Effect of Temperature Degeneracy on Two-Stream Instability in Chip-Based Semiconductor Plasmas

Abstract

The dynamics of electron–hole counter-streaming quantum semiconductor plasmas within an electrostatic framework is investigated by employing the quantum hydrodynamics (QHD) model, considering the effects of Bohm potential, exchange-correlation potential, and arbitrary degenerate pressure. The analysis covers both nearly degenerate and nearly non-degenerate scenarios, addressing distinct time-scale instabilities. Numerical investigations are carried out using typical parameter values for InP and GaN semiconductors to analyze the real frequency and growth rate of the two-stream instabilities. In both regimes, an inverse relationship is observed between species density and instability phase velocity. The system’s instability grows with increasing electron streaming velocity and shrinks with increasing hole streaming velocity. In nearly degenerate plasmas, growth rates are lower when species temperatures are equal compared to differing temperature (\(T_{e}>T_{h}\)) and higher compared to \(T_{e}<T_{h}\). In nearly non-degenerate cases, temperature variation has a negligible effect on the growth rate, underscoring the dominance of other quantum effects. In both, the nearly degenerate and nearly non-degenerate regimes, the exchange-correlation potential enhances plasma instability, while tunneling recoil and degeneracy pressure significantly reduce instability at larger wave numbers. This comprehensive investigation provides valuable insights into the quantum behavior of semiconductor plasmas, informing applications in electronic devices and semiconductor physics.