The dark current characteristics of gallium arsenide doped with silicon and compensated with diffused copper were found to have a pronounced region of current controlled negative differential conductivity (ndc) similar to the characteristics of a thyristor. The resistivity of the semi‐insulating semiconductor was measured to be 105&OHgr; cm for applied voltages up to 2.2 kV, which corresponds to an average electric field of 38 kV/cm. At higher voltages, a transition to a stable high current state was observed with a current rate of rise exceeding 1011A/s. There is evidence of the formation of at least one current filament during this transition. A theoretical model based on drift diffusion and boundary conditions that allows double carrier injection at the contacts has been used to show that the observed negative differential resistance is due to the filling of deep copper acceptors. The model also shows that the ndc curves may be tailored by adjusting the copper concentration. Doping of GaAs with various concentrations of copper was shown to change the dark current characteristics in a way predicted by the model.