  The fabrication of graphene-silicon (Gr-Si) junction inolves the formation of
a parallel metal-insulator-semiconductor (MIS) structure, which is often
disregarded but plays an important role in the optoelectronic properties of the
device. In this work, the transfer of graphene onto a patterned n-type Si
substrate, covered by $Si_3N_4$, produces a Gr-Si device in which the parallel
MIS consists of a $Gr-Si_3N_4-Si$ structure surrounding the Gr-Si junction. The
Gr-Si device exhibits rectifying behavior with a rectification ratio up to
$10^4$. The investigation of its temperature behavior is necessary to
accurately estimate the Schottky barrier height at zero bias, ${\phi}_{b0}=0.24
eV$, the effective Richardson's constant, $A^*=7 \cdot 10^{-10}
AK^{-2}cm^{-2}$, and the diode ideality factor n=2.66 of the Gr-Si junction.
The device is operated as a photodetector in both photocurrent and photovoltage
mode in the visible and infrared (IR) spectral regions. A responsivity up to
350 mA/W and external quantum efficiency (EQE) up to 75% is achieved in the
500-1200 nm wavelength range. A decrease of responsivity to 0.4 mA/W and EQE to
0.03% is observed above 1200 nm, that is in the IR region beyond the silicon
optical bandgap, in which photoexcitation is driven by graphene. Finally, a
model based on two back-to-back diodes, one for the Gr-Si junction. the other
for the $Gr-Si_3N_4-Si$ MIS structure, is proposed to explain the electrical
behavior of the Gr-Si device.
