Embodiments of a low resistivity contact to a semiconductor structure are disclosed. In one embodiment, a semiconductor structure includes a semiconductor layer, a semiconductor contact layer having a low bandgap on a surface of the semiconductor layer, and an electrode on a surface of the semiconductor contact layer opposite the semiconductor layer. The bandgap of the semiconductor contact layer is in a range of and including 0 to 0.2 electron- volts (eV), more preferably in a range of and including 0 to 0.1 eV, even more preferably in a range of and including 0 to 0.05 eV. Preferably, the semiconductor layer is p-type. In one particular embodiment, the semiconductor contact layer and the electrode form an ohmic contact to the p-type semiconductor layer and, as a result of the low bandgap of the semiconductor contact layer, the ohmic contact has a resistivity that is less than 1 x10
-6 ohms-cm
2 .