LED InGaN used as a basic component of the white LED emits with the spectra maximum at 450 nm. YAG:Ce3+ powder is a conventional phosphor with the spectral maximum at 570 nm and shifts the LED color temperature range toward the "warmer" white light. However, this composition gives the so-called "cold" white light, because their radiation does not cover the overall visible range. This "cold" white light is not always comfortable for eyes. Thus if one wants to get the composition of the emitters with "warm" white light, it is necessary to introduce an additional phosphor—some new component, introducing into the spectrum the red component with broad band luminescence and the maximum at 600–750 nm. Prospective for this task are, for instance, materials doped with manganese ions. However, this type of LEDs has a significant disadvantage—the absorption cross-section by manganese ions in the spectral range of 400–600

One can solve this problem with the use of other phosphor activators—CdS(Se) QDs with the maximum of the emission band at 650–700 nm, which introduces into the blue LED emission of the red component. As a result, the mixing of blue, green and red light takes place. In our work we have tried to solve the mentioned problems by means of the FP glasses doped with

**Figure 12** shows the CIE chromaticity coordinates of the FP(CdSe) glass heat treated at *T* = 405°C for 30 and 60 min and **Figure 13** illustrates CIE chromaticity coordinates of the FP(CdS) glass heat treated at *T* = 415°C for10, 30 and 40 min. It is shown the increasing of the heat-treatment duration shifts the chromaticity coordinates from the yellow area (x = 410, y = 370) to the area of

**Figure 12.** CIE chromaticity coordinates of the FP(CdSe) glass heat treated at *T* = 405°C during 30 min (a) and 60 min (b).

the diagram that corresponds to the red color (x = 440, y = 380).

doped with CdS(Se) QDs as luminescence down-shifting material or phosphor.

nm is negligible.

80 Quantum-dot Based Light-emitting Diodes

CdS(Se) QDs.

**3.4. A fluorine-phosphate glass doped with CdS(Se) as a new type of red phosphor**

**Figure 13.** CIE chromaticity coordinates of the FP (CdS) glass heat treated at *T* = 415°C during 10 min (1), 30 min (2), 40 min (3) and 60 min (4).

In this study, a new type of red phosphor representing a fluorine-phosphate glass doped with CdS(Se) were synthesized using technology developed and applied earlier by Vaynberg [1]. These red phosphors with combination of green-yellow phosphors can be applied to fabricate the pc-WLEDs on the blue InGaN chips.

Absolute quantum yield allows estimating efficiency of converting UV light in the visible range that is why it is an important parameter for industrial applications of glasses doped with CdS(Se) QDs as luminescence down-shifting material or phosphor.

#### **3.5. Fluorine-phosphate glasses doped with PbS and PbSe molecular clusters**

Highly concentrated semiconductor components, which can be stored in glasses, is a main difference between FP glasses and previously studied silicate and borosilicate glasses. It is obviously expressed, that the concentration of MCs and QDs, which may be formed in the glass during heat treatment, is also significantly higher. High concentration and the uniform distribution of the activators should lead to high values of absolute quantum yield. DSC curves confirm the high concentration of the activator (**Figure 14**).

The glass transition temperature was found to be 400–408 ± 3°C. Samples were heat treated to induce formation of PbS(Se) QDs at 410°C. Due to the high concentration of sulfur and selenium, crystallization peak induced by the precipitation of PbS(Se) QDs was observed.

As-prepared glasses doped with PbS(Se) demonstrate strong luminescence (when excited in UV spectral region) due to the MCs formation whereas the changes of the absorption coefficient are not large. The heat treatment at temperatures less than *Tg* results in the MCs' growth and increases the luminescence intensity [36–38]. For registration of the emission spectra excited at λ = 405 nm (3.06 eV), we used an EPP2000-UVN-SR (Stellar Net) fiber spectrometer.

**Figure 14.** DSC curves of the initial glasses doped with PbSe (a) and PbS (b).

The optical density spectra of the studied FP glass samples were recorded using a double-beam spectrophotometer Lambda 650. (Perkin Elmer) in the 1.5–5 eV spectral region with 0.1 nm resolution and spectrophotometer Cary 500 (Varian) from 300 to 3000 nm (optical resolution was 0.5 nm).

PL excitation spectrum of the glass doped with MCs(PbS)*<sup>n</sup>* can be observed in spectral range of 250–400 nm (**Figure 15a**). Asymmetric form of the PL excitation band by two (*λ*max = 290 nm and *λ*max = 350 nm) indicates the existence of various sizes of the MCs. **Figure 15b** shows luminescence spectra of MCs(PbS)*<sup>n</sup>* . The broad luminescence band of the MCs shifts from 570 to 700 nm due to the MCs sizes increasing. The absolute quantum yield of the as-prepared glasses doped with PbS (1) and after heat treatment (2) are shown in **Figure 16a**. The absolute

**Figure 15.** PL excitation spectrum of the glass doped with MCs (PbS)*<sup>n</sup>* (*λ*lum = 540 nm) (a) Luminescence spectra of the glasses doped with MCs (PbS)*<sup>n</sup>* : as-prepared (1) and after heat treatment at *T*HT = 410°C within 10 min (2), 20 min (3), 30 min (4) and 40 min (5) (*λ*exc = 250 nm) (b).

quantum yield of the as-prepared glass doped with PbSe (1) and after heat treatment (2) shown in **Figure 16b**. **Figure 16c** shows the photography of the (PbS)*<sup>n</sup>* MCs luminescence at *λ*exc = 365 nm. Absolute quantum yield of the FP glass doped with PbS and PbSe MCs depends on excitation wavelength and changes from 10 to 2% (**Figure 16a** and **b**). The MCs are nucleation centers for the formation of PbS and PbSe QDs. It was shown [33, 36] that QDs formation in FP glasses leads to an increase in its intensity by a factor of five (**Figure 16a** and **b**).

The optical density spectra of the studied FP glass samples were recorded using a double-beam spectrophotometer Lambda 650. (Perkin Elmer) in the 1.5–5 eV spectral region with 0.1 nm resolution and spectrophotometer Cary 500 (Varian) from 300 to 3000 nm (optical resolution

of 250–400 nm (**Figure 15a**). Asymmetric form of the PL excitation band by two (*λ*max = 290 nm and *λ*max = 350 nm) indicates the existence of various sizes of the MCs. **Figure 15b** shows

to 700 nm due to the MCs sizes increasing. The absolute quantum yield of the as-prepared glasses doped with PbS (1) and after heat treatment (2) are shown in **Figure 16a**. The absolute

can be observed in spectral range

(*λ*lum = 540 nm) (a) Luminescence spectra of the

: as-prepared (1) and after heat treatment at *T*HT = 410°C within 10 min (2), 20 min (3), 30

. The broad luminescence band of the MCs shifts from 570

PL excitation spectrum of the glass doped with MCs(PbS)*<sup>n</sup>*

**Figure 14.** DSC curves of the initial glasses doped with PbSe (a) and PbS (b).

**Figure 15.** PL excitation spectrum of the glass doped with MCs (PbS)*<sup>n</sup>*

glasses doped with MCs (PbS)*<sup>n</sup>*

min (4) and 40 min (5) (*λ*exc = 250 nm) (b).

luminescence spectra of MCs(PbS)*<sup>n</sup>*

82 Quantum-dot Based Light-emitting Diodes

was 0.5 nm).

**Figure 16.** (a) Absolute quantum yield for the glasses doped with PbS as-prepared (1) and glass after heat treatment (2), (b) Absolute quantum yield for glass doped with PbSe as-prepared (1) and after heat treatment (2) and (c) photography of the (PbS)*<sup>n</sup>* MCs luminescence at *λ*exc = 365 nm.

The luminescence spectrum of FP (PbS) after heat treatment at *T* = 360°C within 90 min (1) (**Figure 17a**) demonstrates appearance of the second band (980 nm) due to small QDs formation. After heat treatment within 97 min (2) the luminescence band of the MCs was disappeared (**Figure 17a**).

**Figure 17.** (a) Luminescence spectra of FP glass doped with MCs (PbS)*<sup>n</sup>* after heat treatment at 400°C within 90 min (1) and 97 min (2), *E*ex = 3.06 eV and (b) Luminescence intensity in maximum as a function of thermal treatment temperature.

**Figure 18** shows the influence of heating on luminescence spectra. In this experiment, the sample preliminary thermal treated at 380°C was used. The increase of the sample temperature from 20 to 250°C led to seven times decrease of luminescence intensity and to the weak red shift of the luminescence band. This effect is reversible and can be repeated for many times [36]. The luminescence thermal quenching can be explained by a fact that with the temperature rise the electrons in the excited state can occupy high vibrational energy levels, which intersect the ground state level at configuration coordinate diagram. This allows the vibrational relaxation of the excited electrons to the ground state via phonon release without emission of radiation [36].

#### **3.6. Fluorine-phosphate glasses doped with PbS and PbSe quantum dots**

For luminescence measurement (scanning ranges 400–1100 nm and 900–1800 nm) with fixed excitation wavelength (*λ*ex = 808 nm) Stellar Net EPP2000-UVN-SR fiber spectrometer was used (optical resolution 0.5 nm). A semiconductor laser with pumping power 0.1 W excited the luminescence.

When heat-treatment duration or temperature increase, the new band appears with *λ*max = 1000 nm. It is due to the PbSe (S) QD formation with the sizes below 2.0 nm (**Figure 16a**). Increase of the heating temperature and time results in a prominent change of the absorption spectra and appearance of discreet spectra corresponding to QDs.

**Figure 18.** The influence of the temperature of the FP glasses doped with (PbSe)*<sup>n</sup>* MCs on the luminescence intensity..- The luminescence spectra were measured at temperature of (1) 22°C, (2) 50°C, (3) 100°C, (4) 150°C, (5) 200°C and (6) 250°C. Excitation wavelength was of 405 nm. Inset: Luminescence intensity in maximum via the temperature of the sample and photo of the luminescence of the FP glass doped with (PbSe)*<sup>n</sup>* MCs.

To precipitate PbS QDs, glass samples were heat treated at temperature 410°C within 20–90 min (**Figure 19**). Based on hyperbolic band model obtained from *k* × *p* calculations [21], average diameters of these PbS QDs were found to be 3.0, 3.9 and 4.9 nm. QDs sizes were calculated using formula:

CdS(Se) and PbS(Se) Quantum Dots with High Room Temperature Quantum Efficiency... http://dx.doi.org/10.5772/intechopen.68459 85

$$\begin{aligned} \text{http://@d.o.do.org/0.5772/ntetch.eps.68458} \\\\ E\_0 &= 0.41 + \frac{1}{0.0252 \cdot D^2 + 0.283 \cdot D} \end{aligned} \tag{1}$$

where *E*<sup>0</sup> —energy gap of PbS QDs (eV) and *D*—diameter of QDs in nm.

**Figure 18** shows the influence of heating on luminescence spectra. In this experiment, the sample preliminary thermal treated at 380°C was used. The increase of the sample temperature from 20 to 250°C led to seven times decrease of luminescence intensity and to the weak red shift of the luminescence band. This effect is reversible and can be repeated for many times [36]. The luminescence thermal quenching can be explained by a fact that with the temperature rise the electrons in the excited state can occupy high vibrational energy levels, which intersect the ground state level at configuration coordinate diagram. This allows the vibrational relaxation of the excited electrons to the ground state via phonon release without emission of radiation [36].

For luminescence measurement (scanning ranges 400–1100 nm and 900–1800 nm) with fixed excitation wavelength (*λ*ex = 808 nm) Stellar Net EPP2000-UVN-SR fiber spectrometer was used (optical resolution 0.5 nm). A semiconductor laser with pumping power 0.1 W excited

When heat-treatment duration or temperature increase, the new band appears with *λ*max = 1000 nm. It is due to the PbSe (S) QD formation with the sizes below 2.0 nm (**Figure 16a**). Increase of the heating temperature and time results in a prominent change of the absorption

To precipitate PbS QDs, glass samples were heat treated at temperature 410°C within 20–90 min (**Figure 19**). Based on hyperbolic band model obtained from *k* × *p* calculations [21], average diameters of these PbS QDs were found to be 3.0, 3.9 and 4.9 nm. QDs sizes were calculated

The luminescence spectra were measured at temperature of (1) 22°C, (2) 50°C, (3) 100°C, (4) 150°C, (5) 200°C and (6) 250°C. Excitation wavelength was of 405 nm. Inset: Luminescence intensity in maximum via the temperature of the

MCs.

MCs on the luminescence intensity..-

**3.6. Fluorine-phosphate glasses doped with PbS and PbSe quantum dots**

spectra and appearance of discreet spectra corresponding to QDs.

**Figure 18.** The influence of the temperature of the FP glasses doped with (PbSe)*<sup>n</sup>*

sample and photo of the luminescence of the FP glass doped with (PbSe)*<sup>n</sup>*

the luminescence.

84 Quantum-dot Based Light-emitting Diodes

using formula:

Increasing heat-treatment time and temperature leads to shifting of luminescence bands of the PbS QDs to 970, 1300 and 1500 nm (**Figure 19**) and absorption bands (to 920, 1100 and 1400 nm). Stokes shift changes from 80 to 50 meV due to the changing of QDs sizes from 3.0 to 4.9 nm (**Figure 21b**).

**Figure 19.** Luminescence spectra of the glasses doped with PbS QDs with sizes 3 nm (1), 3.9 nm (2), 4.9 nm (3) and *λ*exc = 808 nm.

**Figure 20** shows absorption and luminescence spectra of PbSe QDs formed in glasses. Increasing of the heating time results in prominent changes of absorption spectra of the FP glass doped with PbSe and leads to appearance of discreet spectra corresponding to QDs. Based on hyperbolic band model obtained from tight binding calculation using experimental energy values *Eg* , we can estimate the PbSe QD sizes [39] according to Eq. (2), \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 0.0105 <sup>⋅</sup> *<sup>D</sup>*<sup>2</sup> <sup>+</sup> 0.2655 <sup>⋅</sup> *<sup>D</sup>* <sup>+</sup> 0.0667 (2)

$$\begin{array}{ccccc} & & & \mathbf{\hat{x}} & \mathbf{\hat{y}} & \mathbf{\hat{z}} & \mathbf{\hat{z}} & \mathbf{\hat{z}} & \mathbf{\hat{z}} \\ \mathbf{\hat{x}} & \mathbf{\hat{y}} & \mathbf{\hat{z}} & \mathbf{\hat{z}} & \mathbf{\hat{z}} & \mathbf{\hat{z}} & \mathbf{\hat{z}} \end{array} \tag{2}$$
 
$$\mathbf{\hat{x}} = \mathbf{\hat{x}} \mathbf{\hat{z}} + \mathbf{\hat{z}} \mathbf{\hat{z}} \mathbf{\hat{x}} + \mathbf{\hat{z}} \mathbf{\hat{z}} \mathbf{\hat{z}} + \mathbf{\hat{z}} \mathbf{\hat{z}} \mathbf{\hat{z}} \mathbf{\hat{z}} \tag{3}$$

**Figure 20.** Absorption (a) and luminescence (b) spectra of the glasses doped with PbSe QDs with sizes 2.5 nm (1), 3.0 nm (2), 3.7 nm (4), 5.1 nm (5), *λ*exc = 808 nm.

where *D* is the effective diameter of the quantum dots (nm), *Eg* is the energy gap of PbSe quantum dots (eV) and *Eg* (∞) is the energy bandgap of bulk PbSe semiconductor (0.29 eV).

When heat-treatment time and temperature are increased, absorption peaks shifts to 870–1540 nm and luminescence bands shifts to 1050–1650 nm. Stokes shift of QDs changes from 335 to 60 meV when size varies from 2.5 to 5.1 nm (**Figure 21a**).

It can be deduced that heat-treatment conditions define the formation characteristic of PbS (Se) QDs in glass (such as the beginning growth temperature, growth rate, density in glass matrix, size and size distribution of QDs, etc.).

Because of matching of the PL characteristic with window (1330 nm) of PbSe QD-embedded glass (see the **Figure 4**, curve 3), we choose this glass as the representative sample to characterize the optical amplification at the 1330 nm window. Signals at 1330 nm with different

**Figure 21.** Stokes shift versus QDs diameter for PbS (a) and PbSe (b) QDs.

pump power values were measured. It can be found that the intensity enhances gradually with increasing of power. Even when the pump power reaches from 500 to 1000 mW, no obvious signal saturation is detected. This allows that FP (PbS and PbS) glasses can be potentially applied in broadband amplifiers and confirm the high photo-stability of the QDs synthesized in the FP glasses. We also measured the absorption spectra and quantum yields of FP glasses doped with QDs before and after irradiation during 12 months. No changes in absorption spectra and in quantum yield were detected.

The FP glasses doped with PbSe and PbS QDs are infrared fluorophores, which are efficient, photo-stable and possess short lifetimes. These materials may find unique applications for fluorescent imaging.

## **4. Conclusions**

where *D* is the effective diameter of the quantum dots (nm), *Eg*

60 meV when size varies from 2.5 to 5.1 nm (**Figure 21a**).

**Figure 21.** Stokes shift versus QDs diameter for PbS (a) and PbSe (b) QDs.

matrix, size and size distribution of QDs, etc.).

86 Quantum-dot Based Light-emitting Diodes

quantum dots (eV) and *Eg* (∞) is the energy bandgap of bulk PbSe semiconductor (0.29 eV). When heat-treatment time and temperature are increased, absorption peaks shifts to 870–1540 nm and luminescence bands shifts to 1050–1650 nm. Stokes shift of QDs changes from 335 to

It can be deduced that heat-treatment conditions define the formation characteristic of PbS (Se) QDs in glass (such as the beginning growth temperature, growth rate, density in glass

Because of matching of the PL characteristic with window (1330 nm) of PbSe QD-embedded glass (see the **Figure 4**, curve 3), we choose this glass as the representative sample to characterize the optical amplification at the 1330 nm window. Signals at 1330 nm with different

is the energy gap of PbSe

The CdS and CdSe nanocrystals synthesized in the fluorine-phosphate glass represents a series of excellent emitters in the orange-red spectral region (600–750 nm) in terms of their PL AQY and the FWHM of the PL spectra, and they show the photo- and chemical stability of the emission for a long time.

The photoluminescence quantum yield of CdSe QDs rises monotonically to a maximum value and then decreases gradually with the size increase of QDs. Such a maximum (a PL "bright point") is in 650–750 nm spectral range.

The PL AQY magnitudes for glasses doped with CdS QDs with sizes of 2.3–3.5 nm demonstrate weak dependence on the size and reaches 65%.

We suggest that origin of these dependences is the difference in the interaction mechanisms between CdSe and CdS quantum dots and glass network.

Experimental results suggest that the existence of the PL bright point is a general phenomenon of CdSe QDs and similarly is a signature of an optimal surface structure reconstruction of the nanocrystals grown in a liquid or in a glass. Absolute quantum yield magnitude of luminescence glasses doped with CdS (Se) QDs can reach 50–65%, which is two times higher than it was reported earlier in silicate glasses. It opens up new prospects for using such materials as phosphors for white LEDs and down-convertors for solar cells.

It was shown that heat treatment of the FP glasses leads to formation of (PbS)*<sup>n</sup>* and (PbSe)*<sup>n</sup>* molecular clusters, which exhibit luminescent properties in visible range with quantum efficiency from 2 to 10%. Increasing the heat-treatment temperature results in the PbS and PbSe QDs (sizes of 3–5 nm) formation with high concentration (~1 mol%). The QDs have broadband photoluminescence with quantum efficiency about five times more than MCs (~50%) in the spectral range of 1–1.7 µm. FP glasses doped with PbSe and PbS QDs are infrared fluorophores, which are both efficient and possess short lifetimes. These materials may find unique applications for fluorescent imaging tagging in the near-IR spectral range or as fluorescent materials in the fiber communication range of 1.3–1.5 microns.

#### **Acknowledgements**

Research was funded by Russian Science Foundation (Agreement #14-23-00136).

#### **Author details**

Elena Kolobkova1,2\* and Nikolay Nikonorov1

\*Address all correspondence to: kolobok106@rambler.ru

1 Department of Optical Informatics Technologies and Materials, ITMO University, Saint-Petersburg, Russia

2 St. Petersburg State Institute of Technology (Technical University), St. Petersburg, Russia

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Elena Kolobkova1,2\* and Nikolay Nikonorov1

\*Address all correspondence to: kolobok106@rambler.ru

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1 Department of Optical Informatics Technologies and Materials, ITMO University,

2 St. Petersburg State Institute of Technology (Technical University), St. Petersburg, Russia

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**Provisional chapter**

#### **Quantum Dot–Incorporated Hybrid Light-Emitting Diodes Light-Emitting Diodes**

DOI: 10.5772/intechopen.68356

#### Namig Hasanov Namig Hasanov Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Quantum Dot–Incorporated Hybrid** 

http://dx.doi.org/10.5772/intechopen.68356

#### **Abstract**

Quantum dots are very promising candidates to enhance the performance of hybrid devices. Their size-dependent wavelength tunability owing to quantum size effect, narrow full width at half maximum, high quantum yield, and several other optoelectronic properties enable their use as potential components in GaN-based light-emitting diodes. This chapter explains methods to fabricate color-converted and white light-emitting diodes with the incorporation of semiconductor quantum dots.

**Keywords:** quantum dots, light-emitting diodes, color conversion, white light

#### **1. Introduction**

Thanks to their physical, optical, and electronic properties, semiconductor nanocrystals attracted enormous interest as promising nanomaterials with potential applications in optoelectronics [1]. These nanocrystals can be chemically synthesized with different sizes and shapes including nanowires, nanodiscs, and quantum dots (QDs). Spherical QDs possess several advantages that make them more flexible nanomaterials to be utilized in wider range of applications. QDs can be synthesized as a core, core-shell, or core-multi shell as shown in **Figure 1**. The size of QDs determines their emission wavelength; emission energy of these nanocrystals is related to their quantum confinement property that changes with the radius of the nanocrystals. Thus, it is possible to synthesize nanocrystals emitting with wavelength range covering the whole visible spectrum. This property makes them powerful optoelectronic components. The full width at half maximum (FWHM) of semiconductor QDs is generally in the range of 30–40 nm. Recently, QDs with very high quantum efficiency (one of the main performance measures of QDs) values were reported.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Figure 1.** Schematic diagram showing core, core-shell, and core-multi shell QDs.

Although, QDs exhibit high optical properties, their electrical properties are not at the desired level. Thus, the efficiency of the devices utilizing electrically injected QDs is very low [2]. One of the main reasons for this low performance of QD-incorporated devices is the existence of organic ligands on the surface of QDs that prevents an efficient current injection. On the other hand, ligands play an important role in the enhancement of the stability of QDs. Further research is needed to be done to improve the electrical injection properties of these semiconductor nanocrystals. However, their optical properties can be used to enhance the performance of the devices with lower optical outputs. In the following sections, the device structures incorporating QDs are introduced and their effectiveness is thoroughly discussed.

