**1. Introduction**

In the last few decades, the enormous evolution of social networks and the progress of the Internet of Things (IoT) has made necessary the management of a huge amount of data. For this reason, industry and scientific research has been focused on the development of new technologies to support and to manage the data traffic increase.

Silicon photonics (SP) fits perfectly into this scenario, since it combines the advantages of the mature silicon technology developed in microelectronics with the possibility to further reduce costs simultaneously increasing the transmission speed thanks to the use of light. Hence, SP is currently emerging as an appealing market promising to reach \$4 billion in 2025 (**Figure 1**) [1]. Nowadays, Intel and Luxtera play leadership roles in the SP industry, bringing products to market that can support 100Gb/s of communication throughput.

Silicon photonics is by now a widely consolidated field originating from the pioneering work of Soref et al. [2, 3] and from the manufacture of silicon on insulator (SOI) substrates particularly suitable to the realization of guiding

have been investigated. Some devices use a Fabry-Perot type resonant geometry for compensating the reduction in efficiency [14, 15], others use nanometric metallic structures such as Si nanoparticles (NP) [16], gratings [17] and antennas [18]. Lastly, PDs based on the IPE at room temperature have also been realized by taking advantage of surface plasmonic polaritons on metal strips of nanometric scale (SPP) [19, 20]. Despite of these efforts, however, it was possible to obtain a maximum responsivity of only 30 mA/W for PDs integrated in waveguide configuration [16]. To increase these low responsivity values, deriving from the small probability of the photo-excited carriers of overcoming the Schottky barrier, the reduction of the metal thickness has stood out as a good strategy [21, 22], influencing the research towards the integration of 2D materials with Si. In particular, 2D layered materials have emerged thanks to their exceptional optical and electronic properties, low cost

*Near-Infrared Schottky Silicon Photodetectors Based on Two Dimensional Materials*

In literature it is possible to find various graphene/Si PDs based on FET structures [23, 24]; however, such kind of devices suffer of a high dark current needing of interdigitated electrodes because the electric field in graphene is formed in a small region within 200 nm from the contact. On the other hand, by taking advantage of an IPE approach, it is possible to minimize the dark current thanks to the rectifying nature of Schottky diodes that do not need of interdigitated structures. Graphene has opened the way for the investigation of other 2D layered mate-

In this chapter the topic of NIR PDs based on 2D materials/silicon junctions is discussed. In the first section the theoretical background behind the behavior of junctions based on 2D materials with particular reference to graphene will be explored and compared to the classical theory describing the Schottky junctions using 3D metals. In the second part, several examples of NIR PDs exploiting 2D materials/silicon junctions reported in literature will be presented and discussed.

The responsivity R of a photodetector can be defined as the ratio between the photogenerated current (Iph) to the incident optical power (Pinc). It is very important for the quantification of the PD performance since it is strictly related to the efficiency of the device. This relation is explicated by the following formula:

<sup>¼</sup> <sup>λ</sup>½ � nm

where ηext is the external quantum efficiency, that represents the number of charged carriers generated for each incident photon. The external quantum efficiency depends on the internal quantum efficiency by the equation ηext ¼ Aηint, where ηintis the ratio of the number of charged carriers generated to the number of

The first theoretical model of photoemission from metal to vacuum was published by Fowler in 1931 [32]. Afterwards, in the 60s, the Fowler's theory was extended to the photoemission in the semiconductor by Cohen, Vims and Archer

<sup>1242</sup> <sup>∙</sup> <sup>η</sup>ext (1)

<sup>R</sup> <sup>¼</sup> Iph Pinc

absorbed photons and A is the active material absorption.

rials. Notable attention has been given to transition-metal dichalcogenides (TMDCs) since their very naturally abundant and possess a tunable bandgap in addition to most of graphene properties [25–27]. Recently, several heterostructures TMDCs/Si have been investigated: the formation of a potential barrier at the interface between the two materials has allowed the exploitation of the IPE to realize

and simple fabrication process.

*DOI: http://dx.doi.org/10.5772/intechopen.99625*

**2. Theoretical background**

[33] and Elabd and Kosonocky [21].

**97**

high detectivity and ultrafast NIR PDs [28–31].

