## 3 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, [PERSON] 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 [PERSON] 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 \(\upmu\)W.  
Figure 4: **(a)** Sketch describing the graphene-silicon (Si) Schottky diode investigated in [PERSON] [27]. **(b)** The current-voltage I-V curve at reverse bias (from \(-\)16 to \(-\)15 V). This figure demonstrates the change in diode current by switching on and off the laser at 1550 nm. Reprinted with permission from ([PERSON], [PERSON], [PERSON], [PERSON], [PERSON]. Graphene-Si Schottky IR detector. _IEEE J. Quant. Elect._**2013**, 49, 2589). Copyright (2013) IEEE. Figure 3: Comparison between internal quantum efficiency of 3D, Equation (2), and 2D, Equation (5), materials for three different wavelengths of 0.85, 1.3 and 1.55 \(\upmu\)m.  
In addition, a 2.4 \(\upmu\)A 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 [PERSON] at al. have recently discussed and explained the physics behind the IPE enhancement in junctions involving 2D materials [35]. Subsequently, [PERSON] 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 \(\sim\)5 \(\upmu\)m 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 \(\upmu\)A. The SBH extracted by the electrical measurement is 0.34 eV. More recently, in 2017, [PERSON] 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 \(\uplambda\)2 Si slab layer surrounded between graphene/Si top and Au bottom mirrors as shown in Figure 6a.