#### **2. Color-converter QDs on GaN-based devices**

Since the important inventions mainly by Nakamura, Akasaki, and Amano in the development of GaN-based light-emitting diodes (LEDs) (they received Nobel Prize in Physics for the invention of blue LED in 2014) [3–5], these devices were widely investigated to enhance the external quantum efficiency and optical power as well as to reduce the electrical injection issues [6, 7]. GaN-based LEDs are mostly grown with metalorganic chemical vapor deposition (MOCVD) on c-plane sapphire substrates. The main drawbacks of sapphire as a growth substrate are the lattice mismatch and thermal expansion coefficient mismatch. The former drawback significantly reduces the performance of devices due to the formation of strain in the epitaxial layers. However, the performance of LEDs grown on sapphire is still higher than those grown on other substrates [8]. The higher efficiency can be achieved in the LEDs incorporating InGaN quantum wells in between the p-type and n-type GaN epitaxial layers. **Figure 2** depicts a schematic structure of a typical multiple quantum well InGaN/GaN LED. To achieve blue emission, the special care needs to be taken during the growth of InGaN quantum wells as the emission is mainly realized through the recombination of electrons and holes in these wells. The amount of In incorporated during the growth defines the emission wavelength of the device. Thus, it is possible to achieve high-quality blue emission with the incorporation of the correct amount of In (usually around 15%) [9]. Photoluminescence from an epitaxially grown blue LED is shown in **Figure 3**. In order to fabricate a GaN-based

**Figure 2.** Schematic diagram of multiple quantum well InGaN/GaN LEDs.

Although, QDs exhibit high optical properties, their electrical properties are not at the desired level. Thus, the efficiency of the devices utilizing electrically injected QDs is very low [2]. One of the main reasons for this low performance of QD-incorporated devices is the existence of organic ligands on the surface of QDs that prevents an efficient current injection. On the other hand, ligands play an important role in the enhancement of the stability of QDs. Further research is needed to be done to improve the electrical injection properties of these semiconductor nanocrystals. However, their optical properties can be used to enhance the performance of the devices with lower optical outputs. In the following sections, the device structures incor-

Since the important inventions mainly by Nakamura, Akasaki, and Amano in the development of GaN-based light-emitting diodes (LEDs) (they received Nobel Prize in Physics for the invention of blue LED in 2014) [3–5], these devices were widely investigated to enhance the external quantum efficiency and optical power as well as to reduce the electrical injection issues [6, 7]. GaN-based LEDs are mostly grown with metalorganic chemical vapor deposition (MOCVD) on c-plane sapphire substrates. The main drawbacks of sapphire as a growth substrate are the lattice mismatch and thermal expansion coefficient mismatch. The former drawback significantly reduces the performance of devices due to the formation of strain in the epitaxial layers. However, the performance of LEDs grown on sapphire is still higher than those grown on other substrates [8]. The higher efficiency can be achieved in the LEDs incorporating InGaN quantum wells in between the p-type and n-type GaN epitaxial layers. **Figure 2** depicts a schematic structure of a typical multiple quantum well InGaN/GaN LED. To achieve blue emission, the special care needs to be taken during the growth of InGaN quantum wells as the emission is mainly realized through the recombination of electrons and holes in these wells. The amount of In incorporated during the growth defines the emission wavelength of the device. Thus, it is possible to achieve high-quality blue emission with the incorporation of the correct amount of In (usually around 15%) [9]. Photoluminescence from an epitaxially grown blue LED is shown in **Figure 3**. In order to fabricate a GaN-based

porating QDs are introduced and their effectiveness is thoroughly discussed.

**2. Color-converter QDs on GaN-based devices**

**Figure 1.** Schematic diagram showing core, core-shell, and core-multi shell QDs.

94 Quantum-dot Based Light-emitting Diodes

device emitting light with longer wavelength, a larger amount of In should be introduced into the InGaN compound layer. However, the growth of InGaN layer with larger amounts of In results in the segregation of In [10]. Thus, InGaN/GaN LEDs utilizing more In exhibit significantly lower optical power and external quantum efficiency when compared with the blue LEDs using smaller amounts of In.

**Figure 3.** Photoluminescence of an epitaxially grown blue multiple quantum well InGaN/GaN LED.

To enhance the output performance of InGaN/GaN LEDs emitting the longer wavelength range, QDs can be incorporated as color-converter components [11]. Thus, by utilizing the optical properties of QDs and electrical properties of InGaN/GaN LED structure, it is possible to fabricate a color-converted hybrid LED emitting at longer wavelength. To realize this kind of device, QDs are placed on top surface of InGaN/GaN LED structures. One of the critical points during the construction is to place the correct amount of QDs. As the emission wavelength of the LED and the QDs are different, the process of placing QDs on top can result in either full color conversion or mixed color emission. Thus, the optimized amount of QDs will help to achieve the conversion of blue emission to the emission wavelength of the QDs. The schematic diagram demonstrating the color conversion process described above is shown in **Figure 4**. As it can be clearly seen from the figure, the process starts with the electrical injection of electrons and holes to the quantum wells of InGaN/GaN LEDs. Following their radiative and nonradiative recombination in the wells, carrier relaxation occurs. The radiative recombination results in the generation of photons with the wavelength corresponding to the bandgap of the InGaN wells (In incorporation defines the bandgap of the wells as stated above). The process of photon generation with this kind of electrical injection is called electroluminescence. These photons are absorbed by QDs placed on top of the device. The energy of the photons generated in the InGaN quantum wells should be higher than the bandgap of QDs to result in a successful excitation of charge carriers in QDs. Following the excitation of carriers with the incoming photons, the excited carriers recombine either radiatively or nonradiatively. Radiative recombination leads to the emission of photons with the wavelength corresponding to the bandgap of QDs. This kind of excitation of QDs which is a result of interaction between the photons of InGaN quantum wells and the charge carriers of QDs is called photoluminescence. **Figure 5** demonstrates the emission intensity of a color-converted InGaN/GaN LED incorporating QDs at 10, 20, 30, and 50 mA current levels.

The process of color conversion with the incorporation of semiconductor QDs is an equivalent method to the color conversion utilizing phosphors [12]. However, there are several drawbacks in using these phosphors for down-conversion. The bandwidth of emission in most

**Figure 4.** Schematic diagram color conversion in hybrid color-converted InGaN/GaN-QD LED.

To enhance the output performance of InGaN/GaN LEDs emitting the longer wavelength range, QDs can be incorporated as color-converter components [11]. Thus, by utilizing the optical properties of QDs and electrical properties of InGaN/GaN LED structure, it is possible to fabricate a color-converted hybrid LED emitting at longer wavelength. To realize this kind of device, QDs are placed on top surface of InGaN/GaN LED structures. One of the critical points during the construction is to place the correct amount of QDs. As the emission wavelength of the LED and the QDs are different, the process of placing QDs on top can result in either full color conversion or mixed color emission. Thus, the optimized amount of QDs will help to achieve the conversion of blue emission to the emission wavelength of the QDs. The schematic diagram demonstrating the color conversion process described above is shown in **Figure 4**. As it can be clearly seen from the figure, the process starts with the electrical injection of electrons and holes to the quantum wells of InGaN/GaN LEDs. Following their radiative and nonradiative recombination in the wells, carrier relaxation occurs. The radiative recombination results in the generation of photons with the wavelength corresponding to the bandgap of the InGaN wells (In incorporation defines the bandgap of the wells as stated above). The process of photon generation with this kind of electrical injection is called electroluminescence. These photons are absorbed by QDs placed on top of the device. The energy of the photons generated in the InGaN quantum wells should be higher than the bandgap of QDs to result in a successful excitation of charge carriers in QDs. Following the excitation of carriers with the incoming photons, the excited carriers recombine either radiatively or nonradiatively. Radiative recombination leads to the emission of photons with the wavelength corresponding to the bandgap of QDs. This kind of excitation of QDs which is a result of interaction between the photons of InGaN quantum wells and the charge carriers of QDs is called photoluminescence. **Figure 5** demonstrates the emission intensity of a color-converted

96 Quantum-dot Based Light-emitting Diodes

InGaN/GaN LED incorporating QDs at 10, 20, 30, and 50 mA current levels.

**Figure 4.** Schematic diagram color conversion in hybrid color-converted InGaN/GaN-QD LED.

The process of color conversion with the incorporation of semiconductor QDs is an equivalent method to the color conversion utilizing phosphors [12]. However, there are several drawbacks in using these phosphors for down-conversion. The bandwidth of emission in most

**Figure 5.** Emission intensity of a color-converted InGaN/GaN LED incorporating semiconductor nanocrystal QDs at 10, 20, 30, and 50 mA current levels.

phosphor compound materials is very large, almost spanning the whole visible spectrum. On the other hand, QDs emit with the FWHM of around 40 nm which is significantly smaller than that of the phosphors. Moreover, very large amount of phosphor material is required to achieve the full color conversion. In comparison, QDs can result in color conversion with significantly less amount of material. The optical absorption is another key parameter during the fabrication of a hybrid color-converted device. The color-converter materials should have decent absorption to exhibit high efficiency during the conversion process. QDs can absorb almost all the photons with the wavelength slightly shorter than the emission wavelength of these nanocrystals. On the other hand, phosphors can absorb only narrow range of wavelength. These superior properties of QDs over phosphors make them very promising candidates as efficient color-converter layers.

Although QDs are highly effective in color conversion, their localization in a suitable structure defines their efficiency. QDs generally exhibit significantly high quantum yield when dispersed in a medium-like toluene. However, making close-packed films out of these nanocrystals may result in a significant reduction of quantum yield. The main underlying reason for this behavior can be explained as follows. When QDs are dispersed in toluene, the separation distance between individual QDs is very large. This separation prevents any kind of close interaction between the nanocrystals. However, when they make close-packed solid films, the separation distance between the QDs is very short. This close construction gives rise to the interaction of QDs via nonradiative resonance energy transfer through dipole-dipole coupling process. When a close-packed film is excited with a source, the photogenerated electrons and holes in the QDs builds dipoles (this is called donor in the energy transfer process). These dipoles can create a mirror dipole in the QDs placed in sub-10 nm range (acceptor). The generation of the dipole in the adjacent QD is a nonradiative process owing to the absence of photon generation by the donor QD and absorption by the acceptor QD. Not all of the transferred dipole energies result in the radiative recombination in the acceptor QDs. Thus, a huge amount of energy is lost during the resonance energy transfer process. To prevent this energy transfer resulting from the close interaction of QDs, the QDs should be separated in their solid films. To realize this, QDs can be dispersed in a special matrix. This will help to reduce the quantum yield loss originating from the nonradiative energy transfer [13].

Another important change during the formation of solid films is the shift of emission wavelength. One of the main underlying reasons for this shift is the change in the medium. The refractive index strongly affects the emission wavelength. Moreover, the nonradiative resonance energy transfer between the nanocrystals also plays a significant role in the shift of the peak. The transfer mechanism is depicted in **Figure 6**. In very close proximity in their solid films, there is a high chance of energy transfer through nonradiative dipole-dipole coupling to occur. As it is well known, nanocrystals are not perfectly synthesized; there is a finite size distribution of the synthesized nanocrystals. Nanocrystals with smaller radius exhibit larger bandgap energy owing to the reverse proportionality of the bandgap energy with the nanocrystal radius in the calculation of quantum confinement. Thus, smaller nanocrystals (energy donor) tend to transfer their energy to larger nanocrystals (energy acceptor) close to them. Since the photoluminescence of the donor nanocrystals has a large spectral overlap with the absorbance of the acceptor nanocrystals as well (see **Figure 7**), the donors are able to transfer their excitons to the acceptors. These transferred excitons relax to the ground states and recombine for possible radiative emission. As a result of this transfer, collective emission intensity of the nanocrystals with smaller radius and higher energy (emitting with shorter wavelength) decreases. Moreover, emission intensity of the nanocrystals with larger radius

**Figure 6.** Energy transfer mechanism between smaller (donor) and larger (acceptor) nanocrystals.

**Figure 7.** Spectral overlap between the photoluminescence and absorbance curves of nanocrystals.

and lower energy (emitting with longer wavelength) increases. This results in the red shift of the emission intensity when compared with their emission in toluene.

#### **3. QD-incorporated hybrid white LEDs**

holes in the QDs builds dipoles (this is called donor in the energy transfer process). These dipoles can create a mirror dipole in the QDs placed in sub-10 nm range (acceptor). The generation of the dipole in the adjacent QD is a nonradiative process owing to the absence of photon generation by the donor QD and absorption by the acceptor QD. Not all of the transferred dipole energies result in the radiative recombination in the acceptor QDs. Thus, a huge amount of energy is lost during the resonance energy transfer process. To prevent this energy transfer resulting from the close interaction of QDs, the QDs should be separated in their solid films. To realize this, QDs can be dispersed in a special matrix. This will help to reduce the

Another important change during the formation of solid films is the shift of emission wavelength. One of the main underlying reasons for this shift is the change in the medium. The refractive index strongly affects the emission wavelength. Moreover, the nonradiative resonance energy transfer between the nanocrystals also plays a significant role in the shift of the peak. The transfer mechanism is depicted in **Figure 6**. In very close proximity in their solid films, there is a high chance of energy transfer through nonradiative dipole-dipole coupling to occur. As it is well known, nanocrystals are not perfectly synthesized; there is a finite size distribution of the synthesized nanocrystals. Nanocrystals with smaller radius exhibit larger bandgap energy owing to the reverse proportionality of the bandgap energy with the nanocrystal radius in the calculation of quantum confinement. Thus, smaller nanocrystals (energy donor) tend to transfer their energy to larger nanocrystals (energy acceptor) close to them. Since the photoluminescence of the donor nanocrystals has a large spectral overlap with the absorbance of the acceptor nanocrystals as well (see **Figure 7**), the donors are able to transfer their excitons to the acceptors. These transferred excitons relax to the ground states and recombine for possible radiative emission. As a result of this transfer, collective emission intensity of the nanocrystals with smaller radius and higher energy (emitting with shorter wavelength) decreases. Moreover, emission intensity of the nanocrystals with larger radius

quantum yield loss originating from the nonradiative energy transfer [13].

98 Quantum-dot Based Light-emitting Diodes

**Figure 6.** Energy transfer mechanism between smaller (donor) and larger (acceptor) nanocrystals.

As it is clearly discussed in the previous section, semiconductor QDs can effectively change emission color of a device by fully converting the incoming photons. On the other hand, it is possible to achieve a mixed color emission by utilizing the optimized amounts of the red, blue, yellow, and green QDs. In this context, **Figure 8** shows the CIE chromaticity diagram with the emission wavelengths and chromaticity coordinates. As it can be clearly seen from the diagram, white light is in the center, and it can be observed only by mixing several colors.

As it is well known, the main properties defining a white light emission of a high quality are its correlated color temperature (CCT), color rendering index (CRI), and luminous efficacy of optical radiation (LER). CRI measures how efficiently a white light emitting device reflects the real color of an illuminated object. In order to have a high-quality white light source, CRI should be higher than 90. LER is a measure of how well the produced light is perceived by the human eye. The unit of LER is lumens per watt. It is calculated with the following equation. \_

$$LER = 683 \quad \text{Im} \left| \mathbf{W}\_{\text{op}} \frac{\ln(\lambda) \mathbf{s}(\lambda) d\lambda}{\frac{1}{3} \mathbf{s}(\lambda) d\lambda} \right. \tag{1}$$

*s*(*λ*) is the spectral distribution of the radiated optical power and *V*(*λ*) is the eye sensitivity function. Although mathematically the highest LER is 683 lm/Wop, it is almost impossible to achieve this number experimentally. A high-quality white light source should exhibit LER of

**Figure 8.** CIE Chromaticity diagram with emission wavelengths and chromaticity coordinates.

above 300 lm/Wop [14]. Another important photometric figure-of-merit is CCT. **Figure 9** demonstrates CCT chart on the chromaticity diagram to clearly understand the color quality difference between several CCT values. As it is seen from the figure, the amounts of individual colors define its chromaticity coordinates and consequently its CCT.

It indicates the temperature of a Planck black-body radiator whose perceived color most closely resembles that of the light-source. The optical output of a white light-emitting device can be either cool or warm white light. CCT of a warm white light source is below 3500 K. Warm white (right) and cool white light (left) emission are shown in **Figure 10**. Warm and cool white light sources differ in their areas of applications. For example, in the interior house

**Figure 9.** CIE chromaticity diagram with CCT chart.

**Figure 10.** Cool (left) and warm (right) white light sources.

above 300 lm/Wop [14]. Another important photometric figure-of-merit is CCT. **Figure 9** demonstrates CCT chart on the chromaticity diagram to clearly understand the color quality difference between several CCT values. As it is seen from the figure, the amounts of individual

It indicates the temperature of a Planck black-body radiator whose perceived color most closely resembles that of the light-source. The optical output of a white light-emitting device can be either cool or warm white light. CCT of a warm white light source is below 3500 K. Warm white (right) and cool white light (left) emission are shown in **Figure 10**. Warm and cool white light sources differ in their areas of applications. For example, in the interior house

colors define its chromaticity coordinates and consequently its CCT.

**Figure 9.** CIE chromaticity diagram with CCT chart.

**Figure 8.** CIE Chromaticity diagram with emission wavelengths and chromaticity coordinates.

100 Quantum-dot Based Light-emitting Diodes

design, it is more suitable to use warm white light in the bedrooms, living rooms, and hallways, while cool white light is generally used in kitchen, study rooms, and bathrooms.

In general, to achieve a high-quality white LED with the incorporation of semiconductor QDs, the mixture of blue, green, yellow, and red emission is essential. If blue InGaN/GaN LED is used as an electrically injected device with nearly 450 nm emission, QDs with green, yellow, and red QDs are necessary to generate a white light with a high brightness. The schematics of the hybrid white LED utilizing blue InGaN/GaN LED is depicted in **Figure 11**. As it is shown in **Figure 11(a)** and **(b)**, hybrid white LEDs can be constructed by adding layered and blended QDs. In the layered architecture (**Figure 11(a)**), it is necessary for the QDs to be in the deposition order of red, yellow, and green that results in a device with highest efficiency.

Another architecture for generating white light is utilizing dual wavelength InGaN/GaN LEDs. In this design, only two kinds of semiconductor QDs are incorporated. Dual wavelength multiple quantum well InGaN/GaN LEDs are epitaxially grown on c-plane sapphire

**Figure 11.** White LEDs constructed by adding (a) layered and (b) blended QDs on top of the blue InGaN/GaN LEDs.

substrates [15]. Unintentionally doped thick GaN layer (4 μm) is grown following the deposition of a thin low temperature (550°C) nucleation layer (30 nm). Then a 3 μm thick n-doped GaN layer is grown at high temperature. Si with a doping concentration of 5 × 1018 cm−3 was utilized as a p-type dopant. Three blue quantum wells (2.5 nm) were grown with GaN quantum barrier (10 nm) separation layers. An In composition of 15% was used to achieve blue emission from these three quantum wells. Subsequently, three quantum wells with higher In composition were grown to achieve green emission. p-Type doped 30 nm thick AlGaN layer was grown on top of a 10 nm GaN cap layer to serve as an electron-blocking layer. Utilizing the electron-blocking layer helps to prevent the leakage of excess electrons to the quantum wells to result in carrier imbalance. Finally, a 200 nm thick p-doped GaN layer was deposited on electron-blocking layer. Devices were fabricated with patterning, mesa etching, and electrode deposition. The device can emit the mixture of blue and green colors. The intensity of emission can be modified with the operation current of the device. In our architecture whose construction is described above, green quantum wells are closer to p-contacts when compared with blue quantum wells. Thus, at low current levels, green emission dominates the device output. However, once the current level is increased to a certain value, radiative recombination starts to happen more frequently in blue quantum wells as well. This will increase the blue emission intensity of the dual wavelength device. Once the device is fabricated, quantum dots with yellow and red (or amber) emission are placed on top of fabricated devices either in a layer or in a blended architecture. **Figure 12** shows the schematics of the dual wavelength multiple quantum well InGaN/GaN LED emitting blue and green colors covered with yellow and red semiconductor QDs.

**Figure 12.** Dual wavelength multiple quantum well InGaN/GaN LED-emitting blue and green colors covered with yellow and red quantum dots.

#### **4. FRET-enhanced hybrid LEDs**

substrates [15]. Unintentionally doped thick GaN layer (4 μm) is grown following the deposition of a thin low temperature (550°C) nucleation layer (30 nm). Then a 3 μm thick n-doped GaN layer is grown at high temperature. Si with a doping concentration of 5 × 1018 cm−3 was utilized as a p-type dopant. Three blue quantum wells (2.5 nm) were grown with GaN quantum barrier (10 nm) separation layers. An In composition of 15% was used to achieve blue emission from these three quantum wells. Subsequently, three quantum wells with higher In composition were grown to achieve green emission. p-Type doped 30 nm thick AlGaN layer was grown on top of a 10 nm GaN cap layer to serve as an electron-blocking layer. Utilizing the electron-blocking layer helps to prevent the leakage of excess electrons to the quantum wells to result in carrier imbalance. Finally, a 200 nm thick p-doped GaN layer was deposited on electron-blocking layer. Devices were fabricated with patterning, mesa etching, and electrode deposition. The device can emit the mixture of blue and green colors. The intensity of emission can be modified with the operation current of the device. In our architecture whose construction is described above, green quantum wells are closer to p-contacts when compared with blue quantum wells. Thus, at low current levels, green emission dominates the device output. However, once the current level is increased to a certain value, radiative recombination starts to happen more frequently in blue quantum wells as well. This will increase the blue emission intensity of the dual wavelength device. Once the device is fabricated, quantum dots with yellow and red (or amber) emission are placed on top of fabricated devices either in a layer or in a blended architecture. **Figure 12** shows the schematics of the dual wavelength multiple quantum well InGaN/GaN LED emitting blue and green colors covered with yellow

**Figure 12.** Dual wavelength multiple quantum well InGaN/GaN LED-emitting blue and green colors covered with

and red semiconductor QDs.

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yellow and red quantum dots.

Forster resonance energy transfer (FRET) can enhance the optical power and power conversion efficiency of the conventional color converted and white LEDs. In this context, the relative quantum efficiency of color converter of QDs is increased by nonradiatively transferring extra excitons from the defect states of the closely placed donor QDs. The relative quantum efficiency enhancement mechanism of QDs is explained as follows. The optically excited semiconductor QDs contain excitons that recombine either radiatively or nonradiatively. The so-called "nonradiative" excitons are able to transfer their excitonic energy to the neighboring acceptor QDs before they recombine in defects in the host QDs. This increased the quantum efficiency of the acceptor QDs with increased emission yield. The process of transferring these excitons through nonradiative FRET process with dipole-dipole coupling is called exciton recycling [16].

Electronic band structure of FRET-converted LEDs is depicted in **Figure 13**. Excitons and/ or charge carriers are transported to quantum wells following the electrical injection to blue LEDs. The radiative recombination in the InGaN (In composition of 15%) quantum wells leads to blue emission. This emission optically excites the donor semiconductor QDs. The excitons of these QDs are transferred to the acceptor QDs. The excited acceptor color-converter QDs emit with the emission wavelength corresponding to their bandgap energy. To support the existence of FRET process occurring between the donor and acceptor QDs, several types of experiments can be done. One of the most commonly known methods to examine FRET is measure the lifetimes of the acceptor and donor molecules with time-resolved fluorescence spectroscopy. If FRET occurs, donor's lifetime should be shortened owing to the exciton migration from these host molecules. On the other hand, the acceptor molecules should exhibit longer lifetime in the presence of their donor counterparts thanks to the exciton feeding. Another method to check whether exciton migration in donor-acceptor pairs is present or not is to acquire the photoluminescence excitation spectral behavior of the acceptor QDs in the presence and in the absence of the donor QDs. Although this method can also provide a strong argument on the presence/absence of FRET, the former time-resolved spectroscopy method is more effective in evaluating the efficiency of the FRET process.

**Figure 13.** Electronic band structure of FRET-converted LEDs.

The FRET-based architecture above only demonstrates the enhancement process in the colorconverted LED. However, it is possible to enhance the color quality of white LEDs with the utilization of FRET as well by individually increasing the quantum efficiency of less efficient QD components in the hybrid white emitting devices. Using this way, the intensity of the individual (green, yellow, or red) can be modified. This modification leads to the changes in the chromaticity coordinates of the white light and CCT.

#### **5. Plasmon-enhanced hybrid LEDs**

As it was stated above, FRET is a powerful concept to enhance the efficiency of the color-converter QDs incorporated in hybrid LEDs. Another method to increase the relative quantum yield of these semiconductor QDs is to make use of plasmon-exciton coupling mechanism [17]. Plasmon coupling can be realized by either forming localized surface plasmons or surface plasmon polaritons in the close vicinity of the emitter. Localized surface plasmons result in more pronounced absorption peaks. Moreover, their use within the device structures is more convenient owing to its simple configuration when compared with surface plasmon polaritons. The plasmonic absorption peaks of localized surface plasmons can be easily modified by changing the size of these particles. **Figure 14** shows the absorption spectra of Ag nanoparticles with different deposition thicknesses and same annealing condition. 10, 15, and 20 nm thick electron beam deposited and annealed Ag (films become nanoparticles following the deposition of such thin layers and high temperature annealing) exhibit 450, 504, and 666 nm absorption peaks, respectively.

