applied sciences  
Theoretical Investigation of Responsivity/NEP Trade-off in NIR Graphene/Semiconductor Schottky Photodetectors Operating at Room Temperature  
[PERSON] 12C, [PERSON] 11 and [PERSON] 2,* 2  
temperature. PD noise affects the noise equivalent power (NEP), that is, the minimum detectable optical power, which has a huge impact on both the device sensitivity and the bit error rate (BER) of a communication link. Higher Schottky barriers make it possible to achieve low noise, but they unfortunately also lead to low efficiencies. This efficiency-noise trade-off is a peculiar characteristic of the Schottky PDs based on the IPE.  
In 2006, for the first time, it was theoretically proposed to use Schottky PDs for the detection of near-IR (NIR) wavelengths at room temperature [9], taking advantage of the interference phenomena occurring inside a high-finesse Fabry-Perot microcavity. The main idea was to work with metal/semiconductor junctions characterized by higher SBHs in order to reduce the dark current and then to recover the device efficiency by increasing the metal absorption through the multiple reflections of the optical radiation inside the microcavity. Later, many other strategies were pursued to enhance the efficiency of these devices; indeed, surface plasmon polaritons (SPPs) [10; 11], Si nanoparticles (NPs) [12], metallic antennas [13], and gratings [14] were proposed and investigated. In any case, the measured responsivity was lower than 30 mA/W [12] and 5 mA/W [15] for waveguide and free-space Schottky PDs, respectively. More important, the efficiency-noise trade-off of these Schottky PDs has never been optimized in terms of SBH for achieving high efficiency and low noise at the same time. The low responsivity (i.e., the ratio between the photogenerated current and the incoming optical power) of the Schottky PDs based on metals is mainly due to the small emission probability of the photo-excited carriers from the metal to the Si, related to the momentum mismatch.  
Recently, graphene/Si Schottky PDs have shown higher efficiencies with respect to the metallic counterpart and, even if the physical mechanism behind this enhancement is still under debate, it seems related to the increased emission probability due to the two-dimensionality of the material [16; 17; 18]. Although graphene is characterized by a low optical absorption (2.3%) many approaches based on resonant-cavity-enhanced (RCE) configurations [19; 20], plasmonic structures [21], waveguiding structures [22], and quantum dots [23] have been proposed to overcome this drawback. At present, graphene/Si PDs [18; 22; 24] show superior performance to the corresponding metallic PDs, representing the most promising solution to realize low-cost Si PDs operating in the NIR regime. In addition, graphene offers a novel attractive possibility: the graphene Fermi level (i.e., the SBH with Si), can be simply modified by applying a bias to the junction, making it feasible to optimize the efficiency-noise trade-off.  
In this work we theoretically investigated the responsivity/NEP trade-off in graphene/semiconductor Schottky PDs operating at NIR wavelengths and at room temperature. First, we used the results of the recent literature to derive a responsivity/NEP analytical equation that can be maximized with an appropriate choice of SBH. Then, we reviewed the SBH dependence on the bias applied to the graphene/semiconductor junctions to show how the responsivity/NEP ratio could be maximized in practice. Finally, we numerically calculated both the responsivity and the NEP of graphene/semiconductor PDs discussing their possible applications and highlighting the validity limits of the proposed optimization process. Even if this work was carried out with the aim of gaining greater insight into graphene/Si PDs, it is worth mentioning that we trace here a general methodology which can also be applied to different semiconductors, such as: germanium (Ge), gallium arsenide (GaAs), and aluminum gallium arsenide (AlGaAs).