On the form and stability of electric-field profiles within a negative differential mobility semiconductor

Using a fixed cathode boundary field model we examine analytically the form and stability of inhomogeneous prethreshold electric-field profiles in long bulk negative differential mobility (NDM) semiconductors. We show that the electric-field profiles and their associated current-voltage relationships depend in a detailed way on the characteristics of the bulk material (e.g., the velocity-electric-field relation) and on the boundary conditions imposed on the bulk. We investigate situations leading to the nucleation of a high-field domain at the cathode and find that for its occurrence: 1) the electric field at the cathode boundary must lie within the NDM region; and 2) space-charge neutrality must be approximated within the vicinity of the cathode. When these conditions are satisfied the current instability at threshold is accompanied by bulk electric-field values that are below the threshold field for NDM. The stability conclusions are drawn from a small-signal analysis that avoids many of the approximations of earlier studies. Supplementary numerical computations are included to demonstrate that the subsequent time development of the current instability depends in a detailed way on: 1) conditions at the cathode boundary; and 2) the external circuit. It is shown that the recycling Gunn effect cathode-to-anode transit-time mode in a resistive circuit is not a necessary consequence of the bulk having a region of NDM.