**Figure 14.** Absorption spectra of electron beam-deposited Ag layers with deposition thickness of 10, 15 and 20 nm.

To achieve a successful enhancement in the emission yield, absorption spectrum of plasmonic metal structure should have a decent overlap with the luminescence spectrum of the emitter (semiconductor QD in this particular case). In this context, it is important to choose the correct metal material to achieve a good spectral overlap. Ag is a more convenient material for the emission in near UV and blue. On the other hand, Au can be utilized to get a plasmonic enhancement in the emitters with emission wavelength of more than 500 nm. Moreover, the position of plasmonic structure is also an important feature which needs extra care. The QD and the plasmonic metal should be in close proximity to realize an efficient coupling between them. On the other hand, if these two structures are placed very closely to each other, the emission of QDs will be strongly quenched thanks to nonradiative energy transfer from QDs to the adjacent metal structure. Thus, it is essential to optimize the relative locations of the QDs and the plasmonic metal structure to prevent the nonradiative energy transfer-induced emission loss and to achieve strong exciton-plasmon coupling simultaneously.

The FRET-based architecture above only demonstrates the enhancement process in the colorconverted LED. However, it is possible to enhance the color quality of white LEDs with the utilization of FRET as well by individually increasing the quantum efficiency of less efficient QD components in the hybrid white emitting devices. Using this way, the intensity of the individual (green, yellow, or red) can be modified. This modification leads to the changes in

As it was stated above, FRET is a powerful concept to enhance the efficiency of the color-converter QDs incorporated in hybrid LEDs. Another method to increase the relative quantum yield of these semiconductor QDs is to make use of plasmon-exciton coupling mechanism [17]. Plasmon coupling can be realized by either forming localized surface plasmons or surface plasmon polaritons in the close vicinity of the emitter. Localized surface plasmons result in more pronounced absorption peaks. Moreover, their use within the device structures is more convenient owing to its simple configuration when compared with surface plasmon polaritons. The plasmonic absorption peaks of localized surface plasmons can be easily modified by changing the size of these particles. **Figure 14** shows the absorption spectra of Ag nanoparticles with different deposition thicknesses and same annealing condition. 10, 15, and 20 nm thick electron beam deposited and annealed Ag (films become nanoparticles following the deposition of such thin layers and high temperature annealing) exhibit 450, 504, and 666

**Figure 14.** Absorption spectra of electron beam-deposited Ag layers with deposition thickness of 10, 15 and 20 nm.

the chromaticity coordinates of the white light and CCT.

**5. Plasmon-enhanced hybrid LEDs**

104 Quantum-dot Based Light-emitting Diodes

nm absorption peaks, respectively.

A thin metallic layer can be chemically grown on top of QDs to achieve plasmon-induced enhancement (**Figure 15**-left). However, placing a metal layer directly on the surface of QD would result in nonradiative resonance energy transfer-induced quenching of QD emission. Thus, it is important to insert a spacer shell layer in between the semiconductor QD and metallic shell. Moreover, the thickness of these shells (spacer and metal) cannot be too large; thick shells would block a significant amount of light coming out of QDs. Another useful mechanism to achieve strong coupling between the plasmons generated in metals and excitons in QDs is to make use of blended structure (**Figure 15**-right). In this configuration, chemically synthesized small metallic nanoparticles are mixed with QDs in solution. Later, they will make a solid blended film on a flat surface. However, direct contact of core QDs with metallic nanoparticle would again give rise to a strong quenching of emission owing to nonradiative energy transfer. To prevent nonradiative quenching, QDs can be synthesized in a core-shell configuration such as CdSe/ZnS with optimized shell thickness. In both of the configurations explained above, surface plasmons provide additional radiative channels for the excitons of QDs. This leads to the enhanced emission yield of QDs. The two powerful methods to examine the existence of plasmon-exciton coupling are photoluminescence measurement of QD films and time-resolved photoluminescence decay experiments. The former method shows the photoluminescence peak enhancement of QDs owing to the existence of plasmonic nanostructures in close vicinity. In most cases, there is a peak shift in the plasmon-incorporated films owing to the difference in the absorbance peak of metal and photoluminescence of the emitter; the spectral region of

**Figure 15.** QD-plasmon coupling mechanisms with core-shell (left) and blended (right) configurations.

QDs corresponding to the absorbance peak location of metallic nanostructures gain maximum photoluminescence enhancement. This leads to the shift of photoluminescence peak toward the absorbance peak. The second useful method to examine the existence of plasmon-exciton coupling is to draw the photoluminescence decay curves of QD films in the presence and in the absence of the plasmonic nanostructures. Due to the presence of additional radiative channels in the QD-metal structure, the photoluminesce of this structure should decay faster; the reduction in the lifetime of QD film in the presence of plasmonic metal nanostructures is attributed to the strong plasmon-exciton coupling induced by the increased radiative recombination rate.

The optimized blended and core-shell configurations (**Figure 15**) can be incorporated as efficient color-converter materials on top of blue InGaN/GaN LEDs. These novel architectures would exhibit enhanced power conversion efficiency and optical power when compared with conventional color-converted hybrid LEDs utilizing pure QD film owing to the plasmoninduced quantum efficiency enhancement of QDs.

#### **6. FRET-converted LEDs**

Color conversion process in hybrid LED designs utilizing InGaN/GaN LED structures and QDs can be photonic or excitonic. In photonic color conversion, photons are generated in the quantum wells of InGaN/GaN LEDs following an efficient electrical injection, and they excite the color converter semiconductor QDs placed on top of the structure. In this design, there is a significant separation between QDs and the quantum wells of LEDs. On the other hand, excitonic color conversion process does not involve the generation of photons to excite the semiconductor QDs. In this configuration, excitonic energy of the InGaN quantum wells is directly transferred to the QDs through FRET (nonradiative dipole-dipole coupling). It is possible to achieve white light emission (or any other mixed color emission) by carefully controlling the emission intensity of InGaN quantum wells and the QD film.

The interaction of QDs and the quantum wells of InGaN/GaN LEDs can be realized through constructing several hybrid systems [18, 19]. One of the methods to achieve excitonic color conversion is to place QDs directly on top of the quantum wells (**Figure 16**-right). However, there should be a thin GaN cap layer with optimized thickness to control the amount of transferred nonradiative energy. Very small separation between the donor (InGaN quantum well) and the acceptor (QD) would result in higher emission intensity of QDs and lower intensity of InGaN wells. Thus, by modifying the thickness of cap layer, it is possible to optimize the quality of white light; CCT can be effective shifted. Moreover, QDs can be placed in between the nanopillars of InGaN/GaN LED structure to realize the interaction of QDs and sidewalls of InGaN quantum wells (**Figure 16**-left). Nanopillars can be fabricated either by etching the epitaxially grown bulk LED structure or by selectively growing LED structures in the holes of SiO2 layer on top of a sapphire substrate. Furthermore, LEDs with microholes can be fabricated and QDs can be inserted into these holes to observe the possible coupling between QDs and quantum wells. Energy transfer between the abovementioned donor and acceptor components are examined with photoluminescence, optical power measurements, and time-resolved photoluminescence spectroscopy studies.

**Figure 16.** Schematics of nanopillar-QD (left) and quantum well-QD (right) systems.

#### **Author details**

QDs corresponding to the absorbance peak location of metallic nanostructures gain maximum photoluminescence enhancement. This leads to the shift of photoluminescence peak toward the absorbance peak. The second useful method to examine the existence of plasmon-exciton coupling is to draw the photoluminescence decay curves of QD films in the presence and in the absence of the plasmonic nanostructures. Due to the presence of additional radiative channels in the QD-metal structure, the photoluminesce of this structure should decay faster; the reduction in the lifetime of QD film in the presence of plasmonic metal nanostructures is attributed to the strong plasmon-exciton coupling induced by the increased radiative recombination rate. The optimized blended and core-shell configurations (**Figure 15**) can be incorporated as efficient color-converter materials on top of blue InGaN/GaN LEDs. These novel architectures would exhibit enhanced power conversion efficiency and optical power when compared with conventional color-converted hybrid LEDs utilizing pure QD film owing to the plasmon-

Color conversion process in hybrid LED designs utilizing InGaN/GaN LED structures and QDs can be photonic or excitonic. In photonic color conversion, photons are generated in the quantum wells of InGaN/GaN LEDs following an efficient electrical injection, and they excite the color converter semiconductor QDs placed on top of the structure. In this design, there is a significant separation between QDs and the quantum wells of LEDs. On the other hand, excitonic color conversion process does not involve the generation of photons to excite the semiconductor QDs. In this configuration, excitonic energy of the InGaN quantum wells is directly transferred to the QDs through FRET (nonradiative dipole-dipole coupling). It is possible to achieve white light emission (or any other mixed color emission) by carefully controlling the emission intensity of InGaN quantum wells and the QD film. The interaction of QDs and the quantum wells of InGaN/GaN LEDs can be realized through constructing several hybrid systems [18, 19]. One of the methods to achieve excitonic color conversion is to place QDs directly on top of the quantum wells (**Figure 16**-right). However, there should be a thin GaN cap layer with optimized thickness to control the amount of transferred nonradiative energy. Very small separation between the donor (InGaN quantum well) and the acceptor (QD) would result in higher emission intensity of QDs and lower intensity of InGaN wells. Thus, by modifying the thickness of cap layer, it is possible to optimize the quality of white light; CCT can be effective shifted. Moreover, QDs can be placed in between the nanopillars of InGaN/GaN LED structure to realize the interaction of QDs and sidewalls of InGaN quantum wells (**Figure 16**-left). Nanopillars can be fabricated either by etching the epitaxially grown bulk LED structure or by selectively growing LED structures in the holes of SiO2 layer on top of a sapphire substrate. Furthermore, LEDs with microholes can be fabricated and QDs can be inserted into these holes to observe the possible coupling between QDs and quantum wells. Energy transfer between the abovementioned donor and acceptor components are examined with photoluminescence, optical power measurements,

induced quantum efficiency enhancement of QDs.

and time-resolved photoluminescence spectroscopy studies.

**6. FRET-converted LEDs**

106 Quantum-dot Based Light-emitting Diodes

Namig Hasanov

Address all correspondence to: namig@ntu.edu.sg

Division of Microelectronics, Electrical and Electronic Engineering, Nanyang Technological University, Singapore

#### **References**


[17] Kim N, Hong S, Kang J, Myoung N, Yim S, Jung S, Lee K, Tu C, Park S. Localized surface plasmon-enhanced green quantum dot light-emitting diodes using gold nanoparticles. RSC Advances. 2015;**5**:19624-19629. DOI: 10.1039/C4RA15585H

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[8] Hsueh H, Ou S, Cheng C, Wuu D, Hong R. Performance of InGaN light-emitting diodes fabricated on patterned sapphire substrates with modified top-tip cone shapes.

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[10] Deng Z, Jiang Y, Ma Z, Wang W, Jia H, Zhou J, Chen H. A novel wavelength-adjusting method in InGaN-based light-emitting diodes. Scientific Reports. 2013;**3**:3389. DOI:10.1038/

[11] Huang C, Su Y, Chen Y, Wan C. Hybridization of CdSe/ZnS quantum dots on InGaN/ GaN multiple quantum well light-emitting diodes for pink light emission. 2008. IEEE Photonics Global@Singapore, Singapore. 2008:1-3. DOI: 10.1109/IPGC.2008.4781324 [12] Sheu J, Chang S, Kuo C, Su Y, Wu L, Lin Y, Lai W, Tsai J, Chi G, Wu R. White-light emission from near UV InGaN-GaN LED chip precoated with blue/green/red phosphors. IEEE Photonics Technology Letters. 2003;**15**(1):18-20. DOI: 10.1109/LPT.2002.805852 [13] Xu L, Liu N, Xu J, Yang F, Ma Z, Chen K. Evolution of luminescence properties of CdTe quantum dots in liquid/solid environment. Journal of Nanoscience and Nanotechnology.

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lpor.200710019


#### **Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots** Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots

DOI: 10.5772/intechopen.70300

Fanyao Qu, Alexandre Cavalheiro Dias, Antonio Luciano de Almeida Fonseca, Marco Cezar Barbosa Fernandes and Xiangmu Kong Fanyao Qu, Alexandre Cavalheiro Dias, Antonio Luciano de Almeida Fonseca, Marco Cezar Barbosa Fernandes and

Additional information is available at the end of the chapter Xiangmu Kong

http://dx.doi.org/10.5772/intechopen.70300 Additional information is available at the end of the chapter

#### Abstract

Photonic quantum computer, quantum communication, quantum metrology, and optical quantum information processing require a development of efficient solid-state single photon sources. However, it still remains a challenge. We report theoretical framework and experimental development on a novel kind of valley-polarized single-photon emitter (SPE) based on two-dimensional transition metal dichalcogenides (TMDCs) quantum dots. In order to reveal the principle of the SPE, we make a brief review on the electronic structure of the TMDCs and excitonic behavior in photoluminescence (PL) and in magneto-PL of these materials. We also discuss coupled spin and valley physics, valleypolarized optical absorption, and magneto-optical absorption in TMDC quantum dots. We demonstrate that the valley-polarization is robust against dot size and magnetic field, but optical transition energies show sizable size-effect. Three versatile models, including density functional theory, tight-binding and effective k p method, have been adopted in our calculations and the corresponding results have been presented.

Keywords: single-photon source, quantum dots, transition metal dichalcogenides

#### 1. Introduction

Traditional semiconductors have been used for decades for making all sorts of devices like diodes, transistors, light emitting diodes, and lasers [1]. Due to the advances of technology in fabrication, it is possible not only to make ever pure semiconductor crystals, but also to study heterostructures, in which carriers (electrons or holes) are confined in thin sheets, narrow lines, or even a point [1, 2]. Quantum dots (QDs) are zero-dimensional objects where all the three

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

spatial dimensions are quantized with sizes smaller than some specific characteristic lengths, e.g., the exciton Bohr radius [1, 2]. Because of confinement, electrons in the QDs occupy discrete energy levels, in a similar way as they do in atoms [2, 3]. For these reasons, QDs are also referred to as artificial atoms [1, 2]. In spite of some similarities between the QD and the real atom, the former demonstrates several special characteristics. For instance, its size can vary from a few to hundreds of nanometers, and it can trap from a very small number of electrons (Ne < 10) to 50 100 electrons or more [1]. In addition, the shape of the QD that can be tuned at will determine its spatial symmetry. In turn, the change in spatial symmetry modifies physical properties of the system. As known, the three-dimensional spherically symmetric QDs possess degenerate electron shells, 1s, 2s, 2p, 3s, 3p,… [3]. When the number of electrons is equal to 2, 10, 18, 36,…, the electron shells are completely filled [1], yielding a particularly stable configuration. In contrast, a two-dimensional cylindrically symmetric parabolic potential leads to formation of a two-dimensional shell structure with the magic numbers 2, 6, 12, 20,…[2, 4, 5]. Hence, the lower degree of symmetry in two-dimensional QDs leads to a smaller magic number sequence. Since the shape and size of the QDs can be precisely manufactured, the energy structure of the carriers in the QDs as well as their optical, transport, magnetic, and thermal properties can be engineered in a large scale [1–9].

Various techniques have been developed to produce the QDs such as etching, regrowth from quantum well structures, beam epitaxy, lithography, holograph patterning, chemical synthesis, etc [1, 2]. Consequently, many kinds of QDs emerge. According to the electrical property of their parent material, they can be classified into metal, semiconductor, or super-conducting dots. From geometry point of view, the QDs form two groups: two-dimensional [2, 4, 5, 8] or three-dimensional (3D) [1] dots. The former can be further divided into conventional 2D semiconductor QDs, such as self-assembled- and gated-QDs based on traditional semiconductor quantum wells [4–8, 10], and the novel QDs made from two-dimensional-layered materials (2DLMs) [11–15].

Atomically thin 2DLMs have revolutionized nanoscale materials science [16]. The interatomic interaction within layers is covalent in nature, while the layers are held together by weak van der Waals (vdW) forces. The family of 2D materials, which started with graphene [16], has expanded rapidly over the past few years and now includes insulators, semiconductors, semimetals, metals, and superconductors [17–19]. The most well studied 2D systems beyond graphene, are the silicene, germanene, stanine, and borophene, organic-inorganic hybrid perovskites, insulator hexagonal boron-nitride [17, 18], the anisotropic semiconductor phosphorene, transition metal-carbides, -nitrides, -oxides, and -halides, as well as the transition metal dichalcogenides (TMDCs) [20–28]. Compared with traditional semiconducting materials, the 2DLMs take advantage of inherent flexibility and an atomically-thin geometry. Moreover, because of their free dangling bonds at interfaces [25, 29, 30], two-dimensional-layered materials can easily be integrated with various substrates [17]. They can also be fabricated in complex-sandwiched structures or even suspended to avoid the influence of the substrate [31]. The monolayer TMDCs with infinite geometry exhibit strong carrier confinement in one dimension but preserve the bulk-like dispersion in the 2D plane. In contrast, electrons in a TMDC QD are restricted in three dimensions, which present size tunable electronic and optical properties in addition to the remarkable characteristics related to spin-valley degree of freedom inherited from its 2D bulk materials. Very recently, graphene QDs (GQDs) have attracted intensive research interest due to their high transparency and high surface area. Many remarkable applications ranging from energy conversion to display to biomedicine are prospected [11]. Nevertheless, from quantum nano-devices point of view, the TMDCs have advantages over graphene. For instance, the semiconducting TMDCs have a band gap large enough to form a QD using the electric field, as shown in Figure 1, unlike etched GQDs made on semi-metallic graphene.

spatial dimensions are quantized with sizes smaller than some specific characteristic lengths, e.g., the exciton Bohr radius [1, 2]. Because of confinement, electrons in the QDs occupy discrete energy levels, in a similar way as they do in atoms [2, 3]. For these reasons, QDs are also referred to as artificial atoms [1, 2]. In spite of some similarities between the QD and the real atom, the former demonstrates several special characteristics. For instance, its size can vary from a few to hundreds of nanometers, and it can trap from a very small number of electrons (Ne < 10) to 50 100 electrons or more [1]. In addition, the shape of the QD that can be tuned at will determine its spatial symmetry. In turn, the change in spatial symmetry modifies physical properties of the system. As known, the three-dimensional spherically symmetric QDs possess degenerate electron shells, 1s, 2s, 2p, 3s, 3p,… [3]. When the number of electrons is equal to 2, 10, 18, 36,…, the electron shells are completely filled [1], yielding a particularly stable configuration. In contrast, a two-dimensional cylindrically symmetric parabolic potential leads to formation of a two-dimensional shell structure with the magic numbers 2, 6, 12, 20,…[2, 4, 5]. Hence, the lower degree of symmetry in two-dimensional QDs leads to a smaller magic number sequence. Since the shape and size of the QDs can be precisely manufactured, the energy structure of the carriers in the QDs as well as their optical, transport,

Various techniques have been developed to produce the QDs such as etching, regrowth from quantum well structures, beam epitaxy, lithography, holograph patterning, chemical synthesis, etc [1, 2]. Consequently, many kinds of QDs emerge. According to the electrical property of their parent material, they can be classified into metal, semiconductor, or super-conducting dots. From geometry point of view, the QDs form two groups: two-dimensional [2, 4, 5, 8] or three-dimensional (3D) [1] dots. The former can be further divided into conventional 2D semiconductor QDs, such as self-assembled- and gated-QDs based on traditional semiconductor quantum wells [4–8, 10], and the novel QDs made from two-dimensional-layered materials

Atomically thin 2DLMs have revolutionized nanoscale materials science [16]. The interatomic interaction within layers is covalent in nature, while the layers are held together by weak van der Waals (vdW) forces. The family of 2D materials, which started with graphene [16], has expanded rapidly over the past few years and now includes insulators, semiconductors, semimetals, metals, and superconductors [17–19]. The most well studied 2D systems beyond graphene, are the silicene, germanene, stanine, and borophene, organic-inorganic hybrid perovskites, insulator hexagonal boron-nitride [17, 18], the anisotropic semiconductor phosphorene, transition metal-carbides, -nitrides, -oxides, and -halides, as well as the transition metal dichalcogenides (TMDCs) [20–28]. Compared with traditional semiconducting materials, the 2DLMs take advantage of inherent flexibility and an atomically-thin geometry. Moreover, because of their free dangling bonds at interfaces [25, 29, 30], two-dimensional-layered materials can easily be integrated with various substrates [17]. They can also be fabricated in complex-sandwiched structures or even suspended to avoid the influence of the substrate [31]. The monolayer TMDCs with infinite geometry exhibit strong carrier confinement in one dimension but preserve the bulk-like dispersion in the 2D plane. In contrast, electrons in a TMDC QD are restricted in three dimensions, which present size tunable electronic and optical properties in addition to the remarkable

magnetic, and thermal properties can be engineered in a large scale [1–9].

(2DLMs) [11–15].

112 Quantum-dot Based Light-emitting Diodes

The applications of quantum dots are still mostly restricted to research laboratories, but they are remarkable due to the fact that QDs provide access to the quantum mechanical degrees of freedom of few carriers. Single electron transistors [1–6], the manipulation of one [4–7] or two [1–3] electron spins, manipulation of a single spin in a single magnetic ion-doped QD [4–7] are only some examples. Optically active quantum dots can also be used in both quantum communication and quantum computation [4–7, 12–15]. The emerging field of quantum information technology, as unconditionally quantum cryptography, quantum-photonic communication and computation, needs the development of individual photon sources [12–15, 32, 33]. Recently, individual photon emitters based on defects in TMDC monolayers with different sample types (WSe2 and MoSe2) have been reported, but only operate at cryogenic temperatures [12, 13, 32–35]. In addition, it should be kept in mind that the presence of defects is not always beneficial for the PL signal. For instance, defect-mediated nonradiative recombination might result in an internal quantum yield droop in the defective TMDCs [26–28]. In this context, single quantum emitter based on QD is desirable [14, 15].

In this chapter, we show the optical and magneto-optical properties of the TMDC QD's. We choose MoS2, which has been widely studied in the literature as our example. Three versatile models including density functional theory, tight-binding, and effective k p approach have been adopted in our calculations and the corresponding results have been presented. We show that the valley-polarization is robust against dot size and magnetic field, but the optical transition energies show sizable size effect. Based on the computed optical absorption spectra, a novel kind of valley-polarized single-photon source based on TMDC quantum dot is proposed [15].

Figure 1. (a) Scanning electron microscope image of the WS2 quantum dot studied. The WS2 flake is highlighted by the white dotted line, and the four top gates are labeled as MG, LB, PG, RB. The scale bar represents 5 μ m. (b) Threedimensional schematic view of the device [20]. (Copyright 2015 by the Royal Society of Chemistry. Reprinted with permission).

#### 2. Physical properties of transition metal dichalcogenides

#### 2.1. Electronic band structure of transition metal dichalcogenides

Layered TMDCs have the generic formula MX2, where M stands for a metal and X represents a chalcogen. The monolayer crystal structure of the MoS2, which is one of the most studied TMDCs in the literature is shown in Figure 2. Notice that the monolayer MoS2 has a trigonal prism crystal structure. An inversion asymmetry results in a large direct gap semiconductor with the gap lying at the two inequivalent K-points of the hexagonal Brillouin zone.

The major orbital contribution at the edge of the conduction band (CB) is from d3z2�r<sup>2</sup> orbital of the metal, plus minor contributions from px, and p<sup>y</sup> orbitals of chalcogens. On the other hand, at the edge of the valence band (VB) at the K-point, the most important orbital contribution is due to a combination of dxy and dx2�y<sup>2</sup> of the metal, which hybridize to p<sup>x</sup> and p<sup>y</sup> orbitals of the chalcogen atoms [24]. In addition, there is a strong spin-orbit interaction (SOI), especially in the valence band. The spatial inversion asymmetry along with strong SOI leads to a spin-valley coupling, which results in the spin of electron being locked to the valley [20, 21, 36], as demonstrated in Figure 3(a). Furthermore, the band structure in the K-valley presents time reversal symmetry with that in K<sup>0</sup> -valley. And, it changes dramatically as the number of the layers of the TMDC increases. When the thickness increases, the band gap in MoS2 and other group VI TMDCs decreases, and more importantly, the material becomes an indirect gap semiconductor [37], as shown in Figure 3(b).