#### **Figure 1.**

*Silicon photonics 2019–2025 market forecast [1].*

structures, both in the 1980s. Thus, the possibility to build optoelectronic devices by using CMOS facilities, would allow not only the low costs advocated by telecommunications industry but also the possibility to integrated both electronic and photonic functionalities on the same chip.

In this context silicon-based photodetectors (Si PDs) are a key component able to establish a connection between the world of electronics and photonics. Si PDs working in the visible spectrum can be easily found on the market, however the telecommunications industry requires components operating in the infrared regime, where, unfortunately, silicon has a negligible absorption due to its indirect bandgap of 1.12 eV.

To overcome this drawback the most common approach is based on the integration of germanium (Ge) on silicon. Nonetheless, the performances of these devices are often limited by a relatively high leakage current caused by the lattice mismatch with silicon of 4,3%. This effect can be mitigated by growing a Ge buffer layer on Si by a two steps epitaxial method giving rise to problems of thermal budget and planarity that limit the monolithic Ge integration on Si.

For all these reasons, an all-silicon approach is preferable, and the exploitation of the absorption phenomena based on the internal photoemission effect (IPE) in a Schottky diode is among the most promising and innovative.

In a Schottky diode configuration, the photons incident on a Metal-Si interface, with an energy below the silicon bandgap, can cause the generation of photoexcited carriers in the metal with energy higher than Schottky barrier. This "hot" carriers are injected into the silicon, accelerated by the electric field in the depletion region of the junction and collected as a photocurrent [4–7].

In literature, several examples of IR charged coupled devices (CCDs) based on a Schottky diode can be easily found. The most common example of this family of PDs is based on Pd2Si/Si and PtSi/Si Schottky junctions used for aerospace applications. The main problem with these photodetectors, however, is the requirement of cryogenic temperatures to minimize the noise current due to the low Schottky barrier (SBH) necessary to achieve a reasonable device efficiency [8–13].

Consequently, to exploit the IPE at room temperature, new classes of devices characterized by higher values of SBH, have been proposed. Obviously, this approach leads to a worsening of the performances of PDs and, therefore, different solutions

#### *Near-Infrared Schottky Silicon Photodetectors Based on Two Dimensional Materials DOI: http://dx.doi.org/10.5772/intechopen.99625*

have been investigated. Some devices use a Fabry-Perot type resonant geometry for compensating the reduction in efficiency [14, 15], others use nanometric metallic structures such as Si nanoparticles (NP) [16], gratings [17] and antennas [18]. Lastly, PDs based on the IPE at room temperature have also been realized by taking advantage of surface plasmonic polaritons on metal strips of nanometric scale (SPP) [19, 20]. Despite of these efforts, however, it was possible to obtain a maximum responsivity of only 30 mA/W for PDs integrated in waveguide configuration [16].

To increase these low responsivity values, deriving from the small probability of the photo-excited carriers of overcoming the Schottky barrier, the reduction of the metal thickness has stood out as a good strategy [21, 22], influencing the research towards the integration of 2D materials with Si. In particular, 2D layered materials have emerged thanks to their exceptional optical and electronic properties, low cost and simple fabrication process.

In literature it is possible to find various graphene/Si PDs based on FET structures [23, 24]; however, such kind of devices suffer of a high dark current needing of interdigitated electrodes because the electric field in graphene is formed in a small region within 200 nm from the contact. On the other hand, by taking advantage of an IPE approach, it is possible to minimize the dark current thanks to the rectifying nature of Schottky diodes that do not need of interdigitated structures.

Graphene has opened the way for the investigation of other 2D layered materials. Notable attention has been given to transition-metal dichalcogenides (TMDCs) since their very naturally abundant and possess a tunable bandgap in addition to most of graphene properties [25–27]. Recently, several heterostructures TMDCs/Si have been investigated: the formation of a potential barrier at the interface between the two materials has allowed the exploitation of the IPE to realize high detectivity and ultrafast NIR PDs [28–31].

In this chapter the topic of NIR PDs based on 2D materials/silicon junctions is discussed. In the first section the theoretical background behind the behavior of junctions based on 2D materials with particular reference to graphene will be explored and compared to the classical theory describing the Schottky junctions using 3D metals. In the second part, several examples of NIR PDs exploiting 2D materials/silicon junctions reported in literature will be presented and discussed.

