Impact ionization inn-germanium, 4-9.5°K

A new theory for describing nonequilibrium phenomena involving shallow donor states is applied to the problem of impact ionization of shallow donors in $n$-germanium at low temperatures; it allows the calculation of the whole electron-concentration-field characteristic $n\left(E\right)\mathrm{}$, and not just the breakdown field $E_B$. The results are in good agreement with experiment, especially so for the purer samples considered. The excited states of the donors are shown to be of utmost importance both for the ionization and for the recombination. At one extreme they produce nonlinear effects which provide a strong mechanism for the $S$ breakdown (current-controlled negative resistance) observed experimentally; Kurosawa's mechanism is shown to be correspondingly weak and to be vanishing for electric fields much above 6 V/cm. In normal (non-$S$) breakdown a regime is identified in which, with allowance for the effect of the excited states on ionization, some analogy can be drawn with the usual Price breakdown criterion. A new, non-Price-breakdown regime is shown to result from the effect of impact processes on transitions from the excited states. The border between the two regimes is marked by a strongly temperature-dependent sample-compensation ratio, the purer samples considered lying in the new regime at 7°K. The distribution functions considered for electrons in the conduction band were supposed dominated by acoustic-phonon scattering; some indications were found of the presence of additional scattering mechanisms in less pure samples and at high values of $n$. The conduction-band anisotropy of germanium was taken into account; the donor levels were not assumed to be hydrogenic. No appeal was made to the principle of detailed balance. The results indicate that calculations of this type on nonequilibrium phenomena are now practicable, and that despite the apparent complexity of such systems their qualitative behavior can be understood in terms of a few simple concepts.