In order to get insight into the physical origins of the band gap variations with the number of layers, Figure 4 shows evolutions of the band gaps (a) and band edges (b) of MoS2 as a function of the number of layers. Notice that with increasing layer thickness, the indirect band gap (Γ�K, Γ�Λ) becomes smaller, while the direct excitonic transition ðK�KÞ only slightly changes, as illustrated in Figure 4(a). Note also that the monolayer nð Þ ¼ 1 MoS2 is a direct band gap semiconductor, but it becomes an indirect band gap semiconductor when the number of layers is larger than one. This phase transition is also clearly demonstrated in Figure 4(b). In addition, as the number of layers increases, both the VB and CB edges at K-valley exhibit only slight variation while the degeneracy at Γ is lifted and a splitting of the bands occurs, which

Figure 2. (a) Schematic diagram of crystal structure of MoS2. (b) Coordination environment of Mo (blue sphere) in the structure (the left panel); the middle and the right panels correspond to side- and top- views of the monolayer MoS2 lattice. Sulfur is shown as golden spheres.

Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots http://dx.doi.org/10.5772/intechopen.70300 115

Figure 3. (a) Band structure of monolayer MoS2. The solid curves were obtained using the QUANTUM ESPRESSO package with fully relativistic pseudopotentials under the Perdew-Burke-Ernzerhof generalized-gradient approximation, and a 16 � 16 � 1 k grid. The dashed curves were calculated from the tight-binding model, with cyan (red) representing states that are even (odd) under mirror operation with respect to the Mo plane. v1;<sup>2</sup> and c1;<sup>2</sup> label the bands close to the valence and conduction band edges near the K- and K<sup>0</sup> -points. The inset shows the hexagonal Brillouin zone (pink) associated with the triangular Bravais lattice of MoS2 and an alternate rhombohedral primitive zone (black), and labels the principle high-symmetry points in reciprocal space [36] (Copyright 2015 by American Physical Society, Reprinted with permission). (b) Calculated band structures of (b1) bulk MoS2, (b2) quadrilayer MoS2, (b3) bilayer MoS2, and (b4) monolayer MoS2. The solid arrows indicate the lowest energy transitions. Bulk MoS2 is characterized by an indirect bandgap. The direct excitonic transition occurs at K point with a higher transition energy than that of indirect one [30]. (Copyright 2010 by the American Chemical Society. Reprinted with permission).

pushes the VB maximum to higher energy. The variation of the band gap is largely driven by the variation of the VB at Γ point. Going from a monolayer to a bilayer significantly raises the VB at Γ, resulting in a transition from the direct K�K gap to an indirect Γ�K gap. This dramatic change of electronic structure in monolayer MoS2 results in the jump in monolayer photoluminescence efficiency.

#### 2.1.1. Massive Dirac fermions

2. Physical properties of transition metal dichalcogenides

Layered TMDCs have the generic formula MX2, where M stands for a metal and X represents a chalcogen. The monolayer crystal structure of the MoS2, which is one of the most studied TMDCs in the literature is shown in Figure 2. Notice that the monolayer MoS2 has a trigonal prism crystal structure. An inversion asymmetry results in a large direct gap semiconductor

The major orbital contribution at the edge of the conduction band (CB) is from d3z2�r<sup>2</sup> orbital of the metal, plus minor contributions from px, and p<sup>y</sup> orbitals of chalcogens. On the other hand, at the edge of the valence band (VB) at the K-point, the most important orbital contribution is due to a combination of dxy and dx2�y<sup>2</sup> of the metal, which hybridize to p<sup>x</sup> and p<sup>y</sup> orbitals of the chalcogen atoms [24]. In addition, there is a strong spin-orbit interaction (SOI), especially in the valence band. The spatial inversion asymmetry along with strong SOI leads to a spin-valley coupling, which results in the spin of electron being locked to the valley [20, 21, 36], as demonstrated in Figure 3(a). Furthermore, the band structure in the K-valley presents time

layers of the TMDC increases. When the thickness increases, the band gap in MoS2 and other group VI TMDCs decreases, and more importantly, the material becomes an indirect gap

In order to get insight into the physical origins of the band gap variations with the number of layers, Figure 4 shows evolutions of the band gaps (a) and band edges (b) of MoS2 as a function of the number of layers. Notice that with increasing layer thickness, the indirect band gap (Γ�K, Γ�Λ) becomes smaller, while the direct excitonic transition ðK�KÞ only slightly changes, as illustrated in Figure 4(a). Note also that the monolayer nð Þ ¼ 1 MoS2 is a direct band gap semiconductor, but it becomes an indirect band gap semiconductor when the number of layers is larger than one. This phase transition is also clearly demonstrated in Figure 4(b). In addition, as the number of layers increases, both the VB and CB edges at K-valley exhibit only slight variation while the degeneracy at Γ is lifted and a splitting of the bands occurs, which

Figure 2. (a) Schematic diagram of crystal structure of MoS2. (b) Coordination environment of Mo (blue sphere) in the structure (the left panel); the middle and the right panels correspond to side- and top- views of the monolayer MoS2


with the gap lying at the two inequivalent K-points of the hexagonal Brillouin zone.

2.1. Electronic band structure of transition metal dichalcogenides

reversal symmetry with that in K<sup>0</sup>

114 Quantum-dot Based Light-emitting Diodes

lattice. Sulfur is shown as golden spheres.

semiconductor [37], as shown in Figure 3(b).

To gain insight of physics around the K- and K<sup>0</sup> -points, one can reduce multi-band tightbinding model to a two band k.p model, using Löwdin partitioning method [38]. For the monolayer TMDCs, one gets the Hamiltonian in the first order of k approximation,

Figure 4. (a) Evolution of the band gaps as a function of the number of layers (n). The black circles ðK � KÞ, red squares ðΓ�KÞ, and green diamonds ðΓ�ΛÞ indicate the magnitude of the different band gaps. Hollow symbols indicate the bulk band gaps. (b) Position of the band edge with respect to the vacuum level for the VB at the K-point (orange crosses), VB at Γ(red squares), CB at the K-point (black circles), and CB at Λ (green diamonds) [29]. (Copyright 2014 by the American Physical Society. Reprinted with permission).

$$H(\mathbf{k}, \tau, \mathbf{s}) = \begin{pmatrix} \Delta/2 & at(\tau k\_x - ik\_y) \\ at(\tau k\_x + ik\_y) & -\Delta/2 + \tau s \lambda \\ \end{pmatrix} \tag{1}$$

where Δ ¼ 1:6 eV is the band gap, t ¼ 1:1 eV is the effective hopping parameter, λ ¼ 0:075 eV is the SOI parameter, a ¼ 3:19 Å is the lattice parameter [39], τ ¼ �1 is the valley index. The eigenvalues and eigenvectors can be derived straightforwardly as follows:

$$E\_{\pm}(k\_{\text{x}}\ \ k\_{y}) = \frac{\tau \lambda s}{2} \pm \sqrt{\frac{\left(\Delta - \lambda \tau s\right)^{2}}{4} + t^{2}a^{2}(k\_{x}^{2} + k\_{y}^{2})}\tag{2}$$

and

$$\begin{aligned} \vert c,\ \overrightarrow{k}\ \tau,\ s\_z\rangle &= \vert s\_z\rangle \otimes \begin{pmatrix} \cos\left(\frac{\mathfrak{S}\_n}{2}\right) \\\\ \tau \sin\left(\frac{\mathfrak{S}\_n}{2}\right) e^{i n \phi\_{\frac{\mathfrak{S}\_n}{2}}} \end{pmatrix} \\\vert v,\ \overrightarrow{k}\ \tau,\ s\_z\rangle &= \vert s\_z\rangle \otimes \begin{pmatrix} -\tau \sin\left(\frac{\mathfrak{S}\_n}{2}\right) e^{-i n \phi\_{\frac{\mathfrak{S}\_n}{2}}} \\\\ \cos\left(\frac{\mathfrak{S}\_n}{2}\right) \end{pmatrix} \\\end{aligned} \tag{3}$$

$$\cos\mathfrak{S}\_n = \frac{\Delta + (-1)^n \lambda\_{so}}{2\sqrt{\left(\Delta + (-1)^n \lambda\_{so}\right)^2 + 4t^2 a^2 k^2}} \tag{4}$$

Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots http://dx.doi.org/10.5772/intechopen.70300 117

$$
tan(\phi\_{\vec{k'}}) = \frac{k\_y}{k\_x} \tag{5}
$$

The energy dispersion around the K- and K<sup>0</sup> - points, described by Eq. 2, is shown in Figure 5. In order to see the reliability of the k � p approach, Figure 6 plots the energy spectrum of

Figure 5. Energy dispersion in (a) K-valley and (b) K<sup>0</sup> -valley obtained by the k � p model.

Hðk, τ, sÞ ¼

Physical Society. Reprinted with permission).

116 Quantum-dot Based Light-emitting Diodes

<sup>E</sup>�ðkx, kyÞ ¼ τλ<sup>s</sup>

jc, k!

jv, k!

and

0 @

eigenvalues and eigenvectors can be derived straightforwardly as follows:

2 �

τ, sz〉 ¼ jsz〉 ⊗

τ, sz〉 ¼ jsz〉 ⊗

2

cosϑ<sup>n</sup> <sup>¼</sup> <sup>Δ</sup> þ ð�1<sup>Þ</sup>

Δ=2 atðτkx � ikyÞ atðτkx þ ikyÞ �Δ=2 þ τsλ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>2</sup>a<sup>2</sup>ð<sup>k</sup> 2 <sup>x</sup> <sup>þ</sup> <sup>k</sup><sup>2</sup> yÞ

1

CCCA

1

CCCA

2 <sup>4</sup> <sup>þ</sup> <sup>t</sup>

where Δ ¼ 1:6 eV is the band gap, t ¼ 1:1 eV is the effective hopping parameter, λ ¼ 0:075 eV is the SOI parameter, a ¼ 3:19 Å is the lattice parameter [39], τ ¼ �1 is the valley index. The

Figure 4. (a) Evolution of the band gaps as a function of the number of layers (n). The black circles ðK � KÞ, red squares ðΓ�KÞ, and green diamonds ðΓ�ΛÞ indicate the magnitude of the different band gaps. Hollow symbols indicate the bulk band gaps. (b) Position of the band edge with respect to the vacuum level for the VB at the K-point (orange crosses), VB at Γ(red squares), CB at the K-point (black circles), and CB at Λ (green diamonds) [29]. (Copyright 2014 by the American

s

0

BBB@

0

BBB@

ðΔ þ ð�1Þ

ðΔ � λτsÞ

cos ϑn 2 � �

<sup>τ</sup>sin <sup>ϑ</sup><sup>n</sup> 2 � � e <sup>i</sup>τφ <sup>k</sup> !

�τsin <sup>ϑ</sup><sup>n</sup> 2 � � e �iτφ <sup>k</sup> !

> cos ϑn 2 � �

> > n λso

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n λsoÞ <sup>2</sup> <sup>þ</sup> <sup>4</sup><sup>t</sup> <sup>2</sup>a<sup>2</sup>k 2 <sup>q</sup> (4)

1

A (1)

(2)

(3)

Figure 6. (a) Quasiparticle band structure of monolayer MoS2 calculated by the density functional theory (DFT). (b) A blowup of the rectangular red area in (a). The blue (solid), red (dashed), green (dotted), and purple (dot-dashed) curves correspond to the results obtained by the DFT, and k � p theory of the first order, second order, and third order, respectively. Notice that around the K-point, all methods give almost identical results.

monolayer MoS2 calculated by the first principle and k � p model. It can be found that in the vicinity of the K–(K<sup>0</sup> )–point, they have very good agreement.

#### 2.1.2. Landau levels of monolayer MoS<sup>2</sup>

For a perpendicular magnetic field applied to the MoS2 sheet, we use Peierls substitution Ki ! Π<sup>i</sup> ¼ Ki þ ð Þ e=ℏ Ai, where e is the elementary charge. In the Landau Gauge A ! ¼ ð Þ 0; Bx , we define the operators Π� ¼ τΠ<sup>x</sup> � iΠy, which have the following properties:

$$[\Pi\_{-\prime}, \Pi\_{+}] = \begin{pmatrix} 2\tau/l\_{B}^{2} \end{pmatrix} \tag{6}$$

where the magnetic length is lB <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffi ℏ=eB p ≈ 25:6= ffiffiffi B � � <sup>p</sup> . Using these operators, the destruction and creation operators are introduced in the following way:

$$
\hat{b} = \left(l\_{\mathcal{B}} / \sqrt{2}\right) \Pi\_{-}.
$$

$$
\hat{b}^{\dagger} = \left(l\_{\mathcal{B}} / \sqrt{2}\right) \Pi\_{+} \tag{7}
$$

in the K-(τ ¼ 1) valley, and

$$
\hat{b} = \left(l\_{\text{B}} / \sqrt{2}\right) \Pi\_{+}.
$$

$$
\hat{b}^{\dagger} = \left(l\_{\text{B}} / \sqrt{2}\right) \Pi\_{-}.\tag{8}
$$

in the K<sup>0</sup> (τ ¼ �1) valley. Then, the Hamiltonian in the presence of a perpendicular magnetic field can be well described by

$$\mathbf{H}^{\mathbf{r}=1} = \begin{pmatrix} \frac{\Lambda}{2} & \text{ta}\left(\sqrt{2}/l\_B\right)\hat{b} \\ \text{ta}\left(\sqrt{2}/l\_B\right)\hat{b}^\dagger & -\frac{\Lambda}{2} + \text{s}\lambda \end{pmatrix} . \tag{9}$$

$$\mathbf{H}^{\rm r=-1} = \begin{pmatrix} \Delta & \text{ta}\left(\sqrt{2}/l\_{\rm B}\right)\hat{b}^{\dagger} \\ \text{ta}\left(\sqrt{2}/l\_{\rm B}\right)\hat{b} & -\frac{\Delta}{2} - \text{s}\lambda \end{pmatrix} . \tag{10}$$

It is worth to mention that since the Zeeman effect is vanishingly small (< 5 meV), it is neglected. After some algebra calculations, the Landau levels are obtained as follows:

$$E\_{\pm}(\omega\_{c\nu}n) = \frac{\lambda \pi s}{2} \pm \sqrt{\frac{\left(\Delta - \lambda \pi s\right)^{2}}{4} + t^{2}a^{2}a\_{c}^{2}n} \tag{11}$$

where <sup>n</sup> is an integer and <sup>n</sup> <sup>≥</sup> 1, <sup>ω</sup><sup>c</sup> <sup>¼</sup> ffiffiffi 2 <sup>p</sup> <sup>=</sup>lB. The corresponding Landau fan diagrams of the monolayer MoS2 are shown in Figure 7. The corresponding eigenfunctions are given by

Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots http://dx.doi.org/10.5772/intechopen.70300 119

Figure 7. Conduction band Landau levels of monolayer MoS2 in the vicinity of K- (a) and K<sup>0</sup> - (b) valleys with spin-orbit interaction (SOI). (c) and (d) are the same as (a) and (b), but for the valence band. The blue and red lines correspond to the spin-up and spin-down Landau levels, respectively.

$$\Psi\_{n,\pm}^{\tau=1} = \frac{1}{N\_{\tau=1}^n} \begin{pmatrix} -\alpha\_{\lambda, s\_\gamma \pm}^n \phi\_{n-1} \\ \phi\_n \end{pmatrix} \tag{12}$$

and

monolayer MoS2 calculated by the first principle and k � p model. It can be found that in the

For a perpendicular magnetic field applied to the MoS2 sheet, we use Peierls substitution

½ �¼ Π�, Π<sup>þ</sup> 2τ=l

ℏ=eB p ≈ 25:6= ffiffiffi

^<sup>b</sup> <sup>¼</sup> lB<sup>=</sup> ffiffiffi

^b† <sup>¼</sup> lB<sup>=</sup> ffiffiffi

^<sup>b</sup> <sup>¼</sup> lB<sup>=</sup> ffiffiffi

^b† <sup>¼</sup> lB<sup>=</sup> ffiffiffi

Δ

Δ

It is worth to mention that since the Zeeman effect is vanishingly small (< 5 meV), it is

s

ta ffiffiffi 2 <sup>p</sup> <sup>=</sup>lB � �^<sup>b</sup>

ta ffiffiffi 2 <sup>p</sup> <sup>=</sup>lB � �^<sup>b</sup> � <sup>Δ</sup>

neglected. After some algebra calculations, the Landau levels are obtained as follows:

2 �

2

monolayer MoS2 are shown in Figure 7. The corresponding eigenfunctions are given by

0 B@

> 0 B@

in the K<sup>0</sup> (τ ¼ �1) valley. Then, the Hamiltonian in the presence of a perpendicular magnetic

2 B

B

2 � � <sup>p</sup> <sup>Π</sup>�,

2

2 � � <sup>p</sup> <sup>Π</sup>þ,

2

<sup>2</sup> ta ffiffiffi

<sup>2</sup> ta ffiffiffi

ðΔ � λτsÞ

†

2 <sup>p</sup> <sup>=</sup>lB � �b<sup>b</sup>

2 <sup>p</sup> <sup>=</sup>lB � �b<sup>b</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

2 <sup>4</sup> <sup>þ</sup> <sup>t</sup>

<sup>2</sup> � <sup>s</sup><sup>λ</sup>

� Δ <sup>2</sup> <sup>þ</sup> <sup>s</sup><sup>λ</sup> !

� � (6)

� � <sup>p</sup> . Using these operators, the destruction

� � <sup>p</sup> <sup>Π</sup><sup>þ</sup> (7)

� � <sup>p</sup> <sup>Π</sup>�: (8)

CA, (9)

CA: (10)

(11)

1

†

<sup>2</sup>a<sup>2</sup>ω<sup>2</sup> cn

<sup>p</sup> <sup>=</sup>lB. The corresponding Landau fan diagrams of the

1

¼ ð Þ 0; Bx ,

)–point, they have very good agreement.

Ki ! Π<sup>i</sup> ¼ Ki þ ð Þ e=ℏ Ai, where e is the elementary charge. In the Landau Gauge A

we define the operators Π� ¼ τΠ<sup>x</sup> � iΠy, which have the following properties:

vicinity of the K–(K<sup>0</sup>

118 Quantum-dot Based Light-emitting Diodes

2.1.2. Landau levels of monolayer MoS<sup>2</sup>

where the magnetic length is lB <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffi

in the K-(τ ¼ 1) valley, and

field can be well described by

and creation operators are introduced in the following way:

<sup>H</sup><sup>τ</sup>¼<sup>1</sup> <sup>¼</sup>

<sup>H</sup><sup>τ</sup>¼�<sup>1</sup> <sup>¼</sup>

<sup>E</sup>�ðωc, nÞ ¼ λτ<sup>s</sup>

where <sup>n</sup> is an integer and <sup>n</sup> <sup>≥</sup> 1, <sup>ω</sup><sup>c</sup> <sup>¼</sup> ffiffiffi

$$\Psi\_{n,\pm}^{\pi=-1} = \frac{1}{N\_{\pi=-1}^{n}} \begin{pmatrix} \phi\_n \\ -\beta\_{\lambda,s,\pm}^{\mu} \phi\_{n-1} \end{pmatrix} \tag{13}$$

where

$$\alpha^{\mu}\_{\lambda,s,\pm} = \frac{\text{ta}\left(\sqrt{2}/l\_{\text{B}}\right)\sqrt{n}}{\Delta/2 - E\_{\pm}},\tag{14}$$

$$\beta^{n}\_{\lambda,s,\pm} = \frac{ta\left(\sqrt{2}/l\_{\text{B}}\right)\sqrt{n}}{(-\Delta/2-\lambda s)-E\_{\pm}},\tag{15}$$

$$N\_{\tau=1}^{n,\pm} = \sqrt{(\alpha\_{\lambda\_{\text{av}},s\_{\text{v}},\pm}^{n})^2 + 1},\tag{16}$$

$$N\_{\tau=-1}^{n,\pm} = \sqrt{\left(\beta\_{\lambda\_{\text{ss}}, s\_{\text{\textpi}}, \pm}^{n}\right)^2 + 1},\tag{17}$$

$$\phi\_n = \sqrt{\frac{1}{2^n n!}} \left(\frac{m\omega}{\pi\hbar}\right)^{1/4} e^{-m\alpha r^2/2\hbar} H\_n\left(\sqrt{\frac{m\omega}{\hbar}}r\right),\tag{18}$$

$$H\_n(\mathbf{x}) = (-1)^n e^{x^2} \frac{d^n}{d\mathbf{x}^n} e^{-\mathbf{x}^2}. \tag{19}$$

The eigenfunctions can be written in a compact form as,

$$\Psi\_{n,\pm}^{\pi} = \frac{1}{N\_{\pi}^{\imath,\pm}} \begin{pmatrix} c\_{1,n}^{\imath,\pm} \phi\_{n-\left(\frac{\tau+1}{2}\right)} \\ c\_{2,n,\pm}^{\imath} \phi\_{n-\left(\frac{1-\tau}{2}\right)} \end{pmatrix}.\tag{20}$$

For the special case in which n ¼ 0, the eigenvalues become

$$E\_{n=0}^{\pi=1} = -\frac{\Delta}{2} + \lambda\_{\text{so}} \mathbf{s}\_{\text{z}} \tag{21}$$

$$E\_{n=0}^{t=-1} = \frac{\Delta}{2} \tag{22}$$

and corresponding eigenfunctions turn out to be

$$
\Psi\_0^{\tau=1} = \begin{pmatrix} 0 \\ \phi\_0 \end{pmatrix} \tag{23}
$$

$$
\Psi\_0^{\mathfrak{r}=-1} = \begin{pmatrix} \phi\_0 \\ 0 \end{pmatrix}. \tag{24}
$$

#### 2.2. Optical selection rules

In monolayer TMDCs, both the top of valence bands and the bottom of conduction bands are constructed primarily by the d-orbits of the transition metal atoms. The giant spin-orbit coupling splits the valence bands around the K (K<sup>0</sup> ) valley by 0:5 eV, for MoS2 while the conduction band splitting is neglectable. In addition, time reversal symmetry (TRS) leads to the opposite spin splitting at the K- and K<sup>0</sup> -valleys. Namely the Kramers doublet (K,↑) and (K<sup>0</sup> ,↓) are separated from the other doublet (K<sup>0</sup> ,↑) and (K, ↓) by the spin–orbit interaction (SOI) splitting, as shown in Figure 8.

