Transition metal dichalcogenide (TMD) materials have emerged as promising candidates for thin film solar cells due to their wide bandgap range across the visible wavelengths, high absorption coefficient and ease of integration with both arbitrary substrates as well as conventional semiconductor technologies. However, reported TMD-based solar cells suffer from relatively low external quantum efficiencies (EQE) and low open circuit voltage due to unoptimized design and device fabrication. This paper studies $Pt/WSe_2$ vertical Schottky junction solar cells with various $WSe_2$ thicknesses in order to find the optimum absorber thickness.Also, we show that the photovoltaic performance can be improved via $Al_2O_3$ passivation which increases the EQE by up to 29.5% at 410 nm wavelength incident light. The overall resulting short circuit current improves through antireflection coating, surface doping, and surface trap passivation effects. Thanks to the ${Al_2O_3}$ coating, this work demonstrates a device with open circuit voltage ($V_{OC}$) of 380 mV and short circuit current density ($J_{SC}$) of 10.7 $mA/cm^2$. Finally, the impact of Schottky barrier height inhomogeneity at the $Pt/WSe_2$ contact is investigated as a source of open circuit voltage lowering in these devices
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