Silicon meet graphene for a new family of near-infrared Schottky photodetectors

In recent years graphene has attracted much interest due to its unique properties of flexibility, strong light-matter interaction, high carrier mobility and broadband absorption. In addition, graphene can be deposited on many substrates including silicon with which is able to form Schottky junctions opening the path to the realization of near-infrared silicon photodetectors based on the internal photoemission effect where graphene play the role of the metal. In this work, we review the very recent progress of the near-infrared photodetectors based on Schottky junctions involving graphene. This new family of device promises to overcome the limitations of the Schottky photodetectors based on metals showing the potentialities to compare favorably with germanium photodetectors currently employed in silicon photonics.


Introduction
The field of silicon photonics (Si PDs) is nowadays an emerging market promising to reach a value of more than $4 billion in the 2024 as shown in Figure 1. Indeed, both switching and interconnects of the existing data center will no longer support the huge increase in internet data traffic driven by the social network and video contents.

Introduction
The field of silicon photonics (Si PDs) is nowadays an emerging market promising to reach a value of more than $4 billion in the 2024 as shown in Figure 1. Indeed, both switching and interconnects of the existing data center will no longer support the huge increase in internet data traffic driven by the social network and video contents.  to the graphene area in contact with Si and because the dark current is that one flowing through a reversely biased Schottky diode. In this review article, the emerging field of the NIR IPE-based graphene/Si PDs, is presented. In the first section, IPE theory for junctions involving 2D materials will be elucidated and put in comparison with the classical theory used for metals. Then, the main structures reported in literature will be discussed and their performance will be compared. Finally, it will be highlighted as these PDs have the capabilities to compare with the Ge technology in the field of NIR detection, also offering new advantageous characteristics.

Theoretical Background
In order to quantify the performance of IPE-based PDs, a very important parameter is the internal quantum efficiency η int , i.e., the ratio of the number of charge carriers generated by the PD to the number of absorbed photons. On the other hand, the external quantum efficiency η ext (the ratio of the number of charge carriers generated by the PD to the number of incident photons) is linked to the internal by η ext = A η int , being A the active material absorption. A macroscopic magnitude is the responsivity R, i.e., the ratio of the photogenerated current (I ph ) to the incident optical power (P inc ). The responsivity R is linked to the external quantum efficiency η ext by the following: In 1931, Fowler derived the first model of carrier photoemission from metal into vacuum [25]. In the 1960s, Cohen, Vims and Archer [26] modified Fowler's theory in order to extend the carrier photoemission into semiconductors. Subsequently, Elabd and Kosonocky reviewed the previous model and, under the zero temperature approximation, they obtained that the device internal quantum efficiency η 3D int (number of carriers generated per absorbed photons) can be written as [20]: where the factor 1/8qΦ B0 35 is very often replaced by a generic factor C (named quantum efficiency coefficient) used to put in agreement the theory with the experimental data, hν = 1242/λ 0 (nm) is the photon energy being λ 0 the vacuum wavelength, Φ B0 is the Schottky barrier height (SBH) under zero bias, and q is the electron charge. The 3D apex is used to indicate that the formula refers to junctions involving 3D materials, i.e., metals. Equation (2) was derived for metal-based junctions, i.e., on three-dimensional materials, however, it has been proved that it fails to correctly describe carrier photoemission involving Schottky junctions based on two-dimensional materials [27,28], thus IPE theory must be properly modified in order to be applied to the Graphene/Si junctions whose band diagram is reported in Figure 2. It could be worth mentioning that the band structure of graphene is characterized by a valence and conduction bands touch each other at six-points in the first Brillouin zone. These particular points, where the Fermi energy is set to 0 eV, are named Dirac points. The band structure close to one of the Dirac points, responsible for the electronic properties of graphene, represents the conic surface shown in Figure 2 [29].