We assume that the monolayer TMDCs are exposed to light fields with the energy ℏω and wave vector kl, which is orthogonal to the monolayer plane and much smaller than 1=a. Up to the first order approximation, the light-matter interaction Hamiltonian is described by,

$$\mathcal{H}\_{L-M} = \mathbf{e} \mathbf{v} \cdot \mathbf{A}\_{in\prime} \tag{25}$$

with the light field Ain ¼ A0α^ cos ðk<sup>l</sup> � r � ωtÞ and v ¼ ð1=ℏÞ∇kH being propagation velocity [15]. Here, A<sup>0</sup> and α^ stand for the amplitude and orientation of the polarization field, Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots http://dx.doi.org/10.5772/intechopen.70300 121

Nn,� <sup>τ</sup>¼�<sup>1</sup> ¼

ffiffiffiffiffiffiffiffiffi 1 2nn! r mω

φ<sup>n</sup> ¼

120 Quantum-dot Based Light-emitting Diodes

The eigenfunctions can be written in a compact form as,

For the special case in which n ¼ 0, the eigenvalues become

and corresponding eigenfunctions turn out to be

pling splits the valence bands around the K (K<sup>0</sup>

opposite spin splitting at the K- and K<sup>0</sup>

splitting, as shown in Figure 8.

are separated from the other doublet (K<sup>0</sup>

2.2. Optical selection rules

Ψ<sup>τ</sup>

n,� <sup>¼</sup> <sup>1</sup> Nn,� τ

> E<sup>τ</sup>¼<sup>1</sup> <sup>n</sup>¼<sup>0</sup> ¼ � <sup>Δ</sup>

> > E<sup>τ</sup>¼�<sup>1</sup> <sup>n</sup>¼<sup>0</sup> <sup>¼</sup> <sup>Δ</sup>

Ψ<sup>τ</sup>¼<sup>1</sup> <sup>0</sup> <sup>¼</sup> <sup>0</sup> φ0 � �

Ψ<sup>τ</sup>¼�<sup>1</sup> <sup>0</sup> <sup>¼</sup> <sup>φ</sup><sup>0</sup>

0 � �

In monolayer TMDCs, both the top of valence bands and the bottom of conduction bands are constructed primarily by the d-orbits of the transition metal atoms. The giant spin-orbit cou-

tion band splitting is neglectable. In addition, time reversal symmetry (TRS) leads to the

We assume that the monolayer TMDCs are exposed to light fields with the energy ℏω and wave vector kl, which is orthogonal to the monolayer plane and much smaller than 1=a. Up to the first order approximation, the light-matter interaction Hamiltonian is described by,

with the light field Ain ¼ A0α^ cos ðk<sup>l</sup> � r � ωtÞ and v ¼ ð1=ℏÞ∇kH being propagation velocity [15]. Here, A<sup>0</sup> and α^ stand for the amplitude and orientation of the polarization field,

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

�mωr2=2<sup>ℏ</sup>Hn

<sup>2</sup> <sup>þ</sup> <sup>1</sup>

ffiffiffiffiffiffiffi mω ℏ r

r � �

, (17)

: (19)

: (20)

<sup>2</sup> <sup>þ</sup> <sup>λ</sup>sosz, (21)

<sup>2</sup> (22)

, (23)

: (24)

) valley by 0:5 eV, for MoS2 while the conduc-

,↓)


H<sup>L</sup>�<sup>M</sup> ¼ ev � Ain, (25)

,↑) and (K, ↓) by the spin–orbit interaction (SOI)

, (18)

ðβn <sup>λ</sup>so ,sz ,�Þ

e

n e <sup>x</sup><sup>2</sup> d<sup>n</sup> dxn <sup>e</sup> �x<sup>2</sup>

c τ,� <sup>1</sup>;<sup>n</sup> <sup>φ</sup><sup>n</sup>�ðτþ<sup>1</sup> 2 Þ

cτ

<sup>2</sup>;n,�φ<sup>n</sup>�ð1�<sup>τ</sup>

!

2 Þ

q

πℏ � �<sup>1</sup>=<sup>4</sup>

HnðxÞ ¼ ð�1Þ

Figure 8. Schematic illustration of optical transition rules of the valley and spin in the K- (the left) and K<sup>0</sup> - (the right) valleys. The red (blue) color represents spin-up (down) states.

respectively. For an electron being excited by an incident photon from its initial state ji〉 to a final state jf〉, the transition probability is given by the Fermi's golden rule as, Wf i ¼ 2π=ℏj〈f jH<sup>L</sup>�<sup>M</sup>ji〉j 2 nðEÞ, where nðEÞ is the density of states available for the final state. Since the absorption intensity I is proportional to the transition rate, it can be evaluated by,

$$I = \sum\_{m\_{\ell} \ m\_{\ell \ell} n\_{\ell \ell} n\_v} | < \Psi\_c |\mathcal{H}\_{L-M}| \Psi\_v > |^2 \Lambda \Upsilon\_\prime \tag{26}$$

where Ψ<sup>c</sup> ðΨvÞ is the conduction (valence) band wave function, Λ ¼ γ=π{½ω � ðEcðmc, ncÞ� Evðmv, nvÞÞ�<sup>2</sup> <sup>þ</sup> <sup>γ</sup>2}, and <sup>ϒ</sup> <sup>¼</sup> <sup>f</sup> <sup>c</sup> � <sup>f</sup> <sup>v</sup>, with <sup>f</sup> <sup>i</sup> Fermi-Dirac distribution function, ni the principal quantum number, mi the quantum number associating with orbital angular momentum, i ¼ c, and v referring to conduction and valence band, respectively, mc ¼ m and mv ¼ m<sup>0</sup> , γ a parameter determined by the Lorentzian distribution.

For a circularly polarized (CP) light, α^ ¼ ð1; cos ðωt � σπ=2Þ; 0Þ T, with <sup>σ</sup> ¼ �1 denoting the corresponding positive and negative helicities and T stands for the transpose of a matrix, then the perturbed Hamiltonian becomes,

$$\mathcal{H}\_{L-M} = e^{i\omega t} \hat{\boldsymbol{W}}\_{\sigma}{}^{\dagger} + e^{-i\omega t} \hat{\boldsymbol{W}}\_{\sigma\prime} \tag{27}$$

with <sup>W</sup>^ <sup>σ</sup> <sup>¼</sup> etaA<sup>0</sup> τσ<sup>x</sup> <sup>þ</sup> <sup>i</sup>σσ<sup>y</sup> � �=2ℏ. For example, for <sup>τ</sup> <sup>¼</sup> <sup>1</sup>; sz ¼ �1, the transition rate for the monolayer TMDCs is determined by,

$$<\langle c,\stackrel{\cdot}{k}|\mathbf{H}\_{L-M}^{\mathbb{CP},+}|\upsilon,\stackrel{\cdot}{k}\rangle = \frac{2m\alpha t}{\hbar}\,\delta\_{s\_{\overline{x}\overline{s}},s\_{\overline{x}}}(\sin\phi\_{\overline{k}} + \cos\phi\_{\overline{k}}\cos\theta\_{n})\tag{28}$$

and

$$<\langle \mathbf{c} \mid \stackrel{\cdot}{\mathbf{H}} \mathbf{H}\_{L-M}^{\mathbf{CP}\_{\prime}-} \vert \mathbf{v} \mid \stackrel{\cdot}{k} \rangle = \mathbf{0} \tag{29}$$

The optical transition rate for τ ¼ �1 and sz ¼ �1 can be obtained by replacing þ with �in the H<sup>L</sup>�<sup>M</sup>. From Eqs. (29) and (30), notice that under CP light excitation, a valley and spin polarized emission or absorption light is expected in monolayer MoS2, as shown in Figure 8. In contrast, linearly polarized light does not present valley-selected emission and absorption spectra because both K- and K<sup>0</sup> - valleys absorb light simultaneously.

#### 2.3. Valley polarized photoluminescence and excitonic effects of the monolayer TMDCs

In monolayer TMDCs, strong Coulomb interactions due to reduced screening and strong 2D confinement lead to exceptionally high binding energies for excitons [23, 24, 36], which allow them be able to survive even at room temperature. Hence, the typical absorption spectra are usually characterized by strong excitonic peaks marked by A and B, located at 670 and 627 nm, respectively. The strong spin-orbit interaction in the valence band gives rise to a separation between them, as shown in Figure 9. In addition, an injection of electrons into the conduction band of MoS2, which can be realized by gate-doping [26], photoionization of impurities [28], substrates [25] or functionalization layers [22, 27], leads to the formation of negatively charged excitons ðX�Þ. The peak of the X� is positioned at a lower energy side of neutral exciton with a binding energy about 36 meV for MoS2, see the peak indicated by X� in Figure 10. In addition, the emergence of the charged exciton is accompanied by a transfer of spectral weight from the exciton. Therefore, the intensity ratio between a neutral and charged exciton can be tuned externally. Besides, with increasing the nonequilibrium excess electron density, a red-shift of the excitonic ground-state absorption due to Coulomb-induced band gap shrinkage occurs. It is also worth to point out that on the one hand the trion can provide a novel channel for exciton relaxation, and on the other hand, it can also be excited by an optical phonon into an excitonic state to realize an upconversion process in monolayer WSe2.

In the regime of high exciton density, the exciton-exciton collision leads to exciton annihilation through Auger process or formation of biexciton in the monolayer TMDCs. The biexciton is identified as a sharply defined state in the PL, see P0 in Figure 10 and also XX-peak in Figure 11. The nature of the biexcitonic state is supported by the dependence of its PL intensity on the excitation laser power. At low excitation laser intensity, the peaks P0 and X grow superlinearly and linearly with incident laser power, whereas they increase sub-quadratically and sublinearly with the laser power at sufficiently high laser fluence. The large circular polarization of P0 emission provides a further support for this assignment.

The polarization of the photoluminescence from the TMDCs, which is defined by η ¼ðI<sup>σ</sup><sup>þ</sup> � I<sup>σ</sup>� Þ=ðI<sup>σ</sup><sup>þ</sup> þ I<sup>σ</sup>� Þ, inherits that of the excitation source, where I<sup>σ</sup><sup>þ</sup> (I<sup>σ</sup>� ) is PL intensity of right (left) hand circularly polarized light. Figure 11 illustrates photoluminescence spectra of monolayer WSe2 excited by near-resonant circularly polarized radiation at 15 K. Notice that the peaks for X, X�, and XX all exhibit significant circular polarization. In addition to biexciton emission, the X and X� emission bands also exhibit strong valley polarization.

Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots http://dx.doi.org/10.5772/intechopen.70300 123

Figure 9. Reflection and photoluminescence spectra of ultrathin MoS2 layers. (a) Reflection difference due to an ultrathin MoS2 layer on a quartz substrate, which is proportional to the MoS2 absorption constant. The observed absorption peaks at 1.85 eV (670 nm) and 1.98 eV (627 nm) correspond to the A and B direct excitonic transitions with the energy split from valence band spin-orbital coupling. The inset shows the bulk MoS2 band structure neglecting the relatively weak spinorbital coupling, which has an indirect bandgap around 1 eV and a single higher energy direct excitonic transition at the K point denoted by an arrow. (b) A strong photoluminescence is observed at the direct excitonic transitions energies in a monolayer, respectively [30]. (Copyright 2010 by American Chemical Society, reprinted with permission).

#### 2.4. Defect induced photoluminescence and single photon source

and

spectra because both K- and K<sup>0</sup>

122 Quantum-dot Based Light-emitting Diodes

〈c, k!

state to realize an upconversion process in monolayer WSe2.

polarization of P0 emission provides a further support for this assignment.

emission, the X and X� emission bands also exhibit strong valley polarization.

jHCP,� <sup>L</sup>�<sup>M</sup> <sup>j</sup>v, k!

The optical transition rate for τ ¼ �1 and sz ¼ �1 can be obtained by replacing þ with �in the H<sup>L</sup>�<sup>M</sup>. From Eqs. (29) and (30), notice that under CP light excitation, a valley and spin polarized emission or absorption light is expected in monolayer MoS2, as shown in Figure 8. In contrast, linearly polarized light does not present valley-selected emission and absorption


2.3. Valley polarized photoluminescence and excitonic effects of the monolayer TMDCs

In monolayer TMDCs, strong Coulomb interactions due to reduced screening and strong 2D confinement lead to exceptionally high binding energies for excitons [23, 24, 36], which allow them be able to survive even at room temperature. Hence, the typical absorption spectra are usually characterized by strong excitonic peaks marked by A and B, located at 670 and 627 nm, respectively. The strong spin-orbit interaction in the valence band gives rise to a separation between them, as shown in Figure 9. In addition, an injection of electrons into the conduction band of MoS2, which can be realized by gate-doping [26], photoionization of impurities [28], substrates [25] or functionalization layers [22, 27], leads to the formation of negatively charged excitons ðX�Þ. The peak of the X� is positioned at a lower energy side of neutral exciton with a binding energy about 36 meV for MoS2, see the peak indicated by X� in Figure 10. In addition, the emergence of the charged exciton is accompanied by a transfer of spectral weight from the exciton. Therefore, the intensity ratio between a neutral and charged exciton can be tuned externally. Besides, with increasing the nonequilibrium excess electron density, a red-shift of the excitonic ground-state absorption due to Coulomb-induced band gap shrinkage occurs. It is also worth to point out that on the one hand the trion can provide a novel channel for exciton relaxation, and on the other hand, it can also be excited by an optical phonon into an excitonic

In the regime of high exciton density, the exciton-exciton collision leads to exciton annihilation through Auger process or formation of biexciton in the monolayer TMDCs. The biexciton is identified as a sharply defined state in the PL, see P0 in Figure 10 and also XX-peak in Figure 11. The nature of the biexcitonic state is supported by the dependence of its PL intensity on the excitation laser power. At low excitation laser intensity, the peaks P0 and X grow superlinearly and linearly with incident laser power, whereas they increase sub-quadratically and sublinearly with the laser power at sufficiently high laser fluence. The large circular

The polarization of the photoluminescence from the TMDCs, which is defined by η ¼ðI<sup>σ</sup><sup>þ</sup> � I<sup>σ</sup>� Þ=ðI<sup>σ</sup><sup>þ</sup> þ I<sup>σ</sup>� Þ, inherits that of the excitation source, where I<sup>σ</sup><sup>þ</sup> (I<sup>σ</sup>� ) is PL intensity of right (left) hand circularly polarized light. Figure 11 illustrates photoluminescence spectra of monolayer WSe2 excited by near-resonant circularly polarized radiation at 15 K. Notice that the peaks for X, X�, and XX all exhibit significant circular polarization. In addition to biexciton

〉 ¼ 0 (29)

As known, vacancy defects, impurities, potential wells created by structural defects or local strain or other disorders might be introduced in the growth process of the TMDC materials [12, 13, 32, 33]. They can produce localized states to participate the optical emission and absorption as manifested by P1 to P3 in Figure 10, and the emission bands on the lower energy side of the peak XX in Figure 11. Since the point defects can induce intervalley coupling, the defect-related emission peaks show no measurable circular polarization character. Besides, the excitons, trions, and even biexcitons can be trapped by theses crystal structure imperfections to form corresponding bound quasiparticles. Therefore, delocalized excition, charged exciton and biexciton emissions, and localized ones can coexist in the TMDCs. Interestingly, these carrier trapping centers can act as single-photon emitters to emit stable and sharp emission line [12, 13, 32, 33]. For this kind of single quantum emitter, since the maximum number of

Figure 10. Photoluminescence spectra (PL) of monolayer WSe2 at 50 K for pulsed excitation under applied pump fluences of 0:8 μJ cm�<sup>2</sup> (black curve) and 12 μJ cm�<sup>2</sup> (red curve), respectively. The spectra are normalized to yield the same emission strength for the neutral exciton [40]. (Copyright 2015 by the Nature Publishing Group. Reprinted with permission.)

emitted single photons is limited by the lifetime of the excited state, a saturation of the PL intensity at high excitation laser power is expected.

#### 2.5. Magneto-optical properties of the monolayer TMDCs

The presence of a magnetic field induces a quantization of the energy levels. At high magnetic field, the Landau levels (LLs) form. The transition rate between the conduction–and valence– band Landau levels can be calculated using the eigenfunctions in Eq. 21.

$$\langle \Psi\_{\mathfrak{n}}^{\mathfrak{r},+} | \mathbf{H}\_{L-M}^{\mathrm{CP},\pm} | \Psi\_{\mathfrak{m}}^{\mathfrak{r},-} \rangle = M \, \delta\_{\mathrm{sz},\mathrm{sz}\nu} \left[ (\mathfrak{r} + \sigma) \, \mathfrak{c}\_{1,\mathfrak{n}}^{\mathfrak{r},+} \, \mathfrak{c}\_{2,\mathfrak{m}}^{\mathfrak{r},-} \delta\_{\mathfrak{n},\mathfrak{m}+\mathfrak{r}} + (\mathfrak{r} - \sigma) \, \mathfrak{c}\_{2,\mathfrak{n}}^{\mathfrak{r},+} \, \mathfrak{c}\_{1,\mathfrak{m}}^{\mathfrak{r},-} \delta\_{\mathfrak{n}+\mathfrak{r},\mathfrak{m}} \right] \tag{30}$$

where

$$M = \frac{e t a A\_0}{2 \hbar \mathbf{N}\_{\pi}^{n,+} \mathbf{N}\_{\pi}^{m,-}}.\tag{31}$$

In the presence of magnetic field, both σ<sup>þ</sup> and σ� absorptions take place in each valley. However, there is a great difference in their intensity. For instance, the absorption spectrum intensity of σþ-light is 104 times larger than σ�-light in the K–valley. And, the lowest transition energy absorption spectrum demonstrates a valley polarization, i.e., σ<sup>þ</sup> in the K–valley and σ� in the K<sup>0</sup> –valley, as showed in Figure 12 [41]. In addition, the transition occurs from n ¼ 0 to n ¼ 1 LLs in the K<sup>0</sup> –valley, whereas n ¼ 1 to n ¼ 0 LLs in the K–valley. Therefore, the valley

emitted single photons is limited by the lifetime of the excited state, a saturation of the PL

Figure 10. Photoluminescence spectra (PL) of monolayer WSe2 at 50 K for pulsed excitation under applied pump fluences of 0:8 μJ cm�<sup>2</sup> (black curve) and 12 μJ cm�<sup>2</sup> (red curve), respectively. The spectra are normalized to yield the same emission strength for the neutral exciton [40]. (Copyright 2015 by the Nature Publishing Group. Reprinted with

The presence of a magnetic field induces a quantization of the energy levels. At high magnetic field, the Landau levels (LLs) form. The transition rate between the conduction–and valence–

> τ,þ <sup>1</sup>;<sup>n</sup> c τ,�

<sup>M</sup> <sup>¼</sup> etaA<sup>0</sup> 2ℏNn,<sup>þ</sup> <sup>τ</sup> <sup>N</sup>m,� <sup>τ</sup>

In the presence of magnetic field, both σ<sup>þ</sup> and σ� absorptions take place in each valley. However, there is a great difference in their intensity. For instance, the absorption spectrum intensity of σþ-light is 104 times larger than σ�-light in the K–valley. And, the lowest transition energy absorption spectrum demonstrates a valley polarization, i.e., σ<sup>þ</sup> in the K–valley and σ�

–valley, as showed in Figure 12 [41]. In addition, the transition occurs from n ¼ 0 to

–valley, whereas n ¼ 1 to n ¼ 0 LLs in the K–valley. Therefore, the valley

<sup>2</sup>;<sup>m</sup> δn,mþ<sup>τ</sup> þ ðτ � σÞ c

τ,þ <sup>2</sup>;<sup>n</sup> c τ,�

: (31)

<sup>1</sup>;<sup>m</sup> δ<sup>n</sup>þτ,m� (30)

intensity at high excitation laser power is expected.

〈Ψ<sup>τ</sup>,<sup>þ</sup> <sup>n</sup> <sup>j</sup>HCP,�

where

permission.)

124 Quantum-dot Based Light-emitting Diodes

in the K<sup>0</sup>

n ¼ 1 LLs in the K<sup>0</sup>

<sup>L</sup>�<sup>M</sup> <sup>j</sup>Ψ<sup>τ</sup>,�

2.5. Magneto-optical properties of the monolayer TMDCs

band Landau levels can be calculated using the eigenfunctions in Eq. 21.

<sup>m</sup> 〉 ¼ M δszc,szv ½ðτ þ σÞ c

Figure 11. Circularly polarized photoluminescence (PL) spectra of monolayer WSe2 excited by near-resonant circularly polarized radiation at 15 K. (a) PL for low exciton density with continuous wave excitation at a photon energy of 1:92 eV. (b) PL for high exciton density with pulsed excitation at a photon energy of 1:82 eV. Blue and red curves correspond to the same and opposite circularly polarized states. The emission energies for neutral (X) and charged (X�) excitons and the biexciton (XX) state are indicated by dashed lines. Inset shows schematic diagram of energy dispersion in K- and K0 -valleys and valley-polarized emission. The vertical arrows indicate the electron spin direction. The circles represent conduction and valence band electrons [40]. (Copyright 2015 by the Nature Publishing Group. Reprinted with permission).

polarization remains in the magneto-optical absorption, as showed in Figure 13. It is worth to argue that the higher-order terms in the effective k.p model only induces about 0.1% correction to absorption spectrum intensity [41], which allows us neglect them safely.

Figure 12. Selection rules for the interband transitions between Landau levels in K-valley (the left panel) and in K<sup>0</sup> -valley– valley (the right panel) of monolayer WS2 subjected to a magnetic field along the ^z-direction, excited by a circularly polarized light. The blue and red arrows correspond to σ<sup>þ</sup> and σ� absorptions, respectively [41]. (Copyright 2013 by the American Physical Society. Reprinted with permission).

Figure 13. σ<sup>þ</sup> absorption spectrum of monolayer MoS2 for spin–up states in the K-valley (the left panels) and σ� absorption spectrum for spin–down states in the K<sup>0</sup> -valley (the right panels), for a magnetic field B ¼ 2 ((a) and (d)), 10 ((b) and (e)), 15T ((c) and (f)), respectively.

#### 2.6. TMDC quantum dots and valley polarized single-photon source

The Hamiltonian of the TMDC QDs in polar coordinates is given by [15]

$$\mathbf{H} = \begin{pmatrix} \Delta & t e^{-i\tau \theta} \left( -i\tau \frac{\partial}{\partial\_r} - \frac{1}{r} \frac{\partial}{\partial\_\theta} \right) \\\\ t e^{i\tau \theta} \left( -i\tau \frac{\partial}{\partial\_r} + \frac{1}{r} \frac{\partial}{\partial\_\theta} \right) & -\frac{\Delta}{2} + \tau s \lambda \end{pmatrix}. \tag{32}$$

As a matter of convenience, we get rid of the angular part by using the following ansatz for the eigenfunctions

$$\Psi = \begin{pmatrix} \psi\_a(r, \theta) \\ \psi\_b(r, \theta) \end{pmatrix} = \begin{pmatrix} e^{im\theta} \overline{a}(r) \\ e^{i(m+\pi)\theta} \overline{b}(r) \end{pmatrix} \tag{33}$$

where the quantum number m ¼ j � τ=2, j is the quantum number related to the effective angular momenta J<sup>τ</sup> <sup>e</sup>f f ¼ Lz þ ℏτσz=2 with Lz being the orbital angular momenta in the ^z direction. Then the Schrödinger equation for TMDC QDs, showed in Figure 14, becomes

$$\left(\frac{\Delta}{2} - E\right)\overline{a}(r) = \text{ita}\left(\pi \overline{b}'(r) + \overline{b}(r)\frac{(m+\tau)}{r}\right).$$

$$\left(\frac{\Delta}{2} - \tau s\lambda + E\right)\overline{b}(r) = \text{ita}\left(-\tau \overline{a}'(r) + \overline{a}(r)\frac{m}{r}\right). \tag{34}$$

After some algebra calculations, we get two decoupled equations. They are

$$
\overline{a}''(r) + \frac{\overline{a}'(r)}{r} + \overline{a}(r) \left(\chi - \frac{m^2}{r^2}\right) = 0\tag{35}
$$

and


Figure 12. Selection rules for the interband transitions between Landau levels in K-valley (the left panel) and in K<sup>0</sup>

American Physical Society. Reprinted with permission).

126 Quantum-dot Based Light-emitting Diodes

absorption spectrum for spin–down states in the K<sup>0</sup>

((b) and (e)), 15T ((c) and (f)), respectively.

valley (the right panel) of monolayer WS2 subjected to a magnetic field along the ^z-direction, excited by a circularly polarized light. The blue and red arrows correspond to σ<sup>þ</sup> and σ� absorptions, respectively [41]. (Copyright 2013 by the

Figure 13. σ<sup>þ</sup> absorption spectrum of monolayer MoS2 for spin–up states in the K-valley (the left panels) and σ�


$$
\overline{\sigma}''(r) + \frac{\overline{b}'(r)}{r} + \overline{b}(r) \left(\chi - \frac{(m+\tau)^2}{r^2}\right) = 0\tag{36}
$$

where <sup>χ</sup> <sup>¼</sup> <sup>ð</sup>2E�ΔÞðΔþ2E�2λsτ<sup>Þ</sup> 4t <sup>2</sup>a<sup>2</sup> . These two second order differential equations can be straightforwardly resolved. Finally we obtain,

$$
\overline{\pi}(r) = \overline{N} \left( \frac{2\text{i}at\sqrt{\chi}}{\Delta - 2E} \right) I\_{|m|}(r\sqrt{\chi}) \tag{37}
$$

and

$$\overline{b}(r) = \overline{\mathcal{N}} l\_{|m+\tau|}(r\sqrt{\chi}) \,. \tag{38}$$

where N is the normalization constant and JnðxÞ is Bessel Function of the first kind. Applying the infinite mass boundary condition <sup>ψ</sup>2<sup>ð</sup>R, <sup>θ</sup><sup>Þ</sup> <sup>ψ</sup>1<sup>ð</sup>R, <sup>θ</sup><sup>Þ</sup> <sup>¼</sup> <sup>i</sup>τeiτθ, we obtains the secular equation

$$J\_{|m+\pi|}(\mathbb{R}\sqrt{\chi}) = -\frac{\pi(2at\sqrt{\chi})J\_{|m|}(\mathbb{R}\sqrt{\chi})}{\Delta - 2E},\tag{39}$$

where R is the QD radius, see Figure 14.

