Detailed theory of the negative conductance of bulk negative mobility amplifiers, in the limit of zero ion density

The complex admittance behavior is calculated for a bulk negative conductivity semiconductor, such as n-type GaAs, in the limit of zero doping and zero trapping, when all electrons are due to space-charge limited emissions from the cathode. Two different approximations are used: in the first, in closed analytical form, electron diffusion is neglected; in the second, by computer simulation of the internal space-charge dynamics, it is included. Both approximations agree at low frequencies where they predict a positive device conductance. Both predict a negative conductance, of slightly different magnitude, at frequencies around the reciprocal electron transit time. At higher frequencies the diffusionless theory predicts slowly damped conductance oscillations; diffusion effects strongly increase the damping.