A numerical model for the simulation of ultraviolet sensitive ion-implanted 4H-SiC photodiodes is established. To explain the measured wavelength dependence of the photoresponsivity of such photodiodes, conventional simulation model was modified twofold. First, new experimental data on the optical properties of 4H-SiC were included into the model. Second, the doping dependence of recombination lifetimes was recalibrated, resulting in a stronger recombination of charge carriers in the ion-implanted region near the SiC surface. After the calibration of the model using experimental data, the model was applied for the optimization of the photodiode performance. An improvement of photoresponsivity by about 30% can be achieved by optimizing the thickness of antireflective layer. An improvement by more than 70% can be achieved by lowering doping level to 1 · 1014 cm-3 in the epitaxial layer of 4H-SiC diodes.