From Figures 15 and 16, we see that the bound states formed in a single valley, and Eτ <sup>ð</sup>j<sup>Þ</sup> 6¼ <sup>E</sup><sup>τ</sup> ð�jÞ for both conduction– and valence– bands. In addition, the electron-hole symmetry is broken. Due to the confinement potential, the effective time reversal symmetry (TRS) is broken within a single valley, even without the magnetic field, similarly to graphene QDs [42]. On the other hand, the inverse asymmetry of the crystalline structure, the terms of spin-orbit interaction and the confinement potential, do not commute with the effective inversion operator, defined in a single valley Pe ¼ I<sup>τ</sup> ⊗ σx. Consequently, the QDs do not preserve the electron-hole symmetry in the same valley. However, comparing Figure 15(a, b), we can found that E<sup>τ</sup> <sup>ð</sup>jÞ ¼ <sup>E</sup>�<sup>τ</sup> ð�j<sup>Þ</sup> was still true. This is attributed to the TRS, where THT�<sup>1</sup> <sup>¼</sup> <sup>H</sup>, the TRS operator is defined as T ¼ iτ<sup>x</sup> ⊗ syC, with C being the conjugate complex operator.

#### 2.7. Landau levels in monolayer MoS2 quantum dots

Similarly to what we did in the case of the monolayer TMDCs, for quantum dot subjected to a perpendicular magnetic field, we do the Peierls substitution and use now the symmetric

Figure 14. (a) Schematic of a monolayer MoS2 QD with radius R. (b) Top view of MoS2 crystal structure.

Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots http://dx.doi.org/10.5772/intechopen.70300 129

Figure 15. (a) Wave function profile Ψ<sup>n</sup> and its two components (an, bn) of the lowest two (n ¼ 1, 2) conduction band states in the K–valley with spin–up at j ¼ 1:5. The pink circle indicates that the wave function Ψ<sup>n</sup> is nonzero (even though small) at r ¼ R. Energy spectrum of the lowest four (n ¼ 1, 2, 3, 4) conduction bands (solid curves) and the highest four valence bands (dashed curves) as a function of j, in the K-valley with spin-up (b) and K<sup>0</sup> -valley with spindown (c) of a MoS2 dot. The dot size is R ¼ 40nm and the magnetic field is B ¼ 0 [14]. (Copyright 2016 by the IOP publishing. Reprinted with permission).

gauge, i.e., A ! ¼ ð�By=2;Bx=2Þ. The part of magnetic field Hamiltonian, in polar coordinates is given by

$$\mathcal{H}\_{\mathcal{B}} = \begin{pmatrix} 0 & \frac{ta}{2l\_{\mathcal{B}}^2} \left( -ie^{-ir\theta}r \right) \\\\ \frac{ta}{2l\_{\mathcal{B}}^2} \left( ie^{ir\theta}r \right) & 0 \end{pmatrix}. \tag{40}$$

Then, the total Hamiltonian becomes H þ HB, which leads to the following two-coupled differential equations:

$$\left(\frac{\Delta}{2} - E\right)\overline{a}(r) = \text{i}at\left(\tau \overline{b}'(r) + \overline{b}(r)\left(\frac{(m+\tau)}{r} + \frac{r}{2l\_{\text{B}}^2}\right)\right).$$

$$\left(E + \frac{\Delta}{2} - \lambda s\tau\right)\overline{b}(r) = \text{i}at\left(-\tau \overline{a}'(r) + \overline{a}(r)\left(\frac{m}{r} + \frac{r}{2l\_{\text{B}}^2}\right)\right). \tag{41}$$

In order to solve this eigenvalue problem, let us first decouple these two equations into

$$
\overline{a}''(r) + \frac{\overline{a}'(r)}{r} + \overline{a}(r) \left( -\frac{r^2}{4l\_B^4} - \kappa - \frac{m^2}{r^2} \right) = 0 \tag{42}
$$

and

where N is the normalization constant and JnðxÞ is Bessel Function of the first kind. Applying

From Figures 15 and 16, we see that the bound states formed in a single valley, and

metry is broken. Due to the confinement potential, the effective time reversal symmetry (TRS) is broken within a single valley, even without the magnetic field, similarly to graphene QDs [42]. On the other hand, the inverse asymmetry of the crystalline structure, the terms of spin-orbit interaction and the confinement potential, do not commute with the effective inversion operator, defined in a single valley Pe ¼ I<sup>τ</sup> ⊗ σx. Consequently, the QDs do not preserve the electron-hole symmetry in the same valley. However, comparing Figure 15(a, b), we can

TRS operator is defined as T ¼ iτ<sup>x</sup> ⊗ syC, with C being the conjugate complex operator.

Figure 14. (a) Schematic of a monolayer MoS2 QD with radius R. (b) Top view of MoS2 crystal structure.

Similarly to what we did in the case of the monolayer TMDCs, for quantum dot subjected to a perpendicular magnetic field, we do the Peierls substitution and use now the symmetric

ð�jÞ for both conduction– and valence– bands. In addition, the electron-hole sym-

τ 2at ffiffiffi

<sup>χ</sup> <sup>p</sup> ð ÞJjm<sup>j</sup> <sup>R</sup> ffiffiffi

<sup>ψ</sup>1<sup>ð</sup>R, <sup>θ</sup><sup>Þ</sup> <sup>¼</sup> <sup>i</sup>τeiτθ, we obtains the secular equation

<sup>χ</sup> <sup>p</sup> ð Þ

ð�j<sup>Þ</sup> was still true. This is attributed to the TRS, where THT�<sup>1</sup> <sup>¼</sup> <sup>H</sup>, the

<sup>Δ</sup> � <sup>2</sup><sup>E</sup> , (39)

the infinite mass boundary condition <sup>ψ</sup>2<sup>ð</sup>R, <sup>θ</sup><sup>Þ</sup>

128 Quantum-dot Based Light-emitting Diodes

where R is the QD radius, see Figure 14.

<sup>ð</sup>jÞ ¼ <sup>E</sup>�<sup>τ</sup>

2.7. Landau levels in monolayer MoS2 quantum dots

Eτ

<sup>ð</sup>j<sup>Þ</sup> 6¼ <sup>E</sup><sup>τ</sup>

found that E<sup>τ</sup>

<sup>J</sup>jmþτ<sup>j</sup> <sup>R</sup> ffiffiffi

<sup>χ</sup> <sup>p</sup> ð Þ¼�

Figure 16. Energy spectrum of monolayer MoS2 QD with a radius of 40 nm for the conduction–band in the K- (a) and K<sup>0</sup> - (b) valleys. (c) and (d) are corresponding figures for the valence–band. The blue and red curves correspond to spin–up and spin–down energy levels, respectively.

$$
\overline{b}''(r) + \frac{\overline{b}'(r)}{r} + \overline{b}(r) \left( -\frac{r^2}{4l\_B^4} - \phi - \frac{(m+\tau)^2}{r^2} \right) = 0 \tag{43}
$$

where

$$\kappa = \frac{(m+\tau)}{l\_B^2} + \frac{(\Delta - 2E)(\Delta + 2E - 2\lambda s \tau)}{4l^2 a^2},\tag{44}$$

$$\phi = \frac{m}{l\_B^2} + \frac{(\Delta - 2E)(\Delta + 2E - 2\lambda s \tau)}{4l^2 a^2} \tag{45}$$

Solving these equations, we obtain the following two components of the eigenfunctions

$$\overline{a}(r) = G\_{\xi} \overline{N} r^{|m|} e^{-\frac{r^2}{4l\_{\text{B}}^2}} \,\_1F\_1\left(\frac{1}{2}\left(\kappa l\_{\text{B}}^2 + |m| + 1\right); |m| + 1; \frac{r^2}{2l\_{\text{B}}^2}\right),\tag{46}$$

Valley Polarized Single Photon Source Based on Transition Metal Dichalcogenides Quantum Dots http://dx.doi.org/10.5772/intechopen.70300 131

$$\overline{\boldsymbol{\theta}}(\boldsymbol{r}) = \overline{\boldsymbol{N}} \boldsymbol{r}^{|\boldsymbol{m}+\boldsymbol{\tau}|} e^{-\frac{\boldsymbol{r}^{2}}{4\boldsymbol{l}\_{\mathcal{B}}}} \,\_1F\_1\left(\frac{1}{2}\left(\phi \boldsymbol{l}\_{\mathcal{B}}^2 + |\boldsymbol{m} + \boldsymbol{\tau}| + 1\right); |\boldsymbol{m} + \boldsymbol{\tau}| + 1; \frac{\boldsymbol{r}^2}{2\boldsymbol{l}\_{\mathcal{B}}^2}\right) \tag{47}$$

where

b 00 <sup>ð</sup>rÞ þ <sup>b</sup> 0 ðrÞ r

and spin–down energy levels, respectively.

130 Quantum-dot Based Light-emitting Diodes

<sup>κ</sup> <sup>¼</sup> <sup>ð</sup><sup>m</sup> <sup>þ</sup> <sup>τ</sup><sup>Þ</sup> l 2 B

> <sup>φ</sup> <sup>¼</sup> <sup>m</sup> l 2 B

> > e � r2 4l 2 <sup>B</sup> <sup>1</sup>F<sup>1</sup>

<sup>a</sup>ðrÞ ¼ <sup>G</sup>ξNrjm<sup>j</sup>

where

<sup>þ</sup> <sup>b</sup>ðrÞ � <sup>r</sup><sup>2</sup>

Solving these equations, we obtain the following two components of the eigenfunctions

4l 4 B

Figure 16. Energy spectrum of monolayer MoS2 QD with a radius of 40 nm for the conduction–band in the K- (a) and K<sup>0</sup>

(b) valleys. (c) and (d) are corresponding figures for the valence–band. The blue and red curves correspond to spin–up

� <sup>φ</sup> � <sup>ð</sup><sup>m</sup> <sup>þ</sup> <sup>τ</sup><sup>Þ</sup>

<sup>B</sup> þ jmj þ <sup>1</sup> � �; <sup>j</sup>mj þ <sup>1</sup>;

!

!

<sup>þ</sup> <sup>ð</sup><sup>Δ</sup> � <sup>2</sup>EÞð<sup>Δ</sup> <sup>þ</sup> <sup>2</sup><sup>E</sup> � <sup>2</sup>λsτ<sup>Þ</sup> 4t

<sup>þ</sup> <sup>ð</sup><sup>Δ</sup> � <sup>2</sup>EÞð<sup>Δ</sup> <sup>þ</sup> <sup>2</sup><sup>E</sup> � <sup>2</sup>λsτ<sup>Þ</sup> 4t

r2

2

¼ 0 (43)


, (46)

<sup>2</sup>a<sup>2</sup> , (44)

<sup>2</sup>a<sup>2</sup> (45)

r2 2l 2 B

$$\mathbf{G}\_{\xi} = i\mathcal{W}(\tau m) \left( \frac{4ta(m + \tau Q\_{+}(\tau m))}{\Delta - 2EW(\tau m) - 2\tau \mathbf{s} \lambda Q\_{-}(\tau m)} \right)^{W(\tau m)},\tag{48}$$

$$\mathcal{W}(\tau m) = \mathcal{S}(\tau m + \varepsilon),\tag{49}$$

$$Q\_{\pm}(\tau m) = \frac{1 \pm S(\tau m + \varepsilon)}{2},\tag{50}$$

SðxÞ is the sign function, <sup>1</sup>F1ð Þ a, b, x is the confluent hypergeometric function of the first kind, ε is an arbitrary constant (0 < ε < 1) used to avoid a singularity in the function SðxÞ.

With the eigenfunctions at hand, we can derive the secular equation for the eigenvalues by applying infinite mass boundary condition, i.e.,

$$\frac{{}\_1F\_1\left(\frac{1}{2}\left(\phi l\_B^2 + |m+\tau|+1\right); |m+\tau|+1; \frac{R^2}{2l\_B^2}\right)}{{}\_1F\_1\left(\frac{1}{2}\left(\kappa l\_B^2 + |m|+1\right); |m|+1; \frac{R^2}{2l\_B^2}\right)} = i\tau R^{|m|-|m+\tau|}G\_\xi\tag{51}$$

Figure 17(a) illustrates the energy spectrum of the lowest four spinup conduction bands in the K-valley (τ ¼ 1, s ¼ 1) as a function of magnetic field (B), for the orbital angular momentum m ¼ �0; 1; � 2, in the 70 nm dot. At zero magnetic field, the electronic shells of an artificial atom such as s, p, and d shells emerge. In a certain valley, say the K-valley, the atomic states possess both spin- and orbital–degeneracies such as EðmÞ ¼ Eð�mÞ. In addition, we should emphasize that the energy spectrum in different valleys have time reversal symmetry at B ¼ 0. However, the presence of magnetic field breaks down this symmetry and leads to splittings of the atomic orbitals of the dot. Moreover, in the regime of weak magnetic fields, unlike the monolayer MoS2 in which the energy shows linear B response, valley dependent energy levels with nonlinear B response are observed. Such effect is attributed to the competition of the QD confinement with the magnetic field effect [14].

As B increases, an effective confinement induced by the magnetic field gradually becomes comparable to that of the dot. Hence, their contributions to the electronic energy are balanced. With a further increasing of B, magnetic field effect starts to dominate the features of the energy spectrum. Accordingly, the LLs which show a linear dependence on B, became of the heavily massive Dirac character, are formed just like in the pristine monolayer MoS2. The higher the energy level is, the stronger the magnetic field needed to form the corresponding LL. For instance, the lowest LL is formed around a critical value B ¼ Bc ¼ 2T. Interestingly, in the Hall regime, an energy locked (energy independent on B) mode referring to the lowest

Figure 17. Energy spectrum of the lowest four conduction band states with spin–up in the K-valley (a) and spindown in the K<sup>0</sup> -valley (b), and the highest four valence band states with spin–up in the K-valley (e) and spin-down in the K<sup>0</sup> -valley (f) of a 70 nm MoS2 QD, as a function of the magnetic field, for angular momentum m ¼ 0 (red curves), �1 pink curves), 1 (green curves), �2 (black curves), and 2 (blue curves). The corresponding analogues for a 40 nm dot are shown in (c), (d), (g), and (h), respectively [14]. (Copyright 2016 by the IOP publishing. Reprinted with permission).

spin-down conduction band in the K<sup>0</sup> -valley emerges, as shown in Figure 17(b). It is expected to be an analog to the zero energy mode in gapless graphene, associating with certain topological properties. These novel features of the QD energy spectrum are tunable by QD size [14].

Figure 17(c, d) are the corresponding analogs of Figure 17(a, b), but for a dot with R ¼ 40 nm. Comparing with the 70nm dot (Bc ¼ 2T), here the energy locked mode takes place until Bc ¼ 4T, which turns out to be larger than the one (2 T) for the 70 nm dot, indicating the locked energy modes arise from the competition between the dot confinement and the applied magnetic field [14].

Let us turn to the energy spectrum of the valence band in the dot of R ¼ 70nm. Figure 17(e, f) show the B field dependence of the energy spectrum of the highest four valence bands for several values of angular momentum ms with m ¼ 0, � 1; � 2 in the K-valley with spin-up (τ ¼ 1; s ¼ 1) and K<sup>0</sup> -valley with spindown (τ ¼ �1, s ¼ �1), respectively. In contrast to the conduction band, here we find EðmÞ 6¼ Eð�mÞ even at B ¼ 0 due to the spin–orbit coupling, see Figure 17(a, b, e, f). Besides that, we also observe the emergent locked energy mode around Bc ¼ 2T, but referring to the highest valence band. We should emphasize that the locked energy modes for the conduction and valence bands appear in distinct valleys with opposite spin, see Figure 17(b, e). The corresponding valence band energy spectra for the 40 nm dot are shown in Figure 17(g–h), where the locked energy mode associated with a larger Bc ¼ 4T, also arises from the combined effect of the dot confinement and the applied magnetic field, similar to the conduction band. Therefore, the flat band or energy locked modes appear only in the valence band of the K-valley and the conduction band of the K<sup>0</sup> -valley [14]. The effect of changing the magnetic field direction is showed in Figure 19.

A comparison of the energy spectrum of the 70 nm dot with that of the bulk TMDC (i.e., infinite geometry) is shown in Figure 18. Because of the large effective mass at the band edges,

the LLs of the bulk TMDC scale as <sup>E</sup>�ðωc, nÞ ¼ λτ<sup>s</sup> <sup>2</sup> � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðΔ�λτsÞ 2 <sup>4</sup> þ t <sup>2</sup>a<sup>2</sup>ω<sup>2</sup> cn q in the low energy region, which resembles conventional 2D semiconductors more than Dirac fermions. The n ¼ 0LL appears only in the conduction band of K<sup>0</sup> -valley (and the valence band of K-valley, not shown), implying the lifting of valley degeneracy for the ground state. As magnetic field increases, there is an evolution of the energy spectrum from atomic energies to Landau levels. More specifically, in the regime of weak B field, the atomic structure emerges, where the energy is distinct from that of the bulk case. On the other hand, in the strong field regime, the energy in the bulk TMDC and quantum dot becomes identical because the effective confinement due to the magnetic field dominates physical behaviors of the dot. Note that although the two band model we used here is widely adopted in the literature [39], the model itself still has limitations, e.g., it cannot properly describe the spin splitting of the conduction band, the trigonal warping of the spectrum and the degeneracy breakdown by applied magnetic field

spin-down conduction band in the K<sup>0</sup>

132 Quantum-dot Based Light-emitting Diodes

netic field [14].

the K<sup>0</sup>

(τ ¼ 1; s ¼ 1) and K<sup>0</sup>



to be an analog to the zero energy mode in gapless graphene, associating with certain topological properties. These novel features of the QD energy spectrum are tunable by QD size [14].

Figure 17. Energy spectrum of the lowest four conduction band states with spin–up in the K-valley (a) and spindown in


(f) of a 70 nm MoS2 QD, as a function of the magnetic field, for angular momentum m ¼ 0 (red curves), �1 pink curves), 1 (green curves), �2 (black curves), and 2 (blue curves). The corresponding analogues for a 40 nm dot are shown in (c), (d),

(g), and (h), respectively [14]. (Copyright 2016 by the IOP publishing. Reprinted with permission).

Figure 17(c, d) are the corresponding analogs of Figure 17(a, b), but for a dot with R ¼ 40 nm. Comparing with the 70nm dot (Bc ¼ 2T), here the energy locked mode takes place until Bc ¼ 4T, which turns out to be larger than the one (2 T) for the 70 nm dot, indicating the locked energy modes arise from the competition between the dot confinement and the applied mag-

Let us turn to the energy spectrum of the valence band in the dot of R ¼ 70nm. Figure 17(e, f) show the B field dependence of the energy spectrum of the highest four valence bands for several values of angular momentum ms with m ¼ 0, � 1; � 2 in the K-valley with spin-up

conduction band, here we find EðmÞ 6¼ Eð�mÞ even at B ¼ 0 due to the spin–orbit coupling, see Figure 17(a, b, e, f). Besides that, we also observe the emergent locked energy mode around


Figure 18. Energy spectrum of the conduction band states with spin–up in the K-valley (a) and spin-down in the K<sup>0</sup> -valley (b) of a monolayer MoS2 (dotted curves) and of a MoS2QD with radius R ¼ 70 nm, as a function of the magnetic field.

Figure 19. Energy spectrum of the states with spin-up in the K-valley (a) and spindown in the K<sup>0</sup> -valley (b) of a monolayer MoS2 QD with radius R ¼ 70 nm, as a function of the magnetic field along both positive and negative ^z–direction, for angular momentum m ¼ 0 (red curves), �1 (pink curves), 1 (green curves), �2 (black curves), and 2 (blue curves).

for Landau levels with the same quantum number. However, for usual experimental setups, these effects in the vicinity of the K or K<sup>0</sup> valley in which we are interested play a minor role. Hence it can be safely neglected.

#### 2.8. Optical selection rules in monolayer MoS2 quantum dots

In the QDs as demonstrated in Figure 20, the optical transition matrix elements in the QDs are computed by,

$$
\langle \Psi | \mathcal{H}\_{\rm c} | \mathcal{H}\_{\rm L-M} | \Psi\_{\rm v} \rangle = \left( \frac{\pi A\_0}{\hbar} \right) \delta\_{s\_{\rm tr}, s\_{\rm tr}} [ (\boldsymbol{\tau} - \boldsymbol{\sigma}) \delta\_{\mathfrak{m}\_{\rm tr}, \mathfrak{m}\_{\rm c} + \mathfrak{r}} \boldsymbol{R}\_{-\boldsymbol{\sigma}} + (\boldsymbol{\tau} + \boldsymbol{\sigma}) \delta\_{\mathfrak{m}\_{\rm c}, \mathfrak{m}\_{\rm c} + \mathfrak{r}} \boldsymbol{R}\_{\rm d} ] \rangle\_{\rm \prime} \tag{52}
$$

where szv (szc) denote the valence (conduction) band spin state, R�<sup>σ</sup> ¼ ðR 0 b� <sup>c</sup> avrdr and R<sup>σ</sup> ¼ ðR 0 a� <sup>c</sup> bvrdr with ac=<sup>v</sup> and bc=<sup>v</sup> the radial components of the conduction/valence band spinor. The selection rule for optical transitions in TMDC QDs is defined by mv � mc ¼ �τ and szv ¼ szc, i.e., the angular momentum of the initial and final states differs by �1, but the spin of these two states is the same. The magnitude of transition rates is determined by the integral R�<sup>σ</sup> and R<sup>σ</sup> for the transitions taking place in the valley τ ¼ �σ and σ, respectively. Since jacðrÞj > jbcðrÞj and javðrÞj < jbvðrÞj, the integral R�<sup>σ</sup> is much smaller than the Rσ. As a

Figure 20. Schematic of a monolayer MoS2 circular quantum dot with radius R indicated by a red circle, excited by a light field. A magnetic field B is applied perpendicularly to the MoS2 sheet [15]. (Copyright 2017 by the Nature Publishing Group. Reprinted with permission).

consequence, the absorption in the valley τ ¼ σ is stronger than that in the τ ¼ �σ, which leads to a valley selected absorption. In a special case in which one component of the wave function spinor is equal to zero such as nll ¼ 0 LL, only photons with the helicity σ ¼ τ is absorbed. Then, one obtains a dichroism η ¼ 1. For the linear polarized light, however, there is no valley polarization in the absorption spectrum, in contrast to the case of CPL [15].

for Landau levels with the same quantum number. However, for usual experimental setups, these effects in the vicinity of the K or K<sup>0</sup> valley in which we are interested play a minor role.

MoS2 QD with radius R ¼ 70 nm, as a function of the magnetic field along both positive and negative ^z–direction, for angular momentum m ¼ 0 (red curves), �1 (pink curves), 1 (green curves), �2 (black curves), and 2 (blue curves).

In the QDs as demonstrated in Figure 20, the optical transition matrix elements in the QDs are

<sup>c</sup> bvrdr with ac=<sup>v</sup> and bc=<sup>v</sup> the radial components of the conduction/valence band spinor.