Figure 2.
Band diagram of a graphene/silicon Schottky junction: EF is the metal Fermi level, EV (EC) is the silicon valence (conduction) band, qΦB is the Schottky barrier and qVbi is the built-in potential. NT and N are the total number of states of excited holes and hole having a certain probability to be emitted into silicon.
By following Elabd's approach [20] the number of excited holes NT is: where D(E) is the graphene density of states (DOS) that can be written as , [30]. E is the hole energy referred to the Fermi level, is the reduced Planck constant, vF is the Fermi velocity, and hν is the photon energy. On the other hand, the number of states N occupied by holes having a certain probability to be emitted into silicon is: where P(E) is the carrier emission probability. In three-dimensional materials, P(E) can be expressed as P(E) = (1 − cosϑ)/2 [20], where ϑ is the so defined carrier escape angle [20]. On the contrary, P(E) in graphene assumes a very simple value of ½ because the π orbitals are always normal to the graphene/Si interface, thus the photo-excited hole momenta can have two directions: one pointing towards Si and the other in the opposite direction [27]. Therefore, the graphene internal quantum efficiency η 2D int is [27,28]: The 2D apex is used to indicate that the formula refers to junctions involving 2D materials, i.e., graphene.
In Figure 3 the internal quantum efficiency versus the SBH for three different wavelengths of 0.85 μm, 1.3 μm and 1.55 μm are reported in order to show that in any case the IPE effect is enhanced in junctions involving 2D materials. By following Elabd's approach [20] the number of excited holes N T is: where D(E) is the graphene density of states (DOS) that can be written as D(E) = 2E [30]. E is the hole energy referred to the Fermi level,h is the reduced Planck constant, v F is the Fermi velocity, and hν is the photon energy. On the other hand, the number of states N occupied by holes having a certain probability to be emitted into silicon is: where P(E) is the carrier emission probability. In three-dimensional materials, P(E) can be expressed as P(E) = (1 − cosϑ)/2 [20], where ϑ is the so defined carrier escape angle [20]. On the contrary, P(E) in graphene assumes a very simple value of 1 2 because the π orbitals are always normal to the graphene/Si interface, thus the photo-excited hole momenta can have two directions: one pointing towards Si and the other in the opposite direction [27]. Therefore, the graphene internal quantum efficiency η 2D int is [27,28]: The 2D apex is used to indicate that the formula refers to junctions involving 2D materials, i.e., graphene.
In Figure 3 the internal quantum efficiency versus the SBH for three different wavelengths of 0.85 µm, 1.3 µm and 1.55 µm are reported in order to show that in any case the IPE effect is enhanced in junctions involving 2D materials.

IPE-Based Silicon Photodetectors Based on Graphene Schottky Junctions
Since its discovery in 2004, graphene has been deeply investigated [31]. Indeed, electrons move in graphene as massless particles making it suitable for fast electronics, while the wide absorption (from UV to IR) due to both intra-band and inter-band transitions [32,33] makes the material very useful in the photodetection field in particular for operation at NIR wavelengths. In 2011, Chen et al. demonstrated that graphene is able to form a Schottky junction with Si [34] and this result opened the path to the investigation of IPE in the graphene/silicon junctions for NIR detection.
NIR vertically illuminated IPE-based graphene/Si PDs were reported by Amirmazlaghani et al. in 2013 [27]. These devices are based on exfoliated graphene and show a 9.9 mA/W maximum responsivity at 1550 nm and −16 V of reverse bias applied. Indeed, as shown in Figure 4b, the difference between the photogenerated and dark current is about 51.5 nA under 5.2 μW.

IPE-Based Silicon Photodetectors Based on Graphene Schottky Junctions
Since its discovery in 2004, graphene has been deeply investigated [31]. Indeed, electrons move in graphene as massless particles making it suitable for fast electronics, while the wide absorption (from UV to IR) due to both intra-band and inter-band transitions [32,33] makes the material very useful in the photodetection field in particular for operation at NIR wavelengths. In 2011, Chen et al. demonstrated that graphene is able to form a Schottky junction with Si [34] and this result opened the path to the investigation of IPE in the graphene/silicon junctions for NIR detection.
NIR vertically illuminated IPE-based graphene/Si PDs were reported by Amirmazlaghani et al. in 2013 [27]. These devices are based on exfoliated graphene and show a 9.9 mA/W maximum responsivity at 1550 nm and −16 V of reverse bias applied. Indeed, as shown in Figure 4b, the difference between the photogenerated and dark current is about 51.5 nA under 5.2 µW.

