*2.1.2 Inverse temperature crystallization (ITC) method*

As a radically faster perovskite crystal synthesis approach, the ITC method has widely been applied in recent years. It was observed that the exhibited crystals from such method can be shape-controlled, higher quality, and obtained quicker compared with other growth techniques. Bakr et al. introduced this method to rapidly grow high-quality bulk crystals [50]. As shown in **Figure 2e**, an orange MAPbBr3 crystal and a black MAPbI3 crystal were grown within 3 hours. Chen's group further

#### **Figure 2.**

*2a, schematic of STL method. 2b, image of MAPbI3 with {100} and {112} facets.* CrystEngComm *[47], copyright 2015. 2c, MAPbBr3 crystals from STL method.* J. Cryst. Growth *[48], copyright 2015. 2d, photographs of perovskite crystals with different halide ratio.* Nature Photonics *[49], copyright 2015. 2e, MAPbI3 and MAPbBr3 crystals growth at different time intervals.* Nature Commun. *[50], Copyright 2015. 2f, schematic of crystals growth.* J. Mater. Chem. C *[51], copyright 2016. 2 g, schematic of AVC method.* Science *[15], copyright 2015.*

studied the effect of molar ratio of MAX and PbX2 in the precursor solutions on the crystal quality [52], e.g., perovskite crystals with different sizes and shapes were obtained after a 6-hour ITC crystallization process when changing the MAX: PbX2 ratios from 1:1 to 2:1.

With an aim of growing a large-sized bulk perovskite crystal, such ITC method was further modified. Using such technique, the strategy of incorporation of seed crystal growth has been proven to be favorable for single crystals as large as convenient. Liu's group reported various large-sized perovskite crystals via using the modified ITC method, from which a number of larger-sized crystal (7 mm) were obtained through choosing good-quality seed crystals and repeating and carefully controlling the ITC process several times (**Figure 2f**). Moreover, Liu's group also successfully grew MAPb(BrxI1 − x)3 single crystals with a finely-tuned bandgap [51]. The application of the different solubility of different perovskite single crystals at varying temperatures contributes to the time-saving feature of such ITC method.

### *2.1.3 Anti-solvent vapor-assisted crystallization (AVC) method*

Another main method to grow perovskite crystals is the AVC method (**Figure 2g**), which was first introduced from Bakr's group [15]. In this method, the solvent plays a significant role because two or more solvents should be selected, of which one should be a good solvent that is less volatile, and the other is a bad solvent that is more volatile. The principle of this method can be described as follows: when the bad solvent slowly diffuses into the precursor solution, the proficiency of the crystal formation increases at the bottom of the sample vial owing to the insolubility of the material in the bad solvent. Other groups, like Loi's group and Cao's group, also applied this method to obtain the high-quality crystals [38, 53]. Although the AVC method costs more time than the ITC method, its temperature-irrelevant characteristic is appealing to its widespread use.

#### **2.2 Thin single crystals**

Bulk perovskite single crystals with thick sizes may cause the increase of charge recombination, which would lead to the degradation of their device performance and impede the practical applications. In this regard, growing thin perovskite crystals with a large area represents an effective approach to overcome the above obstacle and thus advances the further practical applications. Bakr et al. introduced a cavitation-triggered asymmetrical crystallization strategy, in which a very short ultrasonic pulse (≈1 s) was applied in the solution to reach a low supersaturation level with anti-solvent vapor diffusion and a thin crystal with several-micrometers grew on the substrates within hours (**Figure 3a**) [54]. Liu's group synthesized perovskite crystal wafers with a much thinner thickness using a dynamic flow micro-reactor system [55]. They put two thin glass slides in parallel into a container with a predefined separation to grow single crystals within the slit channel, as shown in **Figure 3b**. Su's group further used a space-limited ITC method and grew a 120-cm2 single crystal on fluorine-doped tin oxide (FTO)-coated glass, of which the operation and the obtained 0.4-mm-thin single crystal are shown in **Figure 3c** [56]. Meanwhile, Wan et al. reported a space-confined solution-processed method to grow the perovskite single-crystalline films with adjustable thickness from nanometers to micrometers (**Figure 3d**) [57]. Benefitting from the capillary pressure, the perovskite precursor solution filled the whole space between two clean flat substrates, which were clipped together and dipped in the solution.

