Bulk Negative Differential Conductance in High-Purity n-Type Germanium

A theoretical study is made of hot-electron transfer from three light-mass valleys to one heavy-mass valley in n-type Ge, for a constant electric field in the [111] direction. The treatment is based on Boltzmann's equation, taking account of acoustic phonon scattering and impurity scattering between the different valleys. The electron distribution function is approximated by a drifted Maxwellian. The number of electrons, the velocity, and the electron temperature are determined by the exact numerical solution of the conservation equations of electron number, wave vector, and energy for every valley. The velocity-field characteristic is found to exhibit a negative differential conductance for lattice temperatures below 40°K. Uniaxial compressive stress along the field direction reduces the velocity at the threshold. These results are in good agreement with the experimental data reported by Kastalskii.