The selection rule for optical transitions in TMDC QDs is defined by mv � mc ¼ �τ and szv ¼ szc, i.e., the angular momentum of the initial and final states differs by �1, but the spin of these two states is the same. The magnitude of transition rates is determined by the integral R�<sup>σ</sup> and R<sup>σ</sup> for the transitions taking place in the valley τ ¼ �σ and σ, respectively. Since jacðrÞj > jbcðrÞj and javðrÞj < jbvðrÞj, the integral R�<sup>σ</sup> is much smaller than the Rσ. As a

δszv,szc ðτ � σÞδmv,mcþ<sup>τ</sup>R�<sup>σ</sup> þ ðτ þ σÞδmc ½ � ,mvþ<sup>τ</sup>RσÞ , (52)

ðR 0 b�


<sup>c</sup> avrdr and

Hence it can be safely neglected.

134 Quantum-dot Based Light-emitting Diodes

〈ΨcjH<sup>L</sup>�<sup>M</sup>jΨv〉 <sup>¼</sup> <sup>π</sup>A<sup>0</sup>

computed by,

ðR 0 a�

R<sup>σ</sup> ¼

2.8. Optical selection rules in monolayer MoS2 quantum dots

Figure 19. Energy spectrum of the states with spin-up in the K-valley (a) and spindown in the K<sup>0</sup>

ℏ � �

where szv (szc) denote the valence (conduction) band spin state, R�<sup>σ</sup> ¼

In the 2D bulk MoS2, the bottom of the conduction band at the two valleys is characterized by the orbital angular momentum m ¼ 0. In contrast, at the top of the valence band, the orbitals with m ¼ 2 in the K-valley, whereas m is equal to �2 in the K<sup>0</sup> -valley. The valley dependent angular momentum in the valence band allows one to address different valleys by controlling the photon angular momentum, i.e., the helicity of the CP light. Such valley-specific circular dichroism of interband transitions in the 2D bulk has been confirmed [19, 43, 44]. The question is whether its counterpart QD also possesses this exotic optical property. Figure 21(a, b) depict zero-field band-edge optical absorption spectrum of a 70-nm dot pumped by the CP light field. Interestingly, one notices that (i) the polarization of the absorption spectrum is locked with the valley degree of freedom, manifested by the intensity of absorption spectrum with σ ¼ τ being about 106 times stronger than that with σ ¼ τ, and (ii) the spectrum is spin-polarized. Thus, the QDs indeed inherit the valley and spin dependent optical selection rule from their counterpart of 2D bulk MoS2. In spite of the distinction in the spin- and valley-polarization of absorption spectra in the distinct valleys, their patterns are the same required by the time reversal symmetry. In Figure 21(c, f) we show the zero-field optical absorption spectrum as a function of excitation energy for several values of dot-radius within R ¼ 20–80 nm. The involved transitions in Figure 21(c, f) lagged by the numbers have been schematically illustrated in Figure 21(g). Alike conventional semiconductor QDs, several peaks stemmed from discrete excitations of

Figure 21. Zero-field optical absorption spectrum associated with interband transitions between conduction and valenceband ground states of a 70-nm MoS2 dot for the spin-up state in the K-valley (a) and for the spin-down state in the K<sup>0</sup> valley (b), pumped by both clockwise (σþ, blue curve) and anticlockwise (σ�, red curve) circularly polarized light fields. (c–f) Absorption intensity for the spin-down state in the K<sup>0</sup> -valley under the excitation of σ�, for QDs of R ¼ 20, 35, 50, and 80 nm, respectively. (g) Schematic diagram of the involved interband transitions in (c-f) tagged by the numbers. The color of the curves is used to highlight the principle quantum number (n) of transition involved states [15]. (Copyright 2015 by the Nature Publishing Group. Reprinted with permission).

the MoS2 QD are observed. As the dot size decreases, the peaks of absorption spectrum undergo a blue shift. In other words, a reduction of the dot size pushes the electron excitations to take place between higher energy states, as a result of the enhancement of the confinement on carriers induced by a shrink of the dot. Therefore, the spin-coupled valley selective absorption with a tunable transition frequency can be achieved in QDs by varying dot geometry, in contrast to the 2D bulk where a fixed transition frequency is uniquely determined by the bulk band structure. In addition to the blue shift of the transition frequency, the absorption intensity can also be controlled by dot geometry due to size dependence of the peak interval. In fact, an increasing of dot size results in a reduction of the energy separation among confined states. Thus, as the dot size increases, the absorption peaks get closer and closer, see Figure 21(c–f). Eventually, several individual absorption peaks merge together to yield a single compositepeak with an enhanced intensity. For instance, for the 20-nm dot (Figure 21c), the lowest energy peak is generated by only one transition, labeled by (1) (see also Figure 21g). However, for the dot with R ¼ 80nm, we observe a highly enhanced absorption intensity labeled by ð Þ 1 þ 2 þ 3 , which in the 20-nm dot refers to three separated peaks with weak absorption intensities indicated by (1), (2), (3), respectively.

#### 2.9. Magneto-optical properties of monolayer MoS2 quantum dots

With the knowledge of the energy spectrum and eigenfunctions of the QD, we are ready to study its magneto-optical properties. The optical transition matrix in Eq. 27 is applicable to the current case provided that we use newly obtained wavefunctions presented in Eq. 47 and Eq. 48.

Figure 22 shows the magneto-optical absorption spectra for the spin-down states in the K<sup>0</sup> valley of a monolayer MoS2 QD with R ¼ 40 nm excited by left-hand circularly polarized

the MoS2 QD are observed. As the dot size decreases, the peaks of absorption spectrum undergo a blue shift. In other words, a reduction of the dot size pushes the electron excitations to take place between higher energy states, as a result of the enhancement of the confinement on carriers induced by a shrink of the dot. Therefore, the spin-coupled valley selective absorption with a tunable transition frequency can be achieved in QDs by varying dot geometry, in contrast to the 2D bulk where a fixed transition frequency is uniquely determined by the bulk band structure. In addition to the blue shift of the transition frequency, the absorption intensity can also be controlled by dot geometry due to size dependence of the peak interval. In fact, an increasing of dot size results in a reduction of the energy separation among confined states. Thus, as the dot size increases, the absorption peaks get closer and closer, see Figure 21(c–f). Eventually, several individual absorption peaks merge together to yield a single compositepeak with an enhanced intensity. For instance, for the 20-nm dot (Figure 21c), the lowest energy peak is generated by only one transition, labeled by (1) (see also Figure 21g). However, for the dot with R ¼ 80nm, we observe a highly enhanced absorption intensity labeled by

Figure 21. Zero-field optical absorption spectrum associated with interband transitions between conduction and valenceband ground states of a 70-nm MoS2 dot for the spin-up state in the K-valley (a) and for the spin-down state in the K<sup>0</sup>

valley (b), pumped by both clockwise (σþ, blue curve) and anticlockwise (σ�, red curve) circularly polarized light fields.

and 80 nm, respectively. (g) Schematic diagram of the involved interband transitions in (c-f) tagged by the numbers. The color of the curves is used to highlight the principle quantum number (n) of transition involved states [15]. (Copyright


(c–f) Absorption intensity for the spin-down state in the K<sup>0</sup>

136 Quantum-dot Based Light-emitting Diodes

2015 by the Nature Publishing Group. Reprinted with permission).


Figure 22. Absorption spectrum for the spin-down states in the K<sup>0</sup> -valley of a monolayer MoS2 QD with R ¼ 40 nm excited by left-hand circularly polarized light σ�, at the magnetic field B ¼ 0 (a), 2T (b), 10T (c), 15T (d), respectively. The corresponding enumerated optical transitions are schematically shown in Figure 21(g) [15]. (Copyright 2015 by the Nature Publishing Group. Reprinted with permission).

light σ�, for several values of magnetic field ranging from 0 to 15 T. A few interesting features are observed. Firstly, the magneto-optical absorption is also spin- and valley-dependent, as it does in optical absorption spectrum at zero field. In particular the lowest transition energy absorption peak related to the interband transition involving nll ¼ 0 LL is totally valley polarized with dichroism equal to 1. Thus, the polarization of magneto-optical absorption locks with the valley. Secondly, for a fixed value of dot size, increasing (decreasing) the strength of the magnetic field results in a blue (red) shift in the absorption spectrum. This arises from the fact that the magnetic field induces an effective confinement characterized by the magnetic length lB <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffi ℏ=eB p , which is more pronounced for a stronger magnetic field. In addition, the magnetic quantization induced by the magnetic field favors the QD to absorb photons with higher energies. The stronger the magnetic field, the greater the capacity of the QDs to absorb the photons of higher energy. Thirdly, in the high magnetic-field regime the absorption intensity can be highly enhanced by increasing the strength of magnetic field due to increased degeneracy of the LLs.

#### 2.10. Excitonic effect in monolayer MoS2 quantum dots

The optical and magneto-optical absorptions that we have discussed so far are based on the independent electron-hole picture. In reality, there is a strong Coulomb interaction between the electron and hole in MoS2. The full treatment of the Coulomb interaction using manybody theory is beyond the scope of this chapter. However, the excitonic effects in absorption spectrum of the monolayer MoS2 QDs can be properly addressed by an exact diagonalization, which is adopted in this work. The Hamiltonian used to describe the exciton is, <sup>H</sup>ðre,rhÞ ¼ <sup>H</sup>eðreÞ þ <sup>H</sup>hðrhÞ þ <sup>V</sup><sup>e</sup>�<sup>h</sup>ðr<sup>e</sup> � <sup>r</sup>hÞ, where <sup>H</sup><sup>e</sup>ðh<sup>Þ</sup> is the single electron (hole) Hamiltonian in QDs (see Eq. 1) and V<sup>e</sup>�<sup>h</sup> is the electron-hole Coulomb interaction given by <sup>V</sup><sup>e</sup>�<sup>h</sup>ðjr<sup>e</sup> � <sup>r</sup>hjÞ ¼ ð1=4πErE0Þðe<sup>2</sup>=jr<sup>e</sup> � <sup>r</sup>hjÞ. Here <sup>E</sup><sup>0</sup> is the permittivity, <sup>E</sup><sup>r</sup> is the dielectric constant, and r<sup>e</sup> and r<sup>h</sup> respectively stand for the position of electron and hole. An exciton can be understood as a coherent combination of electron-hole pairs. Thus, the wavefunctions of an exciton can be constructed based on a direct product of single-particle wave functions for the electron and hole. Since the electron-hole Coulomb interaction is larger than or at least in the same magnitude as the quantum confinement in the MoS2 QDs, the excitonic effect play an very important role. Hence the single-particle wavefunctions should be modified due to the presence of the Coulomb interaction. Therefore, to get quick convergence of numerical calculation, instead of using simple single-particle wavefunction, we use the modified one to construct the exciton states, i.e., χjðre,hÞ ¼ N exp ð�re, <sup>h</sup>=rbÞΨjðre, <sup>h</sup>Þ, where the exponential factor is a hydrogen-like s-wave state, N is the normalization constant, Ψ<sup>j</sup> is the wave function of the Hamiltonian H<sup>e</sup>;h, and rb is the exciton bohr radius, which has the value of rb � 1 nm in MoS2 [24]. Then, the exciton wave function Ψexc can be straightforwardly written as,

$$\Psi\_{\rm acc}^{\nu}(\mathbf{r}\_{\rm e}, \mathbf{r}\_{\rm h}) = \sum\_{i,j} \mathbf{C}\_{i,j}^{\nu} \ \chi\_i(\mathbf{r}\_{\rm e}) \ \chi\_j(\mathbf{r}\_{\rm h}) . \tag{54}$$

with the superscript ν referring to the ν-th exciton state. Within the Hilbert space made of states of electron-hole pairs {χiðreÞχjðrhÞ}, the matrix element of Coulomb integral reads,

$$\mathcal{V}\_{prsq}^{\text{e-h}} = -\frac{e^2}{4\pi\epsilon\_0\epsilon\_r} \left[ \int \frac{\chi\_p^\*(\mathbf{r\_e})\chi\_r^\*(\mathbf{r\_h})\chi\_s(\mathbf{r\_h})\chi\_q(\mathbf{r\_e})}{|\mathbf{r\_e} - \mathbf{r\_h}|} d\mathbf{r\_e} d\mathbf{r\_h} \right. \tag{55}$$

which involves the wave function χ<sup>i</sup> of the electron and hole in the absence of Coulomb interaction, with j ¼ p, r, s, q indicating the state index. We should emphasize that Eq. 55 contains both the direct interaction between the electron and hole, i.e., Eq. 55 at p ¼ q and r ¼ s,

$$V\_{prp}^{\text{e}-\text{h,dir}} = -\frac{e^2}{4\pi\epsilon\_0\epsilon\_r} \left\{ \left| \frac{|\chi\_p(\mathbf{r\_e})|^2 |\chi\_r(\mathbf{r\_h})|^2}{|\mathbf{r\_e} - \mathbf{r\_h}|} d\mathbf{r\_e} d\mathbf{r\_h} \right. \tag{56} \right. \tag{57}$$

and the exchange interaction, i.e., Eq. 55 at s ¼ p and r ¼ q,

light σ�, for several values of magnetic field ranging from 0 to 15 T. A few interesting features are observed. Firstly, the magneto-optical absorption is also spin- and valley-dependent, as it does in optical absorption spectrum at zero field. In particular the lowest transition energy absorption peak related to the interband transition involving nll ¼ 0 LL is totally valley polarized with dichroism equal to 1. Thus, the polarization of magneto-optical absorption locks with the valley. Secondly, for a fixed value of dot size, increasing (decreasing) the strength of the magnetic field results in a blue (red) shift in the absorption spectrum. This arises from the fact that the magnetic field induces an effective confinement characterized by the magnetic

magnetic quantization induced by the magnetic field favors the QD to absorb photons with higher energies. The stronger the magnetic field, the greater the capacity of the QDs to absorb the photons of higher energy. Thirdly, in the high magnetic-field regime the absorption intensity can be highly enhanced by increasing the strength of magnetic field due to increased

The optical and magneto-optical absorptions that we have discussed so far are based on the independent electron-hole picture. In reality, there is a strong Coulomb interaction between the electron and hole in MoS2. The full treatment of the Coulomb interaction using manybody theory is beyond the scope of this chapter. However, the excitonic effects in absorption spectrum of the monolayer MoS2 QDs can be properly addressed by an exact diagonalization, which is adopted in this work. The Hamiltonian used to describe the exciton is, <sup>H</sup>ðre,rhÞ ¼ <sup>H</sup>eðreÞ þ <sup>H</sup>hðrhÞ þ <sup>V</sup><sup>e</sup>�<sup>h</sup>ðr<sup>e</sup> � <sup>r</sup>hÞ, where <sup>H</sup><sup>e</sup>ðh<sup>Þ</sup> is the single electron (hole) Hamiltonian in QDs (see Eq. 1) and V<sup>e</sup>�<sup>h</sup> is the electron-hole Coulomb interaction given by <sup>V</sup><sup>e</sup>�<sup>h</sup>ðjr<sup>e</sup> � <sup>r</sup>hjÞ ¼ ð1=4πErE0Þðe<sup>2</sup>=jr<sup>e</sup> � <sup>r</sup>hjÞ. Here <sup>E</sup><sup>0</sup> is the permittivity, <sup>E</sup><sup>r</sup> is the dielectric constant, and r<sup>e</sup> and r<sup>h</sup> respectively stand for the position of electron and hole. An exciton can be understood as a coherent combination of electron-hole pairs. Thus, the wavefunctions of an exciton can be constructed based on a direct product of single-particle wave functions for the electron and hole. Since the electron-hole Coulomb interaction is larger than or at least in the same magnitude as the quantum confinement in the MoS2 QDs, the excitonic effect play an very important role. Hence the single-particle wavefunctions should be modified due to the presence of the Coulomb interaction. Therefore, to get quick convergence of numerical calculation, instead of using simple single-particle wavefunction, we use the modified one to construct the exciton states, i.e., χjðre,hÞ ¼ N exp ð�re, <sup>h</sup>=rbÞΨjðre, <sup>h</sup>Þ, where the exponential factor is a hydrogen-like s-wave state, N is the normalization constant, Ψ<sup>j</sup> is the wave function of the Hamiltonian H<sup>e</sup>;h, and rb is the exciton bohr radius, which has the value of rb � 1 nm in MoS2 [24]. Then, the exciton wave function Ψexc can be straightforwardly

ℏ=eB p , which is more pronounced for a stronger magnetic field. In addition, the

length lB <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffi

138 Quantum-dot Based Light-emitting Diodes

degeneracy of the LLs.

written as,

2.10. Excitonic effect in monolayer MoS2 quantum dots

Ψ<sup>ν</sup>

excðre,rhÞ ¼ <sup>X</sup>

i, j Cν

i,j χiðreÞ χjðrhÞ, (54)

$$V\_{prpr}^{\rm e-h,ex} = -\frac{e^2}{4\pi\epsilon\_0\epsilon\_r} \left[ \int \frac{\chi\_p^\*(\mathbf{r\_e})\chi\_r^\*(\mathbf{r\_h})\chi\_p(\mathbf{r\_h})\chi\_r(\mathbf{r\_e})}{|\mathbf{r\_e} - \mathbf{r\_h}|} d\mathbf{r\_e} d\mathbf{r\_h}.\tag{57}$$

To calculate Coulomb interaction defined in Eq. 55, we expand 1=jr<sup>e</sup> � rhj in terms of halfinteger Legendre function of the second kind Qm�1=2, i.e.,

$$\frac{1}{|\mathbf{r}\_{\mathbf{e}} - \mathbf{r}\_{\mathbf{h}}|} = \frac{1}{\pi \sqrt{r\_{\mathbf{e}} r\_{\mathbf{h}}}} \sum\_{m=0}^{\bullet} \epsilon\_{m} \cos \left[ m (\Theta\_{\mathbf{e}} - \Theta\_{\mathbf{h}}) \right] Q\_{m - 1/2}(\xi), \tag{58}$$

which is widely used in many-body calculations [45]. Here θ<sup>e</sup>ðh<sup>Þ</sup> is the polar angle of the position vector <sup>r</sup><sup>e</sup>ðh<sup>Þ</sup> in the 2D plane of MoS2, <sup>ξ</sup> ¼ ðr<sup>2</sup> <sup>e</sup> <sup>þ</sup> <sup>r</sup><sup>2</sup> <sup>h</sup>Þ=2rerh, E<sup>m</sup> ¼ 1 for m ¼ 0 and E<sup>m</sup> ¼ 2 for m 6¼ 0. The exciton energy and the corresponding wavefunction can be obtained by diagonalization of the matrix of many-particle Hamiltonian Hðre,rhÞ. With the exciton state at hand (Eq. 54), we are ready to the determine the excitonic absorption involving a transition from the ground state j0〉 to exciton state jf〉 ¼ jΨexc〉,

$$A(\omega) = \sum\_{f} |\langle 0 \mathcal{P} | f \rangle| \,\delta \{ \hbar \omega - E\_{\text{exc}}^{\prime} \}\_{\prime} \tag{59}$$

where E<sup>ν</sup> exc and ℏω are the exciton- and photon-energy, respectively, and <sup>P</sup> <sup>¼</sup> <sup>X</sup> i, j δsz,sz0〈χijH<sup>L</sup>�<sup>M</sup>jχj〉 ai,sz hj,sz<sup>0</sup> is the polarization operator, with ai,sz and hj,sz<sup>0</sup> being the electron and hole annihilation operators. After straightforward calculation, we finally obtain

$$A(\omega) = \sum\_{\nu} \left( \delta\_{sz,sz'} \sum\_{i,j} \mathbf{C}\_{i,j}^{\nu} \langle \chi\_i | \mathcal{H}\_{L-M} | \chi\_j \rangle \right) \delta \{\hbar \omega - E\_{exc}^{\nu} \}. \tag{60}$$

Figure 23. Excitonic effects on zero-field optical absorption spectra for the spin-down states in the K<sup>0</sup> -valley of monolayer MoS2 QD with R ¼ 20 nm (a), 35 nm (b), 50 nm (c), and 80 nm (d) under the excitation of the left-hand circularly polarized light σ�. The Fermi energy is chosen as 0. The vertical dashed line separates two distinct regions of the absorption spectrum: left-hand side for excitonic absorption and right-hand side for single-particle like absorption. To be consistent with the experimental report of excitonic absorption energy, a right shift of photon energy of 700 meV is made [15]. (Copyright 2015 by the Nature Publishing Group. Reprinted with permission.)

In our numerical calculations, we have used five modified single-particle basis functions with angular momentum ranging from �2.5 to 1.5. Figure 23 shows that there is an exciton absorption peak located at around 550 meV (i.e., exciton binding energy) below the band-edge absorption. And, the excitonic absorption peak shifts monotonically to higher absorption energy as the dot size is increased. Above the band gap, however, the spectrum is similar to what we found in previous sections in the band-to-band transitions using the independent electron-hole model. Since the exciton absorption peak is far away from the band-edge absorption, one can in principle study them separately. And, the Coulomb interaction between electron-hole pair does not change the valley selectivity and our general conclusion. Finally, it is worth to remarking that one can shift the excitonic absorption peak to a higher absorption energy, by varying the band gap parameter (Δ) in our model Hamiltonian.

#### Author details

Fanyao Qu1 \*, Alexandre Cavalheiro Dias<sup>1</sup> , Antonio Luciano de Almeida Fonseca<sup>1</sup> , Marco Cezar Barbosa Fernandes<sup>1</sup> and Xiangmu Kong<sup>2</sup>

\*Address all correspondence to: fanyao@unb.br


#### References

In our numerical calculations, we have used five modified single-particle basis functions with angular momentum ranging from �2.5 to 1.5. Figure 23 shows that there is an exciton absorption peak located at around 550 meV (i.e., exciton binding energy) below the band-edge absorption. And, the excitonic absorption peak shifts monotonically to higher absorption energy as the dot size is increased. Above the band gap, however, the spectrum is similar to what we found in previous sections in the band-to-band transitions using the independent electron-hole model. Since the exciton absorption peak is far away from the band-edge absorption, one can in principle study them separately. And, the Coulomb interaction between electron-hole pair does not change the valley selectivity and our general conclusion. Finally, it is worth to remarking that one can shift the excitonic absorption peak to a higher absorption energy, by varying the band gap parameter

MoS2 QD with R ¼ 20 nm (a), 35 nm (b), 50 nm (c), and 80 nm (d) under the excitation of the left-hand circularly polarized light σ�. The Fermi energy is chosen as 0. The vertical dashed line separates two distinct regions of the absorption spectrum: left-hand side for excitonic absorption and right-hand side for single-particle like absorption. To be consistent with the experimental report of excitonic absorption energy, a right shift of photon energy of 700 meV is made [15].


Figure 23. Excitonic effects on zero-field optical absorption spectra for the spin-down states in the K<sup>0</sup>

(Copyright 2015 by the Nature Publishing Group. Reprinted with permission.)

(Δ) in our model Hamiltonian.

140 Quantum-dot Based Light-emitting Diodes


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**Provisional chapter**

## **Widely Tunable Quantum-Dot Source Around 3 μm**

**Widely Tunable Quantum-Dot Source Around 3 μm**

DOI: 10.5772/intechopen.70753

Alice Bernard, Marco Ravaro, Jean-Michel Gerard, Michel Krakowski, Olivier Parillaud, Bruno Gérard, Ivan Favero and Giuseppe Leo Michel Krakowski, Olivier Parillaud, Bruno Gérard, Ivan Favero and Giuseppe Leo Additional information is available at the end of the chapter

Alice Bernard, Marco Ravaro, Jean-Michel Gerard,

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70753

#### **Abstract**

We propose a widely tunable parametric source in the 3 μm range, based on intracavity spontaneous parametric down conversion (SPDC) of a quantum-dot (QD) laser emitting at 1.55 μm into signal and idler modes around 3.11 μm. To compensate for material dispersion, we engineer the laser structure to emit in a higher-order transverse mode of the waveguide. The width of the latter is used as a degree of freedom to reach phase matching in narrow, deeply etched ridges, where the in-plane confinement of the QDs avoids nonradiative sidewall electron-hole recombination. Since this design depends critically on the knowledge of the refractive index of In1−xGax Asy P1−y lattice matched to InP at wavelengths where no data are available in the literature, we have accurately determined them as a function of wavelength (λ = 1.55, 2.12 and 3 μm) and arsenic molar fraction (y = 0.55, 0.7 and 0.72) with a precision of ±4 × 10−3. A pair of dichroic dielectric mirrors on the waveguide facets is shown to result in a continuous-wave optical parametric oscillator (OPO), with a threshold around 60 mW. Emission is tunable over hundreds of nanometers and expected to achieve mW levels.

