Electrostatic wave propagation and self-streaming effect in an electron-hole plasma

Abstract

Electrostatic nonlinear waves which transfer energy through the semiconductor are investigated. A quantum hydrodynamic plasma system composed of self-streaming electrons and holes is examined. The basic equations are reduced to one evolution equation called a modified nonlinear Schrödinger (mNLS) equation. The stability and instability regions are studied with respect to the wavenumber and different plasma effects such as degenerate pressure, Bohm potential, and collisions. The mNLS equation is solved analytically to obtain three kinds of nonlinear envelope wave packet modes. It is found that there are different regions of stability and instability depending on various quantum effects. The electrons’ and holes’ self-streaming velocity is studied and manipulated for the three types of nonlinear envelope waves ‘dark soliton, bright soliton, and rogue wave’. The dark envelope wave packet is generated in a stable region. When the electrons and holes streaming velocities become faster, the wave amplitude becomes taller and the pulses have higher frequency. The bright envelope wave packet exists in the unstable region. For low streaming velocities, the rogue wave amplitude becomes shorter, however, when the streaming velocities reach a critical value the amplitude increases suddenly six times. The self-heating could be produced as the tunneling electrons and holes exchange their energy with the lattice, which may decrease the lifetime of the semiconductors. The present results are helpful in realizing the physical solution to the intrinsic heating problem in semiconductors.