Two-Phonon Transitions in the Impurity Conduction in Semiconductors

Abstract

The two-phonon transition rate for carrier transfer from an occupied impurity center to an empty one was calculated on the basis of the formalism given by Gummel and Lax for the multiphonon processes in the Born-Oppenheimer and deformation-potential approximations. The general formula for the two-phonon transition rate was investigated in detail in the case of simple parabolic band in two regions of temperature. Numerical data are given for $n$- and $p$-type Si and Ge. It is shown that two-phonon transitions can play a role in impurity conduction in materials with low mobility of carriers and low impurity concentration.