**Keywords:** quantum dots, laser diode, near infrared, InGaAsP, tunable source, OPO

#### **1. Introduction**

The tunability of currently available integrated sources is limited to a few tens of nanometers at most, via temperature or current control. While this is not a problem for most applications, certain fields like wavelength division multiplexing and spectroscopy are in demand of sources with broader tunability and choice of spectral range. Spectroscopy, especially, requires wideband, continuously tunable sources with narrow emission lines. The 2–4 μm wavelength interval

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

is of particular interest since it contains various peaks of atmospheric and hydrocarbon molecules, with important applications in environmental monitoring, security, and medicine [1–4]. This spectral region is at the frontier between the emission ranges of diodes and quantum cascade lasers (QCLs), and to date most existing sources around 3 μm, such as short-wavelength QCLs [5, 6] or GaSb diodes [7], are only available in laboratories. Interband cascade lasers (ICLs) are the only sources commercially available in this wavelength range, albeit at a high price [8– 10]. Moreover, the tunability range of all these devices is limited to a few tens of nanometers. As a consequence, individual laser diodes are used for each spectroscopic line of absorption, which increases the price of a complete diagnosis based on several lines. In this context, nonlinear optics offers a solution for widely wavelength tunable sources, bulky tabletop optical parametric oscillators (OPOs) being commonly used to provide high-quality, tunable beams. Most miniaturized OPOs have been demonstrated in LiNbO3 [11, 12], but an OPO threshold has been achieved in a GaAs micrometric waveguide [13] with a potential span of 500 nm. Like GaAs, InP is an attractive material for its high χ(2) and mature technology, especially for emission at 1.55 μm.

Here we report on the design of an InGaAsP/InP QD laser diode emitting at 1.55 μm, optimized for intracavity spontaneous parametric down conversion (SPDC) around 3.11 μm via modal phase matching. The use of QDs is justified by the choice of narrow, deeply etched structures insofar they have been shown to trap carriers and limit surface recombination [14], and narrow-ridge, low-threshold InAs/InP QD lasers have already been demonstrated [15]. In order to estimate the phase mismatch accurately, a precise knowledge of the refractive indices is critical at pump, signal, and idler wavelengths. While the index of InGaAsP lattice matched to InP is well known at 1.55 μm [16–20], to date only one publication deals with its measurement at longer wavelengths [21], and none exists at 3 μm. This makes it crucial to accurately characterize its refractive index up to 3.14 μm, outside of the scope covered by literature data.

#### **2. Tunable source design**

#### **2.1. Laser diode design**

We propose a 1.55 μm source optimized for SPDC around 3.11 μm. This design results from back-and-forth optimizations between optical and electrical simulations, to jointly facilitate electron-hole injection, increase the conversion efficiency, and reduce losses. The conduction band and composition profile of this structure are shown in **Figure 1**. To compensate for the material dispersion, the laser diode is conceived so as to favor lasing on the TE20 mode (the second order in the direction of growth). To achieve this, the refractive index kept small in the center of the waveguide. As a consequence, the TE20 mode confinement inside the active area is stronger than for the TE00 mode. **Figure 2** shows the modes TE00 and TE20 supported by the waveguide at a wavelength of 1.55 μm. In order to achieve an efficient electron injection despite the conduction band increase in the core center, we reduce the series resistance with two strategies. Firstly, we introduce compositional gradients at the interfaces. Secondly, the waveguide core is only lightly doped. **Figure 3** depicts the conduction band and doping profile of the structure. An electrical simulation of this device using the software Nextnano yields a transparency current of 26 A/cm2 at the transparency threshold.

**Figure 1.** Conduction band and composition profile of the structure.

**Figure 2.** The first two even modes supported by the waveguide at λ = 1.55 μm.

#### **2.2. Nonlinear properties**

is of particular interest since it contains various peaks of atmospheric and hydrocarbon molecules, with important applications in environmental monitoring, security, and medicine [1–4]. This spectral region is at the frontier between the emission ranges of diodes and quantum cascade lasers (QCLs), and to date most existing sources around 3 μm, such as short-wavelength QCLs [5, 6] or GaSb diodes [7], are only available in laboratories. Interband cascade lasers (ICLs) are the only sources commercially available in this wavelength range, albeit at a high price [8– 10]. Moreover, the tunability range of all these devices is limited to a few tens of nanometers. As a consequence, individual laser diodes are used for each spectroscopic line of absorption, which increases the price of a complete diagnosis based on several lines. In this context, nonlinear optics offers a solution for widely wavelength tunable sources, bulky tabletop optical parametric oscillators (OPOs) being commonly used to provide high-quality, tunable beams. Most miniaturized

GaAs micrometric waveguide [13] with a potential span of 500 nm. Like GaAs, InP is an attrac-

Here we report on the design of an InGaAsP/InP QD laser diode emitting at 1.55 μm, optimized for intracavity spontaneous parametric down conversion (SPDC) around 3.11 μm via modal phase matching. The use of QDs is justified by the choice of narrow, deeply etched structures insofar they have been shown to trap carriers and limit surface recombination [14], and narrow-ridge, low-threshold InAs/InP QD lasers have already been demonstrated [15]. In order to estimate the phase mismatch accurately, a precise knowledge of the refractive indices is critical at pump, signal, and idler wavelengths. While the index of InGaAsP lattice matched to InP is well known at 1.55 μm [16–20], to date only one publication deals with its measurement at longer wavelengths [21], and none exists at 3 μm. This makes it crucial to accurately characterize its refractive index up to 3.14 μm, outside of the scope covered by

We propose a 1.55 μm source optimized for SPDC around 3.11 μm. This design results from back-and-forth optimizations between optical and electrical simulations, to jointly facilitate electron-hole injection, increase the conversion efficiency, and reduce losses. The conduction band and composition profile of this structure are shown in **Figure 1**. To compensate for the material dispersion, the laser diode is conceived so as to favor lasing on the TE20 mode (the second order in the direction of growth). To achieve this, the refractive index kept small in the center of the waveguide. As a consequence, the TE20 mode confinement inside the active area is stronger than for the TE00 mode. **Figure 2** shows the modes TE00 and TE20 supported by the waveguide at a wavelength of 1.55 μm. In order to achieve an efficient electron injection despite the conduction band increase in the core center, we reduce the series resistance with two strategies. Firstly, we introduce compositional gradients at the interfaces. Secondly, the waveguide core is only lightly doped. **Figure 3** depicts the conduction band and doping profile of the structure. An electrical simulation of this device using the software Nextnano yields

at the transparency threshold.

tive material for its high χ(2) and mature technology, especially for emission at 1.55 μm.

[11, 12], but an OPO threshold has been achieved in a

OPOs have been demonstrated in LiNbO3

146 Quantum-dot Based Light-emitting Diodes

literature data.

**2. Tunable source design**

a transparency current of 26 A/cm2

**2.1. Laser diode design**

To achieve Type-II phase matching despite the error bars on the dispersion model and the fabrication tolerances, we use the ridge width as a crucial degree of freedom. **Figure 4** shows the phase mismatch at degeneracy vs. ridge width and pump wavelength, defined as

$$\Delta \mathbf{n} = \mathbf{n} \left( \mathbf{T} \mathbf{E}\_{\text{av}} \, 1.55 \,\upmu \mathbf{m} \right) - \left[ \mathbf{n} \left( \mathbf{T} \mathbf{E}\_{\text{av}} \, 3.11 \,\upmu \mathbf{m} \right) + \mathbf{n} \left( \mathbf{T} \mathbf{M}\_{\text{av}} \, 3.11 \,\upmu \mathbf{m} \right) \right] \Big| \tag{1}$$

where the refractive indices are provided by our experimental data, presented in Part 2, and an interpolation of literature data [20]. By changing the ridge width from 3 to 7 μm, we are able to achieve phase matching for pump wavelengths of 1.50–1.60 μm. Furthermore, a variation in phase mismatch of ±0.02 can be compensated for by setting the correct ridge size. The ridge width thus acts as a gross parameter to meet the phase-matching condition, which can be set after wafers have been grown and characterized.

During operation, temperature provides a supplementary degree of freedom to tune the pump wavelength and reach a wide range of frequencies. **Figure 5** shows the wavelengths

**Figure 3.** Conduction band and doping profile of the structure.

**Figure 4.** Phase mismatch in a deeply etched structure vs. ridge width and pump wavelength.

**Figure 5.** Emitted wavelengths for a device of ridge width 3.3 μm, emitting at 1.55 μm at 20°C.

ridge width thus acts as a gross parameter to meet the phase-matching condition, which can

During operation, temperature provides a supplementary degree of freedom to tune the pump wavelength and reach a wide range of frequencies. **Figure 5** shows the wavelengths

be set after wafers have been grown and characterized.

148 Quantum-dot Based Light-emitting Diodes

**Figure 3.** Conduction band and doping profile of the structure.

**Figure 4.** Phase mismatch in a deeply etched structure vs. ridge width and pump wavelength.

of signal and idler emitted beams, for a source of ridge width 3.3 μm, emitting at a pump wavelength of 1.55 μm at 20°C. The dependency of quantum dots wavelength emission with temperature was assumed to be 0.5 nm/K from [22].

**Figure 6** shows the profiles of the interacting modes, at a pump wavelength of 1.55 μm and signal and idler 3.11 μm. The expected conversion efficiency at a pump wavelength of 1.55 μm is 240% W−1 cm−2. For an intracavity power of 100 mW, this corresponds to a parametric gain of 0.5 cm−1. Since common InP QD lasers at 1.55 μm emit up to 20 mW outside the cavity without facet coatings [23], the above hypothesis on the intracavity power is very reasonable. The losses experimented by the mode at 3.11 μm are mainly expected to stem from free-carrier

**Figure 6.** Field intensity of the three interacting modes in the SPDC process, at a pump wavelength of 1.55 μm.

**Figure 7.** Intracavity pump power necessary for OPO threshold, vs. ridge length, for a few values of facet reflectivities.

absorption in doped layers, which we estimate at about 0.34 cm−1 for the TE00 mode. Reaching the OPO threshold in this device is therefore a challenging but achievable task, if mirror losses are minimized as in [13]. **Figure 7** shows the intracavity pump power necessary to reach oscillation for different mirror reflectivities and cavity lengths, assuming a conversion efficiency of 240%W−1 cm−2 and propagation losses of 0.34 cm−1.

#### **3. Index measurement**

#### **3.1. Principle**

The evaluation of refractive indices was performed through an m-lines setup. This measurement relies on the determination of the coupling angle inside a slab waveguide of the material of interest. Our samples consist of a layer of In1-xGax AsyP1-y lattice matched to InP grown over InP. As a result of the index contrast, the quaternary alloy acts as a planar waveguide. A diffraction grating was deposited or etched on the surface. The samples are mounted vertically on a rotating mount, and a laser is shone horizontally on the grating (**Figure 8**). Whenever the angle of light diffracted into the surface layer matches the bounce angle of a guided mode, coupling occurs. The guided light is collected by a detector placed at the exit facet of the sample. Coupling angles are given by the conservation of momentum

$$\left\| \overrightarrow{k\_n} \right\| \sin \left( \Theta \right) = \left\| \overrightarrow{k\_n} \right\| + m \left\| \overrightarrow{k\_s} \right\| \tag{2}$$

where

‖→*k in*‖ is the wave vector of the incident light, ‖→*<sup>k</sup> <sup>m</sup>*‖ is the wave vector of the mth guided mode, and ‖→*<sup>k</sup> <sup>g</sup>*‖ is the vector associated to the grating, of amplitude 2π/Λ (Λ being the period) and direction perpendicular to the grating lines, in the grating plane.

This equation leads to

$$N = \sin\left(\Theta\right) + m\,\lambda/\Lambda\tag{3}$$

where N is the effective index of the mth propagating mode. This measurement therefore estimates precisely the effective indices of the guided modes, as long as the period, wavelength, and coupling angles are known.

#### **3.2. Sample fabrication**

The planar structures were grown by molecular beam epitaxy and characterized by X-ray diffraction and photoluminescence prior to processing. An electronic resist with average thickness 70 nm was deposited on the surface (MAN2401 spin coated at 6000 rpm), and diffraction gratings were written by electronic lithography. The samples were then either used as such or very shallowly etched in a chemical solution before removing the resist. Both methods lead to shallow gratings on the guiding layer surface.

#### **3.3. Optical setup**

absorption in doped layers, which we estimate at about 0.34 cm−1 for the TE00 mode. Reaching the OPO threshold in this device is therefore a challenging but achievable task, if mirror losses are minimized as in [13]. **Figure 7** shows the intracavity pump power necessary to reach oscillation for different mirror reflectivities and cavity lengths, assuming a conversion efficiency

**Figure 7.** Intracavity pump power necessary for OPO threshold, vs. ridge length, for a few values of facet reflectivities.

The evaluation of refractive indices was performed through an m-lines setup. This measurement relies on the determination of the coupling angle inside a slab waveguide of the

grown over InP. As a result of the index contrast, the quaternary alloy acts as a planar waveguide. A diffraction grating was deposited or etched on the surface. The samples are mounted vertically on a rotating mount, and a laser is shone horizontally on the grating (**Figure 8**). Whenever the angle of light diffracted into the surface layer matches the bounce angle of a guided mode, coupling occurs. The guided light is collected by a detector placed at the exit facet of the sample. Coupling angles are given by the conservation

*kin*‖ *sin*(*θ*) <sup>=</sup> ‖→

*km*‖ <sup>+</sup> *<sup>m</sup>* ‖→

AsyP1-y lattice matched to InP

*kg*‖ (2)

of 240%W−1 cm−2 and propagation losses of 0.34 cm−1.

material of interest. Our samples consist of a layer of In1-xGax

**3. Index measurement**

150 Quantum-dot Based Light-emitting Diodes

**3.1. Principle**

of momentum

‖→

Three laser beams are combined with a precision of 0.01°: (1) a visible one (λ = 543 nm) for alignment and period measurements, (2) a tunable fibered laser around 1.55 μm, and (3) a free-space laser diode emitting at either 3.14 or 3.17 μm. The sample is placed on the axis of a rotating stage driven by a motor of step 0.001° and is precisely aligned so that the diffraction grating lines lie in the vertical direction (**Figure 9**). The light output at its exit facet is collected

**Figure 8.** Coupling condition.

**Figure 9.** Optical setup for effective-index measurements.

with a detector placed after a slit (not shown here) and a focusing lens. All the detection setup is mounted on the stage, and it rotates rigidly with the sample. We used the same samples and gratings at 1.55 and 3 μm since the direction of the second-order diffracted beam at 1.55 μm roughly corresponds to the first order at 3.11 μm. To find the angle of normal incidence, measurements were done in a single long scan, with symmetric angles. Since all facets of a sample are cleaved and reflective, whenever θ<sup>1</sup> is a coupling angle, the light couples as well in the other direction for θ2 = −θ<sup>1</sup> and reflects on the back facet, reaching the detector (**Figure 10**). Thus the angle of normal incidence was taken to be (θ<sup>1</sup> + θ2 )/2. This reduces the error bar due to a possible misalignment of the beams and to the motor backlash.

In order to determine the grating period, the visible laser was shone on the sample. Under the Littrow condition, the diffracted beam exits through the entrance slit and is collected through a beam splitter on a photodiode (**Figure 11**). The grating period is retrieved through the equality

2 *sin*(*θ*) = *mλ* /*Λ* (4)

**Figure 10.** Determination of the angle of normal incidence.

**Figure 11.** Optical setup for measuring the grating period.

#### **3.4. Results**

with a detector placed after a slit (not shown here) and a focusing lens. All the detection setup is mounted on the stage, and it rotates rigidly with the sample. We used the same samples and gratings at 1.55 and 3 μm since the direction of the second-order diffracted beam at 1.55 μm roughly corresponds to the first order at 3.11 μm. To find the angle of normal incidence, measurements were done in a single long scan, with symmetric angles. Since all facets of a sample

In order to determine the grating period, the visible laser was shone on the sample. Under the Littrow condition, the diffracted beam exits through the entrance slit and is collected through a beam splitter on a photodiode (**Figure 11**). The grating period is retrieved through the equality

2 *sin*(*θ*) = *mλ* /*Λ* (4)

is a coupling angle, the light couples as well in the

)/2. This reduces the error bar due

and reflects on the back facet, reaching the detector (**Figure 10**).

+ θ2

are cleaved and reflective, whenever θ<sup>1</sup>

**Figure 9.** Optical setup for effective-index measurements.

152 Quantum-dot Based Light-emitting Diodes

= −θ<sup>1</sup>

**Figure 10.** Determination of the angle of normal incidence.

Thus the angle of normal incidence was taken to be (θ<sup>1</sup>

to a possible misalignment of the beams and to the motor backlash.

other direction for θ2

A typical result of coupling measurement is shown in **Figure 12**. The position of the peaks is determined with a precision of 0.01°. Since the effective indices are a function of material index and thickness of the guiding layer, each measured value corresponds to a range of possible {material index, thickness} pairs. This is represented in **Figure 13**, where one line corresponds to the space of parameters that minimize the difference between measured and theoretical indexes. Since more than one effective index is measured, it is possible to determine the right pair {material index, thickness}, at the crossing point. **Figure 14** shows the average difference between measured and effective indices. Waveguides support three modes at 1.55 μm, two at

**Figure 12.** Determination of the refractive index and thickness for a slab of In0.67Ga0.33As0.72P0.28 at λ = 1.55 μm. Each line shows the possible range of data corresponding to the measured value of the effective index of a given waveguide mode.

**Figure 13.** Coupling measurement into a slab of In0.67Ga0.33As0.72P0.28 on InP at a wavelength of 1.55 μm.

**Figure 14.** Determination of the refractive index and core thickness for a slab of In0.67Ga0.33As0.72P0.28 on InP at a wavelength of 1.55 μm. This figure shows the mean difference between calculated and measured effective indices. Area width gives an estimation of the error.

2.12 μm, and one at 3.14 μm. In order to derive the effective index at 3 μm, the guide thicknesses were estimated from the data at 1.55 μm (**Table 1**).

**Figures 15**–**17** show the measured refractive indices as a function of As fraction, at wavelengths of 1.55, 2.12, and 3.14 μm. The data at 1.55 μm was compared to the model presented in [20]. At 2.12 and 3.14 μm, no model being available in the literature, we trace the data against a linear regression versus the molar fraction of As(y). The refractive index of InP from [24] was taken into account. **Figure 18** shows the refractive index versus wavelength, against a one-oscillator fit calculated from the Afromowitz model [25]. The fit parameters are presented in **Table 2**.


The lattice mismatch was measured by X-ray diffraction. Ga and As fraction are deduced through the model presented in [26].

**Table 1.** Physical properties and measured indices of the studied samples.

**Figure 15.** Refractive index measured at 1.55 μm vs. y, compared to [20].

**Figure 14.** Determination of the refractive index and core thickness for a slab of In0.67Ga0.33As0.72P0.28 on InP at a wavelength of 1.55 μm. This figure shows the mean difference between calculated and measured effective indices. Area width gives

**Figure 13.** Coupling measurement into a slab of In0.67Ga0.33As0.72P0.28 on InP at a wavelength of 1.55 μm.

an estimation of the error.

154 Quantum-dot Based Light-emitting Diodes

**Figure 16.** Refractive index measured at 2.12 μm vs. y (data plotted against a linear fit).

#### **3.5. Discussion**

The accuracy of this measurement is determined by several factors.


**Figure 17.** Refractive index measured at 3.14 μm vs. y (data plotted against a linear fit).

**3.5. Discussion**

156 Quantum-dot Based Light-emitting Diodes

The accuracy of this measurement is determined by several factors.

**Figure 16.** Refractive index measured at 2.12 μm vs. y (data plotted against a linear fit).

of 0.1 nm. This leads to a 0.3 × 10−3 error bar on the effective index.

explained by local variations of the resist filling factor and depth.

has a negligible impact on the effective indices.

error on the effective index of 3 × 10−5.

to the lattice mismatch observed in [16].

• Values of the grating period were determined by repeated measurements with a precision

• The uncertainty due to sample misalignment can be estimated at 0.5 × 10−3. This may be

• In order to estimate the impact of the thin layer of photoresist on the effective indices, we performed a set of measurements on a sample covered with a thin photoresist grating. Then we etched it shallowly, removed the resist, and took a new set of data. The estimated thickness diminishes by 11 nm. This is in agreement with a profilometry of the etched grating depth, yielding 15 nm. The estimated core index is raised by 0.7 × 10−3, a value lower than the possible variation of twice the experimental error. Thus we conclude that the resist

• While the laser beam alignment and position of the sample with respect to the rotating stage are adjusted in each measurement, one could point out that the axis of the rotating motor could be slightly misaligned with respect to the vertical axis and introduce a systematic error. A simple observation of the height of the beam reflection as the motor rotates indicates that the angle could be at most of 0.5 mrad. This leads, after a calculation, to an

• Finally, incertitude on the composition is the most important. It is determined by the photoluminescence and lattice mismatch of the samples, with a precision of ~1%, through the model described in [26]. This corresponds to an uncertainty on the effective index of 4 × 10−3. The deviation of our measurements with respect to literature and to a linear fit is in the range of 10−2 to 2 × 10−2. This is in agreement with the observed variations of index due

**Figure 18.** Refractive index of InGaAsP lattice matched to InP vs. wavelength for y = 0.72, 0.70, and 0.55. A one-oscillator fit (Afromowitz model) is added.


**Table 2.** Parameters of the Afromowitz model inferred from the index measurements: a and b are extracted by a linear regression from (n<sup>2</sup> –1)−1 = a E2 + b, where E is the wavelength energy in eV.

## **Acknowledgements**

This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the project DOPO. Authors thank the Commissariat à l'Energie Atomique and Direction Générale de l'Armement for PhD funding.

#### **Author details**

Alice Bernard1,2, Marco Ravaro1 , Jean-Michel Gerard<sup>2</sup> , Michel Krakowski<sup>3</sup> , Olivier Parillaud3 , Bruno Gérard3 , Ivan Favero1 and Giuseppe Leo1\*

\*Address all correspondence to: giuseppe.leo@univ-paris-diderot.fr

1 Laboratoire Matériaux et Phénomènes Quantiques, UMR 7162, Université Paris Diderot – CNRS, Paris, France


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**Author details**

Bruno Gérard3

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CNRS, Paris, France

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, Ivan Favero1

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, Jean-Michel Gerard<sup>2</sup>

1 Laboratoire Matériaux et Phénomènes Quantiques, UMR 7162, Université Paris Diderot –

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2 University Grenoble Alpes, CEA, INAC-PHELIQS, Grenoble, France

3 III-V Lab, Thales Research and Technology, Palaiseau, France

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## *Edited by Morteza Sasani Ghamsari*

Quantum dot-based light emitting diodes were assigned to bringing together the latest and most important progresses in light emitting diode (LED) technologies. In addition, they were dedicated to gain the perspective of LED technology for all of its advancements and innovations due to the employment of semiconductor nanocrystals. Highly selective, the primary aim was to provide a visual source for high-urgency work that will define the future directions relating to the organic light emitting diode (OLED), with the expectation for lasting scientific and technological impact. The editor hopes that the chapters verify the realization of the mentioned aims that have been considered for editing of this book. Due to the rapidly growing OLED technology, we wish this book to be useful for any progress that can be achieved in future.

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Quantum-dot Based Light-emitting Diodes

Quantum-dot Based Light-

emitting Diodes

*Edited by Morteza Sasani Ghamsari*