Electrostatic nonlinear waves which transfer energy through the semiconductor are investi-
gated. 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 nonlin-
ear Schr ̈odinger (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 depend-
ing 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.

Electron–hole pairs in semiconductors can be stimulated by a laser beam with energy larger than the energy gap of the semiconductor. The interaction between an electron–hole plasma with a laser beam can be a source of instability. The dependence of the instability on the electron and hole temperatures and the unperturbed potential of the incident laser are examined. Using Maxwell’s equations along with electron–hole fluid equations, an evolution equation describing the system is obtained. The latter is reduced to an energy equation that characterizes localized pulse propagation.