Currently, more promising approaches have been employed to grow thin single crystals with high quality and large scale. A one-step printing geometrically-confined

**107**

**Figure 3.**

**3.1 Optical properties**

*Single Crystal Hybrid Perovskite Optoelectronics: Progress and Perspectives*

lateral crystal growth method (**Figure 3e**) was introduced by Sung's group to obtain a large-scaled single crystal [58]. During the process, a cylindrical metal roller with a flexible poly-(dimethyl-siloxane) (PDMS) mold was wrapped and then rolled on a preheated SiO2 substrate (180°C) with an ink supplier filled with the precursor solution. Alternatively, millimeter-sized single crystals were synthesized by Song's group by a facile seed-inkjet-printing approach (**Figure 3f**) [59]. Perovskite precursor solution was injected onto a silicon wafer, and then the ordered seeds were formed on the substrate with the evaporation of the droplets. Thereafter, the substrate with a saturated perovskite solution was covered and the single crystals can be grew as the solvent dried at room temperature. Seeds were used to inhibit the random nucleation

*3a, schematic of cavitation-triggered asymmetrical method.* Adv. Mater. *[54], Copyright 2016. 3b, schematic of ultrathin crystal wafer growth.* Adv. Mater. *[55], Copyright 2016. 3c, schematic of the laminar MAPbBr3 crystal films preparation.* Adv. Mater. *[56], Copyright 2017. 3d, schematic for the growth of perovskite thin crystals.* J. Am. Chem. Soc. *[57], copyright 2016. 3e, schematic of geometrically-confined lateral crystal growth method.* Nature Commun. *[58], Copyright 2017. 3f, schematic of the scalable growth for perovskite crystal* 

As discussed above, some optimized space-limited approaches have been introduced and developed to synthesize perovskite thin crystals in recent years. Especially, size−/thickness-controlled thin crystals have also been widely used in various optoelectronic devices. With the aim to growing large-scaled and thicknesscontrolled thin crystals with longer carrier diffusion lengths, fewer defects, and higher efficiency, more promising strategies will be rewarding in the future.

**3. Optoelectronic characterizations of perovskite single crystals**

There are two normal ways to study the optical properties of hybrid perovskite crystals: absorption and PL measurements. Bakr et al. characterized the steady-state

*DOI: http://dx.doi.org/10.5772/intechopen.95046*

and trigger the growth of single crystals.

*films using an inkjet printing method.* Sci. Adv. *[59], Copyright 2018.*

*Single Crystal Hybrid Perovskite Optoelectronics: Progress and Perspectives DOI: http://dx.doi.org/10.5772/intechopen.95046*

#### **Figure 3.**

*3a, schematic of cavitation-triggered asymmetrical method.* Adv. Mater. *[54], Copyright 2016. 3b, schematic of ultrathin crystal wafer growth.* Adv. Mater. *[55], Copyright 2016. 3c, schematic of the laminar MAPbBr3 crystal films preparation.* Adv. Mater. *[56], Copyright 2017. 3d, schematic for the growth of perovskite thin crystals.* J. Am. Chem. Soc. *[57], copyright 2016. 3e, schematic of geometrically-confined lateral crystal growth method.* Nature Commun. *[58], Copyright 2017. 3f, schematic of the scalable growth for perovskite crystal films using an inkjet printing method.* Sci. Adv. *[59], Copyright 2018.*

lateral crystal growth method (**Figure 3e**) was introduced by Sung's group to obtain a large-scaled single crystal [58]. During the process, a cylindrical metal roller with a flexible poly-(dimethyl-siloxane) (PDMS) mold was wrapped and then rolled on a preheated SiO2 substrate (180°C) with an ink supplier filled with the precursor solution. Alternatively, millimeter-sized single crystals were synthesized by Song's group by a facile seed-inkjet-printing approach (**Figure 3f**) [59]. Perovskite precursor solution was injected onto a silicon wafer, and then the ordered seeds were formed on the substrate with the evaporation of the droplets. Thereafter, the substrate with a saturated perovskite solution was covered and the single crystals can be grew as the solvent dried at room temperature. Seeds were used to inhibit the random nucleation and trigger the growth of single crystals.

As discussed above, some optimized space-limited approaches have been introduced and developed to synthesize perovskite thin crystals in recent years. Especially, size−/thickness-controlled thin crystals have also been widely used in various optoelectronic devices. With the aim to growing large-scaled and thicknesscontrolled thin crystals with longer carrier diffusion lengths, fewer defects, and higher efficiency, more promising strategies will be rewarding in the future.