IPE-Based Silicon Photodetectors Based on Graphene Schottky Junctions
Since its discovery in 2004, graphene has been deeply investigated [31]. Indeed, electrons move in graphene as massless particles making it suitable for fast electronics, while the wide absorption (from UV to IR) due to both intra-band and inter-band transitions [32,33] makes the material very useful in the photodetection field in particular for operation at NIR wavelengths. In 2011, Chen et al. demonstrated that graphene is able to form a Schottky junction with Si [34] and this result opened the path to the investigation of IPE in the graphene/silicon junctions for NIR detection.
NIR vertically illuminated IPE-based graphene/Si PDs were reported by Amirmazlaghani et al. in 2013 [27]. These devices are based on exfoliated graphene and show a 9.9 mA/W maximum responsivity at 1550 nm and −16 V of reverse bias applied. Indeed, as shown in Figure 4b, the difference between the photogenerated and dark current is about 51.5 nA under 5.2 μW.  In addition, a 2.4 µA of dark current was measured while an SBH and ideality factor of 0.44-0.47 eV and 1.3-2.1 were extracted from the IV Schottky characteristic, respectively. In this paper, the authors point out the measured responsivity is much higher than that one estimated by Equation (2). This discrepancy has been explained by claiming that a new IPE theory must be derived when 2D materials are involved in the junction. Indeed, they derived a modified model (Equation (5)) for a better prediction with the experimental data. It is worth mentioning that Levy at al. have recently discussed and explained the physics behind the IPE enhancement in junctions involving 2D materials [35]. Subsequently, Goykhman et al. reported on a near-infrared graphene/Si Schottky PD integrated with a waveguide realized starting from a silicon-on-insulator (SOI) substrate. In this device the single graphene layer (SLG) is grown by chemical vapor deposition CVD system [36] (Figure 5).
In addition, a 2.4 μA of dark current was measured while an SBH and ideality factor of 0.44-0.47 eV and 1.3-2.1 were extracted from the IV Schottky characteristic, respectively. In this paper, the authors point out the measured responsivity is much higher than that one estimated by Equation (2). This discrepancy has been explained by claiming that a new IPE theory must be derived when 2D materials are involved in the junction. Indeed, they derived a modified model (Equation (5)) for a better prediction with the experimental data. It is worth mentioning that Levy at al. have recently discussed and explained the physics behind the IPE enhancement in junctions involving 2D materials [35]. Subsequently, Goykhman et al. reported on a near-infrared graphene/Si Schottky PD integrated with a waveguide realized starting from a silicon-on-insulator (SOI) substrate. In this device the single graphene layer (SLG) is grown by chemical vapor deposition CVD system [36] (Figure 5). The PD is constituted by a Si rib waveguide on which a SLG/Au layer acting as Schottky contact has been deposited. The collecting Ohmic contact is realized in aluminum (Al) and deposited on the Si substrate as shown on Figure 5a. The optical beam propagating along the Si waveguide is able to excite the plasmonic modes at SLG/Si interface. The photodetector length and width are ~5 μm and 310 nm, respectively. At 1 V of reverse bias applied, a responsivity at 1550 nm and dark current of 0.085 A/W and 20 nA were experimentally measured. Finally, the authors show that responsivity abruptly increases up to 0.37 A/W at −3 V. The authors explain this abrupt increase by the combined effect of two processes: avalanche multiplication within the Si depletion region and thermionic-field emission (TFE) [37] through the graphene/Si Schottky junction. Under avalanche conditions, the dark current also increases up to 3 μA. The SBH extracted by the electrical measurement is 0.34 eV.
