Instabilities of inertial transport in semiconductors

A derivation of the potential and the current-voltage relation is given for collisionless (inertial) transport of electron carriers in high-mobility low effective-mass one-dimensional short space-charge limited semiconductor diodes. No instability for longitudinal fluctuations is found, but transverse spatial instabilities or current filament formation is predicted by minimum entropy production. The negative differential resistance that gives rise to the transverse spatial instabilities restricts the range of stable device operation where a minimum current density is found.