#### **2. Theoretical background**

The responsivity R of a photodetector can be defined as the ratio between the photogenerated current (Iph) to the incident optical power (Pinc). It is very important for the quantification of the PD performance since it is strictly related to the efficiency of the device. This relation is explicated by the following formula:

$$\mathbf{R} = \frac{\mathbf{I}\_{\rm ph}}{\mathbf{P}\_{\rm inc}} = \frac{\lambda \text{[nm]}}{\mathbf{1} \mathbf{2} \mathbf{4} \mathbf{2}} \bullet \boldsymbol{\eta}\_{\rm ext} \tag{1}$$

where ηext is the external quantum efficiency, that represents the number of charged carriers generated for each incident photon. The external quantum efficiency depends on the internal quantum efficiency by the equation ηext ¼ Aηint, where ηintis the ratio of the number of charged carriers generated to the number of absorbed photons and A is the active material absorption.

The first theoretical model of photoemission from metal to vacuum was published by Fowler in 1931 [32]. Afterwards, in the 60s, the Fowler's theory was extended to the photoemission in the semiconductor by Cohen, Vims and Archer [33] and Elabd and Kosonocky [21].

structures, both in the 1980s. Thus, the possibility to build optoelectronic devices by using CMOS facilities, would allow not only the low costs advocated by telecommunications industry but also the possibility to integrated both electronic and

*Light-Emitting Diodes and Photodetectors - Advances and Future Directions*

In this context silicon-based photodetectors (Si PDs) are a key component able to establish a connection between the world of electronics and photonics. Si PDs working in the visible spectrum can be easily found on the market, however the telecommunications industry requires components operating in the infrared regime, where, unfortunately, silicon has a negligible absorption due to its indirect bandgap of 1.12 eV.

To overcome this drawback the most common approach is based on the integration of germanium (Ge) on silicon. Nonetheless, the performances of these devices are often limited by a relatively high leakage current caused by the lattice mismatch with silicon of 4,3%. This effect can be mitigated by growing a Ge buffer layer on Si by a two steps epitaxial method giving rise to problems of thermal budget and

For all these reasons, an all-silicon approach is preferable, and the exploitation of the absorption phenomena based on the internal photoemission effect (IPE) in a

In a Schottky diode configuration, the photons incident on a Metal-Si interface,

In literature, several examples of IR charged coupled devices (CCDs) based on a Schottky diode can be easily found. The most common example of this family of PDs is based on Pd2Si/Si and PtSi/Si Schottky junctions used for aerospace applications. The main problem with these photodetectors, however, is the requirement of cryogenic temperatures to minimize the noise current due to the low Schottky barrier (SBH) necessary to achieve a reasonable device efficiency [8–13].

Consequently, to exploit the IPE at room temperature, new classes of devices characterized by higher values of SBH, have been proposed. Obviously, this approach leads to a worsening of the performances of PDs and, therefore, different solutions

with an energy below the silicon bandgap, can cause the generation of photoexcited carriers in the metal with energy higher than Schottky barrier. This "hot" carriers are injected into the silicon, accelerated by the electric field in the depletion

photonic functionalities on the same chip.

*Silicon photonics 2019–2025 market forecast [1].*

**Figure 1.**

**96**

planarity that limit the monolithic Ge integration on Si.

Schottky diode is among the most promising and innovative.

region of the junction and collected as a photocurrent [4–7].

By following the Elabd approach, it is possible to obtain the expression of ηint by starting with the consideration of the number of excited carriers NT is:

$$\mathbf{N}\_{\rm T} = \int\_{0}^{\rm hv} \mathbf{D}(\mathbf{E}) \mathbf{d} \mathbf{E} \tag{2}$$

where hv is the incident photon energy, E is the carriers energy referred to Fermi level and the argument function of the integral D Eð Þ is the absorber material density of state (DOS). On the other hand, not all the excited carriers can be emitted from the metal into semiconductor, indeed only those localized to energies higher than Schottky barrier have a certain probability of being emitted. Therefore, the number of states occupied by charge carriers that have a probability P(E) of being emitted in the silicon can be written as:

$$\mathbf{N} = \int\_{q\Phi\_{\rm{BO}}}^{\rm{hv}} \mathbf{D}(\mathbf{E}) \mathbf{P}(\mathbf{E}) d\mathbf{E} \tag{3}$$