## **3. Optoelectronic characterizations of perovskite single crystals**

#### **3.1 Optical properties**

There are two normal ways to study the optical properties of hybrid perovskite crystals: absorption and PL measurements. Bakr et al. characterized the steady-state absorption and PL properties for MAPbBr3 and MAPbI3 crystals, as shown in **Figure 4a** and **b** [50]. Sharp band edges were observed in the absorption plots and the band gap values were determined to be 2.18 eV for MAPbBr3 crystals and 1.51 eV for MAPbI3 crystals; while the PL intensity peaks are located at 574 nm for MAPbBr3 and 820 nm for MAPbI3. As for the MAPbCl3 one, absorption measurement result revealed an edge at 435 nm (**Figure 4c**) [60]. Clearly, the optical absorption of perovskite crystals exhibited a clear-cut sharp band edge, which indicated that the single crystals are predominantly free from grain boundaries and have relatively low structural defects and trap densities.

More recently, there have been more broad publications on the apparent disparity in optical properties (i.e., absorption and PL) between perovskite single crystals and thin films, which can be attributed to the incorrect measurements as a result of reabsorption effects. Snaith's group performed a detailed investigation of the optical properties of MAPbBr3 crystals as compared to those of the polycrystalline films by employing light transmission spectroscopy, ellipsometry, and spatially resolved and time-resolved PL spectroscopy [61]. They showed that the optical properties of the perovskite crystals were almost identical to those of polycrystalline films, and their observations indicated that the perovskite polycrystalline films were much closer to possessing 'single-crystal-like' optoelectronic properties than previously thought, and also highlighted the discrepancies in the estimation of trap densities from the electronic and optical methods (**Figure 4d**). For the further development of perovskite crystals, more detailed experimental investigations combined with theoretical calculations that focus on the optical features are required, which would assist in the preparation of the high-quality perovskite single crystals and the development of the high-performance device applications.

### **3.2 Charge transport properties**

As for hybrid perovskite crystals, in addition to the remarkable optical properties, their promising electrical properties have caught the great attention. In general, there are five common methods to measure the transport mobilities in perovskite crystals, including the space charge limited current (SCLC), time-offlight (TOF), Hall Effect, THz pulse and field-effect transistor (FET) measurement methods. Among these methods, the SCLC method is widely employed to determine the carrier mobility and trap density of perovskite crystals. The current–voltage (*I-V*) curve can be divided into three parts: the first region, where an Ohmic contact exists, hence the conductivity can be estimated; the second region is the trap-filling region, which is increased sharply at trap-filled limit voltage (*V*TFL); and the third region, known as the child region. Trap density (*n*trap) can be obtained by following the relation: *n*trap = (2*V*TFL*εε*0)/(*eL*<sup>2</sup> ), where *ε*0 is the vacuum permittivity, *ε* is the relative dielectric constant, *L* is the crystal thickness, and *e* is the electron

#### **Figure 4.**

*Steady-state absorption (4a) and PL spectra (4b) of MAPbBr3 and MAPbI3 crystals, respectively.* Nature Commun*. [50], Copyright 2015.* **4c***, steady-state absorption and PL spectra of MAPbCl3 crystal. Insets: Band gap for the above single crystals.* J. Phys. Chem. Lett*. [60], Copyright 2015, 4d, normalized PL decays for MAPbBr3 film (red) and crystal (blue) excited at 447nm. Inset shows the zoom on the shorter time scale.*  Nature Commun. *[61], Copyright 2017.*

**109**

*Single Crystal Hybrid Perovskite Optoelectronics: Progress and Perspectives*

)/(9*εε*0*V*<sup>2</sup>

cm−3 and a *μ* of 38 cm2

from which the Hall mobility was calculated to be 10 cm2

charge creation and remarkably high *μ* as high as 500–800 cm2

[66], from which the field-effect *μ* values are up to 4.7 and 1.5cm2

*n*-channel devices, respectively (**Figure 5h**).

charge. Moreover, the mobility (*μ*) is determined by fitting the *I-V* curve with

designed the hole-only device (**Figure 5a**), and a large hole mobility of 67.27 cm2

crystal was measured by Bakr's group with *n*trap = 3.1 × 1010 cm−3 and *μ* = 42 cm2

was estimated [62]. An SCLC method was also applied on MAPbBr3 crystals, with

[60]. Another method to measure the *μ* is the TOF method. Bakr's group obtained the *μ* via using the TOF method (**Figure 5b**) [15], from which *μ* can be defined by

and *τ*t is the transit time that be provided by the transient current under different driving voltages [67, 68]. The same method was also applied by Huang's group and the

two methods, Bakr et al. also carried out the complementary Hall Effect measure-

[15]. Meanwhile, Huang's group applies the Hall Effect measurement [68], and they showed the crystals were slightly *p*-doped with a low free holes concentration. Thereafter, Podzorov's group increased the conductivity of MAPbBr3 single crystals by sputtering Ti on the flat-faceted single crystal to form Hall bars (**Figure 5d**) [64],