More recently, in 2017, Casalino et al. have reported on vertically-illuminated graphene/Si Schottky PDs incorporated into a Fabry-Perot optical microcavity [38]. The resonant cavity consists of a λ/2 Si slab layer surrounded between graphene/Si top and Au bottom mirrors as shown in Figure  6a. The optical cavity is able to enhance the interaction of the light with graphene in order to increase its absorption. In this work, the authors prove that the device responsivity peaks coincide with the resonances of the Fabry-Perot microcavity and that the responsivity increases with the number of light round trips of the cavity. Thanks to the multiple reflections in the cavity, the graphene absorption increases up to 8% leading to a maximum responsivity increasing with the reverse voltage applied and reaching a maximum of ~20 mA/W at −10 V (Figure 6b); this value is the highest reported so far for free-space illuminated Si PDs at 1550 nm. In addition, the authors prove the SBH dependence on applied reverse voltage. Finally, the dark current at −10 V has been measured as 147 μA while the device bandwidth has been estimated in 120 MHz. The PD is constituted by a Si rib waveguide on which a SLG/Au layer acting as Schottky contact has been deposited. The collecting Ohmic contact is realized in aluminum (Al) and deposited on the Si substrate as shown on Figure 5a. The optical beam propagating along the Si waveguide is able to excite the plasmonic modes at SLG/Si interface. The photodetector length and width are~5 µm and 310 nm, respectively. At 1 V of reverse bias applied, a responsivity at 1550 nm and dark current of 0.085 A/W and 20 nA were experimentally measured. Finally, the authors show that responsivity abruptly increases up to 0.37 A/W at −3 V. The authors explain this abrupt increase by the combined effect of two processes: avalanche multiplication within the Si depletion region and thermionic-field emission (TFE) [37] through the graphene/Si Schottky junction. Under avalanche conditions, the dark current also increases up to 3 µA. The SBH extracted by the electrical measurement is 0.34 eV.
More recently, in 2017, Casalino et al. have reported on vertically-illuminated graphene/Si Schottky PDs incorporated into a Fabry-Perot optical microcavity [38]. The resonant cavity consists of a λ/2 Si slab layer surrounded between graphene/Si top and Au bottom mirrors as shown in Figure 6a. The optical cavity is able to enhance the interaction of the light with graphene in order to increase its absorption. In this work, the authors prove that the device responsivity peaks coincide with the resonances of the Fabry-Perot microcavity and that the responsivity increases with the number of light round trips of the cavity. Thanks to the multiple reflections in the cavity, the graphene absorption increases up to 8% leading to a maximum responsivity increasing with the reverse voltage applied and reaching a maximum of~20 mA/W at −10 V (Figure 6b); this value is the highest reported so far for free-space illuminated Si PDs at 1550 nm. In addition, the authors prove the SBH dependence on applied reverse voltage. Finally, the dark current at −10 V has been measured as 147 µA while the device bandwidth has been estimated in 120 MHz. In order to increase the low graphene absorption of the previous device (only 8%), the same author has theoretically proposed a resonant cavity-enhanced (RCE) graphene/Si PD working at 1550 nm based on IPE [39]. Device is essentially a Fabry-Perot interferometer constituted by three layers of crystalline Si, graphene and hydrogenated amorphous Si surrounded by two high-reflectivity Bragg mirrors as shown in Figure 7a. The optical field enhancement allows increasing the single-layer graphene optical absorption up to 100%. The optoelectronic transduction mechanism is based on IPE where the photoexcited carriers are emitted from graphene to Si. In this work, it has been theoretically proved that an optimized device can reach an external quantum efficiency of 35% and responsivity of 0.43 A/W, as shown in Figure 7b. Finally, device speed and noise, have been discussed. Very recently this family of devices have demonstrated the capability to work also at wavelengths longer than 1550 nm [28]. Indeed, in the Casalino's work [28] vertically-illuminated silicon PD operating at 2 μm has been reported. The sketch of the device is shown in Figure 8a; it is a graphene/silicon Schottky junctions whose electrical parameters are carefully extracted at various In order to increase the low graphene absorption of the previous device (only 8%), the same author has theoretically proposed a resonant cavity-enhanced (RCE) graphene/Si PD working at 1550 nm based on IPE [39]. Device is essentially a Fabry-Perot interferometer constituted by three layers of crystalline Si, graphene and hydrogenated amorphous Si surrounded by two high-reflectivity Bragg mirrors as shown in Figure 7a. The optical field enhancement allows increasing the single-layer graphene optical absorption up to 100%. The optoelectronic transduction mechanism is based on IPE where the photoexcited