This article reports on scaling effects calculated with ohmic contacts on various types of high and low resistivity semiconductors, from near-intrinsic to heavily compensated. The investigation was performed using a finite element computation. It is shown that small ohmic contacts exhibit Schottky-like energy band diagrams on compensated and uncompensated semiconductors. It is shown that the currents of ideal ohmic contacts scale with the contact's perimeter below critical contact size and with area for larger contacts. Bulk velocity saturation effect is shown to introduce non-linearity and asymmetry in the current-voltage characteristics even for ideal ohmic contacts. The effect of finite contact recombination velocity is analyzed. In compensated semiconductors, the deep level carrier capture cross-sections have no effect on resistivity, but may play an important role in the device dc characteristics.