A two-dimensional model was developed to simulate the optoelectronic characteristics of indium-gallium-nitride (InξGa1-ξN), thin-film, Schottky-barrier-junction solar cells. The solar cell comprises a window designed to reduce the reflection of incident light, Schottky-barrier and ohmic front electrodes, an n-doped InξGa1-ξN wafer, and a metallic periodically corrugated back-reflector (PCBR). The ratio of indium to gallium in the wafer varies periodically in the thickness direction, and thus the optical and electrical constitutive properties of the alloy also vary periodically. This material nonhomogeneity could be physically achieved by varying the fractional composition of indium and gallium during deposition. Empirical models for indium nitride and gallium nitride, combined with Vegard's law, were used to calculate the optical and electrical constitutive properties of the alloy. The periodic nonhomogeneity aids charge separation and, in conjunction with the PCBR, enables incident light to couple to multiple surface plasmon-polariton waves and waveguide modes. The profile of the resulting chargecarrier-generation rate when the solar cell is illuminated by the AM1.5G spectrum was calculated using the rigorous coupled-wave approach. The steady-state drift-diffusion equations were solved using COMSOL, which employs finite-element methods, to calculate the current density as a function of the voltage. Mid-band Shockley- Read-Hall, Auger, and radiative recombination rates were taken to be the dominant methods of recombination. The model was used to study the effects of the solar-cell geometry and the shape of the periodic material nonhomogeneity on efficiency. The solar-cell efficiency was optimized using the differential evolution algorithm.