carriers are emitted from graphene to Si. In this work, it has been theoretically proved that an optimized device can reach an external quantum efficiency of 35% and responsivity of 0.43 A/W, as shown in Figure 7b. Finally, device speed and noise, have been discussed. In order to increase the low graphene absorption of the previous device (only 8%), the same author has theoretically proposed a resonant cavity-enhanced (RCE) graphene/Si PD working at 1550 nm based on IPE [39]. Device is essentially a Fabry-Perot interferometer constituted by three layers of crystalline Si, graphene and hydrogenated amorphous Si surrounded by two high-reflectivity Bragg mirrors as shown in Figure 7a. The optical field enhancement allows increasing the single-layer graphene optical absorption up to 100%. The optoelectronic transduction mechanism is based on IPE where the photoexcited carriers are emitted from graphene to Si. In this work, it has been theoretically proved that an optimized device can reach an external quantum efficiency of 35% and responsivity of 0.43 A/W, as shown in Figure 7b. Finally, device speed and noise, have been discussed. Very recently this family of devices have demonstrated the capability to work also at wavelengths longer than 1550 nm [28]. Indeed, in the Casalino's work [28] vertically-illuminated silicon PD operating at 2 μm has been reported. The sketch of the device is shown in Figure 8a; it is a graphene/silicon Schottky junctions whose electrical parameters are carefully extracted at various Very recently this family of devices have demonstrated the capability to work also at wavelengths longer than 1550 nm [28]. Indeed, in the Casalino's work [28] vertically-illuminated silicon PD operating at 2 µm has been reported. The sketch of the device is shown in Figure 8a; it is a graphene/silicon Schottky junctions whose electrical parameters are carefully extracted at various temperature increasing from 280 to 315 K. The Schottky barrier is 0.62 eV at 300 K and shows a dependence on temperature ascribed to interface defects. Devices show a responsivity of 0.16 mA/W (Figure 8b) at zero bias. It corresponds to internal responsivities of at least 7.2 mA/W. Measured dark current is~3 µA at −6 V while the estimated bandwidth is in the KHz range due to the very high series resistance. The proposed devices show the potentialities to work also at wavelength longer than 2 micron.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 11 temperature increasing from 280 to 315 K. The Schottky barrier is 0.62 eV at 300 K and shows a dependence on temperature ascribed to interface defects. Devices show a responsivity of 0.16 mA/W (Figure 8b) at zero bias. It corresponds to internal responsivities of at least 7.2 mA/W. Measured dark current is ~3 μA at −6V while the estimated bandwidth is in the KHz range due to the very high series resistance. The proposed devices show the potentialities to work also at wavelength longer than 2 micron. A summary of all the aforementioned devices are reported in Table 1 for comparison.

Conclusions
In this work an overview of near-infrared Si PDs based on IPE occurring in graphene, has been presented. Firstly, we have described how IPE theory needs to be properly modified in junctions A summary of all the aforementioned devices are reported in Table 1 for comparison.

Conclusions
In this work an overview of near-infrared Si PDs based on IPE occurring in graphene, has been presented. Firstly, we have described how IPE theory needs to be properly modified in junctions involving two-dimensional material, showing as this effect is intrinsically enhanced with respect to classical device based on 3D materials (metals). Then we have described and discussed in detail the most common configurations reported in recent literature including both vertically-illuminated and waveguide structures. Finally, a quantitative comparison of selected device has been given and summarized in Table 1.
In some cases, this new family of devices shows performance that is already comparable to PDs based on Ge technology utilized in Si photonics for both telecom and datacom applications. In addition, these devices show the potentialities for working at longer wavelengths opening perspectives for new applications including optical communications, light-radars and biomedical imaging. However, the possibility to integrate 2D materials like graphene in Si technology for high-volume production remains a crucial point that needs to be properly addressed in the next future.