Although the above measurement approaches have been widely used in the perovskite crystals, the obtained results from different groups are sometimes different. Sargent et al. demonstrated that one main challenge that may explain these order-of-magnitude discrepancies is that the Hall Effect, TOF, and SCLC methods all probe the mobilities near the respective Fermi levels during the experiments, and the (non-equilibrium, high-injection-level) Fermi level is widely different in each experiment [64]. In this regard, they developed a contactless method to measure the mobility of a perovskite crystal directly [64]. Plus, THz pulse measurement was also used to estimate *μ*. David et al. used a two-color laser plasma in dry air to generate multi-THz pulses and excited the large MAPbI3 single crystals and detected the electric field by an air-biased coherent detection scheme with 1–30 THz ultrabandwidth after normal incidence reflection off the crystal facet (**Figure 5e**, **f**) [65]. Such spectra measurements indicate the ultrafast dynamics and efficiencies of free

FETs are the fundamental components to realize digital integrated circuits, which are also often used as a platform to evaluate charge transport mechanism in the active materials. In this regard, bottom-gate, top-contact FETs were fabricated via using micrometer-thin MAPbX3 (X = Cl, Br, and I) crystals as active layer (**Figure 4g**)

Carrier lifetime (*τ*) is an important parameter that should be considered when designing an optoelectronic device. Upon excitation by photons, the active materials will be in an excited state. After that, the photo-induced holes and electrons will recombine back to the ground state. Usually, if this recombination process, that is, the carrier lifetime of carriers, is sufficiently long, a high performance device will be expected. The *τ* of semiconductors strongly depends on the nature, dimension, and purity of the materials. Generally, *τ* can be obtained from the PL decay, transient absorption, as well as the transient photo-voltage decay and impedance methods [69]. Among these methods, the PL decay approach has been widely applied. The superposition of fast and slow components of carrier dynamics from the PL spectra measurement result yield *τ* ≈ 41 and 357 ns for MAPbBr3 (**Figure 5i**) [15, 70, 71]. Transient absorption (TA) also suggests the recombination property of excitons which is used to determine the carrier lifetime through a bi-exponential fitting [60]. The carrier diffusion length *L*D can be further

ments on perovskite crystals, confirming the *μ* ranging from 20 to 60 cm2

), where *J* is the current density. Liu's group

/Vs [15]. *I-V* response of a MAPbCl3

/Vs (**Figure 5c**) [63]. Apart from the above

/Vs.

/(*Vτ*t), where *d* is the sample thickness, *V* is the applied voltage,

/Vs

/Vs

/Vs

/Vs. Furthermore,

/Vs in *p*- and

*DOI: http://dx.doi.org/10.5772/intechopen.95046*

electron *μ* was verified to be 24.0 ± 6.8 cm2

Mott-Gurney's law: *μ* = (8*JL*<sup>3</sup>

an *n*trap of 5.8 × 109

the equation: *μ* = *d*<sup>2</sup>

charge. Moreover, the mobility (*μ*) is determined by fitting the *I-V* curve with Mott-Gurney's law: *μ* = (8*JL*<sup>3</sup> )/(9*εε*0*V*<sup>2</sup> ), where *J* is the current density. Liu's group designed the hole-only device (**Figure 5a**), and a large hole mobility of 67.27 cm2 /Vs was estimated [62]. An SCLC method was also applied on MAPbBr3 crystals, with an *n*trap of 5.8 × 109 cm−3 and a *μ* of 38 cm2 /Vs [15]. *I-V* response of a MAPbCl3 crystal was measured by Bakr's group with *n*trap = 3.1 × 1010 cm−3 and *μ* = 42 cm2 /Vs [60]. Another method to measure the *μ* is the TOF method. Bakr's group obtained the *μ* via using the TOF method (**Figure 5b**) [15], from which *μ* can be defined by the equation: *μ* = *d*<sup>2</sup> /(*Vτ*t), where *d* is the sample thickness, *V* is the applied voltage, and *τ*t is the transit time that be provided by the transient current under different driving voltages [67, 68]. The same method was also applied by Huang's group and the electron *μ* was verified to be 24.0 ± 6.8 cm2 /Vs (**Figure 5c**) [63]. Apart from the above two methods, Bakr et al. also carried out the complementary Hall Effect measurements on perovskite crystals, confirming the *μ* ranging from 20 to 60 cm2 /Vs [15]. Meanwhile, Huang's group applies the Hall Effect measurement [68], and they showed the crystals were slightly *p*-doped with a low free holes concentration. Thereafter, Podzorov's group increased the conductivity of MAPbBr3 single crystals by sputtering Ti on the flat-faceted single crystal to form Hall bars (**Figure 5d**) [64], from which the Hall mobility was calculated to be 10 cm2 /Vs.

