The intervalley transfer mechanism of negative resistivity in bulk semiconductors

Abstract

A theoretical study is made of hot-electron transfer from the light-mass central valley to the surrounding heavy-mass satellite valleys in n-type GaAs, InP and CdTe. The treatment is based on Boltzmann's equation, taking account of electron-electron and polar mode intravalley scattering and deformation potential scattering between the central valley and the satellite valleys. Using isotropic effective masses, the electron distribution function in each valley is approximated by a displaced Maxwellian and the number of electrons, the displacement and the electron temperature are determined by exact numerical solution of the conservation equations of electron number, wave vector and energy for every valley. The current-density-field characteristic is calculated and is found to exhibit a negative differential resistance between threshold and valley fields of 3200 and 5800 v cm-1 in GaAs, 6650 and 9750 v cm-1 in InP and between 14 250 and 26 000 v cm-1 in CdTe. The following more detailed results are obtained for GaAs. The central valley temperature increases with field from an assumed lattice temperature of 300 °K to 680 °K at threshold and 2400 °K at the valley. The satellite valley temperature increases very slowly, reaching only 360 °K at the valley. The ratio of satellite to central valley populations increases to 10% at threshold and 90% at the valley. Approximation to the distribution functions by two-term spherical harmonic expansions produces negligible error in the population ratio and current density but raises the central valley temperature by up to 20% at the valley field. The threshold field initially decreases with hydrostatic pressure and then increases rapidly; the negative resistance disappears at 25.5 kb. With the exception of the valley fields, which may be too low, all the theoretical results which were obtained without attempting to adjust any of the uncertain material parameter values are in good or fair agreement with data derived from experiments on the Gunn effect in GaAs, InP and CdTe.