Copper-based ternary CuSb(S/Se)(2) compound semiconductors are showing promise for ultrathin photovoltaic devices. The high absorption coefficient of these semiconductors makes them suitable for very thin absorber, where maximum absorption can be achieved in a photovoltaic device with only nanometers thick CuSb(S/Se)(2) based thin films. The device structure under consideration consists of AZO/i-ZnO/n-CdS/absorber layer/back contact, as the constituent material layers. The device structure is simulated using one dimensional solar cell capacitance simulator (SCAPS 1D) under one sun illumination and considering flat band approximation for the back contact and CuSb(S/Se)(2) interface. The optimized single junction device efficiencies are approximately 14% and approximately 10.18% with CuSbS2 and CuSbSe2 absorbers, respectively. Further, the impact of various material parameters such as thickness, acceptor concentration of bulk absorber layer, donor concentration of CdS buffer layer, and defects present at bulk absorber layer and at the buffer/absorber interface is discussed in correlation with the photovoltaic performance of the considered devices. The bandgap of CuSb(S/Se)(2) reduces linearly with Se alloying, and their impact on device performance is quantified in terms of capacitance voltage (CV), capacitance frequency (Cf), and impedance spectra of the photovoltaic device.