Two-Stream Instability in Hot-Electron Systems of Many-Valley Semiconductors

Abstract

Feasibility of observing growing two-stream instability arising from the interaction of hot electrons in many-valley semiconductors (germanium and silicon) has been investigated by the use of Boltzmann equation. The anisotropy of the band structure has been incorporated in the dispersion relation by successive coordinate transformations and by the Herring-Vogt transformation in crystal momentum space. Drift velocities, temperatures, and densities of individual valleys have been calculated by modifying the theory of Reik and Risken and using these values the dispersion relationships have been evaluated for the (1, 0, 0), (1, 1, 1), and (1, 1, 0) directions for germanium and for the (1, 1, 1) and (1, 0, 0) direction for silicon. The calculation based on the collisionless Boltzmann equation shows a positive growth rate for the (1, 1, 1) direction in germanium, but collision damping is so severe in the hot electron region that no net growth of instability may occur. In all other cases, both in germanium and silicon the waves are damped at all wavevectors even without collision damping because of Landau damping.