Downstream of all these considerations and taking advantage of Eqs. (2–3), the

*Energy band diagram of a graphene/n-Si Schottky junction with the conical representation of a Dirac point. EV*

where the apex 2D indicates that the formula is referred to a bi-dimensional

From the plot of the (5) and (4) it is evident that the IPE effect is enhanced by using graphene material, as showed in the **Figure 3** where the trend of the internal quantum efficiency versus the wavelength is reported for three different SBHs.

ð Þ hv <sup>2</sup> � <sup>q</sup>ϕB0 ð Þ<sup>2</sup>

*int at vary wavelengths for three different value of Schottky barriers: 0.4, 0.5*

ð Þ hv <sup>2</sup> (5)

graphene quantum efficiency can be written:

*DOI: http://dx.doi.org/10.5772/intechopen.99625*

material [34, 35].

**Figure 3.**

*and 0.6 eV.*

**99**

*Comparison between η*

3*D int and η*<sup>2</sup>*<sup>D</sup>*

**Figure 2.**

η2D int <sup>¼</sup> <sup>N</sup> NT ¼ 1 2 ∙

*(EC): Silicon valence (conduction) band; EF: Metal Fermi level; qΦB: Schottky barrier.*

*Near-Infrared Schottky Silicon Photodetectors Based on Two Dimensional Materials*

where P(E) is the charge carrier emission probability.

Elabd and Kosonocky formulated, with the zero-temperature approximation, the internal quantum efficiency in junctions involving 3D materials (metals) by the following [21]:

$$\eta\_{\rm int}^{\rm 3D} = \frac{\rm N}{\rm N\_T} = \frac{1}{8 \rm q\phi\_{\rm Bo}} \bullet \frac{\left(\rm hv - q\phi\_{\rm B0}\right)^2}{\rm hv} \tag{4}$$

being ϕB0 the Schottky barrier height (SBH) at zero bias, hv ¼ 1242*=*λ0[nm] the photon energy (λ<sup>0</sup> is the wavelength in vacuum condition) and q the electron charge. Very often a generic factor C (named quantum efficiency coefficient) replaces the factor 1*=*8qϕB0 in order to achieve a better agreement between the theory and the experimental data. In order to achieve the expression (4) it is necessary to take P Eð Þ¼ ð Þ 1 � cos ϑ *=*2, where ϑ is named carrier escape angle [21]. Elabd and Kosonocky in their work outline also as the diminishing of the thickness of the metal causes an enhancement of the efficiency due to the increased emission probability P(E).

The 3D apex in the Elabd and Kosonocky Eq. (4) indicates the internal quantum efficiency for a metal-based junction, i.e. for a 3D material, but this equation fails to correctly describe the behavior of a junction based on 2D materials [34, 35] due to the different expressions to use for both the density of state D(E) and the emission probability P(E).

This issue has been discussed in detail for graphene [34, 36]. Graphene has a band structure characterized by valence and conduction bands which touch in six points of the Brillouin zone. These points are termed Dirac points and represent the zero level of energy. In the graphic representation of the band diagram of a graphene/n-Si Schottky junction (**Figure 2**) one of these Dirac points is represented with a conical surface [37].

Unlike metals, Graphene shows a density-of-state function D(E) linearly dependent on the energy according to the formula: D Eð Þ¼ <sup>2</sup>∣E<sup>∣</sup> nℏ2v2 F [38], where ℏ is the reduced Plank constant and vF is the Fermi velocity. On the other hand, as discussed in Ref. [27], the emission probability P(E) simply can be taken equal to 1/2 because the graphene π orbital are always perpendicular to graphene/Si interface and therefore the momenta of the photo-excited carriers can only have two directions: towards the Si semiconductor or in the opposite direction [34].

