Propagation of space-charge waves in a conductor exhibiting a differential negative resistance

Conditions for the growth and propagation of infinitesimal space-charge waves in the presence of a differential negative resistance are derived. It is assumed that: The charge carriers are electrons. The differential negative resistance is due to field-induced transfer of electrons to zero-mobility states. The rate of escape from these states is independent of electric field. Effects due to momentum and energy relaxation can be neglected. A rough extension of the linear theory to the problem of the steady state mobile domain is made and it is inferred that the velocity of the domain in n-type golddoped Ge at 20 °K is equal to the phase velocity of the wave associated with conditions pertaining near the drift-current peak. Order of magnititude agreement with experiment is obtained. Applying the same criteria to n-type GaAs and comparing with the observed domain velocity yields a rough estimate for the time constant of scattering to low-mobility states, namely of the order of or less than 10 -12 sec. However, this is short enough to suggest that momentum and energy relaxation effects ought to be included in a description of negative resistance effects in this material.