Mode Coupling and Two-Stream Instabilities in Semiconductors

The quantum hydrodynamic model is used to investigate the arbitrary degenerate electron/hole stream instabilities in ballistic semiconductors or semiconductor plasmas (semiplasmas) for a wide range of impurity doping, number density, and temperatures. It is observed that, while the instability in classical plasma regime is always of single k-range type, the double-range instability can occur in degenerate plasma regime. Different types of carrier counter-streaming instabilities are classified and parametrically studied in arbitrarily doped ballistic semiconductors. The parametric study of counter-stream instability in silicon at room temperature shows that the doping scheme has fundamental effect on electron-electron and hole-hole instabilities but no effect on electron-hole instability. Other parameters, such as the electron temperature and stream speed, have significant effects on the unstable wavenumber range and the growth rate. It is remarked that the electron stream in n-type semiconductors becomes unstable at somewhat lower limit of the stream speed than that of holes in a p-type silicon semiconductors. A description based on the energy exchange between unstable modes is given for different instability types. It is found that the instability in asymmetric doped semiconductors (electron-electron and hole-hole) is of symmetric type without energy exchange between the modes, while, for symmetric doped semiconductors (electron-hole), it is of asymmetric type with the energy exchange. Finally, it is found that the electron and hole spin exchange-correlation effects enhance the two-stream instability.