*Near-Infrared Schottky Silicon Photodetectors Based on Two Dimensional Materials DOI: http://dx.doi.org/10.5772/intechopen.99625*

**Figure 2.**

By following the Elabd approach, it is possible to obtain the expression of ηint by

D Eð ÞdE (2)

D Eð ÞP Eð ÞdE (3)

hv (4)

nℏ2v2 F [38], where ℏ is the

ðhv 0

where hv is the incident photon energy, E is the carriers energy referred to Fermi level and the argument function of the integral D Eð Þ is the absorber material density of state (DOS). On the other hand, not all the excited carriers can be emitted from the metal into semiconductor, indeed only those localized to energies higher than Schottky barrier have a certain probability of being emitted. Therefore, the number of states occupied by charge carriers that have a probability P(E) of

starting with the consideration of the number of excited carriers NT is:

*Light-Emitting Diodes and Photodetectors - Advances and Future Directions*

NT ¼

N ¼

where P(E) is the charge carrier emission probability.

η3D int <sup>¼</sup> <sup>N</sup> NT ðhv qϕB0

<sup>¼</sup> <sup>1</sup> 8qϕBo

photon energy (λ<sup>0</sup> is the wavelength in vacuum condition) and q the electron charge. Very often a generic factor C (named quantum efficiency coefficient) replaces the factor 1*=*8qϕB0 in order to achieve a better agreement between the theory and the experimental data. In order to achieve the expression (4) it is necessary to take P Eð Þ¼ ð Þ 1 � cos ϑ *=*2, where ϑ is named carrier escape angle [21]. Elabd and Kosonocky in their work outline also as the diminishing of the thickness of the metal causes an enhancement of the efficiency due to the increased emission

Elabd and Kosonocky formulated, with the zero-temperature approximation, the internal quantum efficiency in junctions involving 3D materials (metals) by the

being ϕB0 the Schottky barrier height (SBH) at zero bias, hv ¼ 1242*=*λ0[nm] the

The 3D apex in the Elabd and Kosonocky Eq. (4) indicates the internal quantum efficiency for a metal-based junction, i.e. for a 3D material, but this equation fails to correctly describe the behavior of a junction based on 2D materials [34, 35] due to the different expressions to use for both the density of state D(E) and the emission

This issue has been discussed in detail for graphene [34, 36]. Graphene has a band structure characterized by valence and conduction bands which touch in six points of the Brillouin zone. These points are termed Dirac points and represent the

graphene/n-Si Schottky junction (**Figure 2**) one of these Dirac points is represented

reduced Plank constant and vF is the Fermi velocity. On the other hand, as discussed in Ref. [27], the emission probability P(E) simply can be taken equal to 1/2 because the graphene π orbital are always perpendicular to graphene/Si interface and therefore the momenta of the photo-excited carriers can only have two directions:

Unlike metals, Graphene shows a density-of-state function D(E) linearly

zero level of energy. In the graphic representation of the band diagram of a

dependent on the energy according to the formula: D Eð Þ¼ <sup>2</sup>∣E<sup>∣</sup>

towards the Si semiconductor or in the opposite direction [34].

<sup>∙</sup> hv � <sup>q</sup>ϕB0 ð Þ<sup>2</sup>

being emitted in the silicon can be written as:

following [21]:

probability P(E).

probability P(E).

**98**

with a conical surface [37].

*Energy band diagram of a graphene/n-Si Schottky junction with the conical representation of a Dirac point. EV (EC): Silicon valence (conduction) band; EF: Metal Fermi level; qΦB: Schottky barrier.*

Downstream of all these considerations and taking advantage of Eqs. (2–3), the graphene quantum efficiency can be written:

$$\eta\_{\rm int}^{\rm 2D} = \frac{\rm N}{\rm N\_T} = \frac{1}{2} \bullet \frac{\left(\rm hv\right)^2 - \left(\rm q\phi\_{\rm B0}\right)^2}{\left(\rm hv\right)^2} \tag{5}$$

where the apex 2D indicates that the formula is referred to a bi-dimensional material [34, 35].

From the plot of the (5) and (4) it is evident that the IPE effect is enhanced by using graphene material, as showed in the **Figure 3** where the trend of the internal quantum efficiency versus the wavelength is reported for three different SBHs.

#### **Figure 3.**

*Comparison between η* 3*D int and η*<sup>2</sup>*<sup>D</sup> int at vary wavelengths for three different value of Schottky barriers: 0.4, 0.5 and 0.6 eV.*
