Boundary conditions and high-field domains in GaAs

In the approximations usually employed, the behavior of a GaAs sample in high fields is determined by Poisson's equation and current continuity plus appropriate boundary conditions. It has been demonstrated recently that boundary conditions can determine such properties as the threshold for Gunn oscillations and their amplitude [1]. In this paper we go through all the stationary solutions that can be obtained for different values of carrier concentration and field at the cathode. The method employed is that of the "field of directions," used extensively by Boer and associates [2], mainly for CdS. By means of this analysis, it is possible to understand many diverse phenomena found experimentally or predicted by computer solutions, e.g., 1) the finding of Shaw, Solomon, and Grubin [3] that, for a cathode field in the negative differential conductivity (NDC) range, the Gunn threshold occurs at a current density
j \cong nev_{d}(E_{c})
, where
n
is carrier concentration and
v_{d}(E_{c})
the drift velocity at the cathode field; 2) the switching, decrease of current with increasing voltage, and hysteresis found by Kroemer [1] for a sample with a shallow Schottky barrier; 3) the switching that occurs in some samples, after the initiation of Gunn oscillations, to a low-resistance state with an avalanche region at the anode.