This study focuses on finite element method simulations of various contacts on high resistivity, "semi-insulating," semiconductors in general, and detector grade CdTe, in particular. The results of this study confirm that the simplified approach assuming depletion approximation is not suitable for analyses of semi-insulating semiconductors. Furthermore, the space charge in such devices is usually dominated by the free charge carriers. The forward current in Schottky diodes may be much higher than expected from the bulk majority carrier concentration. It is shown that the minority current is often much higher than the majority current. These results indicate that a full computer simulation is vital in order to describe the microscopic conditions inside the device, as well as the macroscopic behavior of the device.