Disturbance of Phonon Distribution by Hot Electrons

Calculations are made of the steady-state phonon distribution at low temperatures and high electric fields in a many-valley semiconductor, and numerical evaluation is carried out for $n$-germanium for which all parameters involved are known. It is concluded that the departure from thermal equilibrium will be significant for germanium samples in which the product of carrier concentration $n$ and cross-dimension $L$ is of the order of ${10}^{13}$/${\mathrm{cm}}^2$, and will of course increase as the $\mathrm{nL}$ product increases beyond this value. The disturbed phonon distribution is found to be quite anisotropic. The relaxation time tensor and the mobility $\mu$ in the presence of the disturbed distribution are calculated. It is found that, when the disturbance is not too large, $\mu \propto {\mathrm{}\left(\mathrm{nL}\right)\mathrm{}}^{-}\frac{3}{4}{E}^{-}\frac{1}{2}$, where $E$ is electric field intensity. This has been shown to agree with experimental data for $n$-Ge at 4°K. The question of whether these effects have been observed in $p$-Ge is discussed.