Although the above measurement approaches have been widely used in the perovskite crystals, the obtained results from different groups are sometimes different. Sargent et al. demonstrated that one main challenge that may explain these order-of-magnitude discrepancies is that the Hall Effect, TOF, and SCLC methods all probe the mobilities near the respective Fermi levels during the experiments, and the (non-equilibrium, high-injection-level) Fermi level is widely different in each experiment [64]. In this regard, they developed a contactless method to measure the mobility of a perovskite crystal directly [64]. Plus, THz pulse measurement was also used to estimate *μ*. David et al. used a two-color laser plasma in dry air to generate multi-THz pulses and excited the large MAPbI3 single crystals and detected the electric field by an air-biased coherent detection scheme with 1–30 THz ultrabandwidth after normal incidence reflection off the crystal facet (**Figure 5e**, **f**) [65]. Such spectra measurements indicate the ultrafast dynamics and efficiencies of free charge creation and remarkably high *μ* as high as 500–800 cm2 /Vs. Furthermore, FETs are the fundamental components to realize digital integrated circuits, which are also often used as a platform to evaluate charge transport mechanism in the active materials. In this regard, bottom-gate, top-contact FETs were fabricated via using micrometer-thin MAPbX3 (X = Cl, Br, and I) crystals as active layer (**Figure 4g**) [66], from which the field-effect *μ* values are up to 4.7 and 1.5cm2 /Vs in *p*- and *n*-channel devices, respectively (**Figure 5h**).

Carrier lifetime (*τ*) is an important parameter that should be considered when designing an optoelectronic device. Upon excitation by photons, the active materials will be in an excited state. After that, the photo-induced holes and electrons will recombine back to the ground state. Usually, if this recombination process, that is, the carrier lifetime of carriers, is sufficiently long, a high performance device will be expected. The *τ* of semiconductors strongly depends on the nature, dimension, and purity of the materials. Generally, *τ* can be obtained from the PL decay, transient absorption, as well as the transient photo-voltage decay and impedance methods [69]. Among these methods, the PL decay approach has been widely applied. The superposition of fast and slow components of carrier dynamics from the PL spectra measurement result yield *τ* ≈ 41 and 357 ns for MAPbBr3 (**Figure 5i**) [15, 70, 71]. Transient absorption (TA) also suggests the recombination property of excitons which is used to determine the carrier lifetime through a bi-exponential fitting [60]. The carrier diffusion length *L*D can be further

#### **Figure 5.**

*5a, dark* I-V *curve of hole-only MAPbI3 crystal device.* J. Energy Chem. *[62], Copyright 2018. 5b, ToF traces of MAPbBr3 crystal.* Science *[15], copyright 2015. 5c, transient current curves of perovskite crystal devices.* Science *[63], copyright 2015. 5d, schematic of hall effect measurement.* Adv. Mater. *[64], Copyright 2016. 5e, schematic of time-resolved multi-THz spectroscopy experiment.* **5f***, incident (black), transmitted (blue) and reflected (red) multi-THz pulses after interaction with the crystal.* Energy Environ. Sci*. [65], Copyright 2015. 5 g, schematic of bottom-gate, top-contact perovskite crystal FET. 5 h, transfer characteristics of a MAPbCl3 device.*  Nature Commun. *[66], Copyright 2018. 5i, PL time decay trace of a MAPbBr3 crystal.* Science *[15], copyright 2015.*

estimated based on the equation: *L*D = [((*k*BT)/*eμτ*)]1/2, where *k*B is Boltzmann's constant and *T* is the sample temperature. From the above-examined values of *μ* and *τ*, *L*D was calculated [63, 64].
