Semiconductor switching devices include a wide band-gap power transistor, a wide band-gap surge current transistor that coupled in parallel to the power transistor, and a wide band-gap driver transistor that is configured to drive the surge current transistor. Substantially all of the on-state output current of the semiconductor switching device flows through the channel of the power transistor when a drain-source voltage of the power transistor is within a first voltage range, which range may correspond, for example, to the drain-source voltages expected during normal operation. In contrast, the semiconductor switching device is further configured so that in the on-state the output current flows through both the surge current transistor and the channel of the power transistor when the drain-source voltage of the power transistor is within a second, higher voltage range.