Phonon and electron distributions in high electric fields

Abstract

The coupled Boltzmann equations for the electron and acoustic phonon distributions in high electric fields are set up. Similar in form to the disturbed electron distribution, the disturbed phonon distribution should be well approximated by a sum of two terms, the first, N 0(ϵ p), dependent on phonon energy only, while the second, q x g p(ϵ p ), represents an excess of phonons with q in the direction of carrier drift. Solutions are obtained for the case in which the deviation of the phonon distribution from its thermal equilibrium value is small, although that of the electrons need not be. These are evaluated for a lattice temperature such that equipartition is valid for the thermal equilibrium distribution. It is found that the disturbance is proportional to carrier concentration and phonon lifetime, and should be measurable in n-Ge at 30°K in properly chosen samples. For a given q it increases strongly with field, starting from zero field, but reaches a peak at fairly low fields after which it is steady or declines with field. The disturbance also decreases monotonically with increasing q of the phonons. The effect on carrier transport of the disturbance is opposite for the two terms mentioned. The increase of N o over the thermal equilibrium value gives an increase in scattering, which of course tends to decrease mobility. The q x g p term produces a phonon drag effect that tends to increase mobility. At very low fields the latter would predominate.