Nonlinearity in the theory of hot electrons due to excess of charge carriers in the presence of electric field

The excess of nonequilibrium charge carriers due to heating by strong electric fields influences the nonlinear current-voltage characteristics in semiconductors substantially. It is shown that in general the electron gas heating results in a change of the carrier concentration in the conduction band due to the dependence of the recombination rate on the electron temperature. This nonequilibrium carrier density leads to an extra nonlinearity coefficient in the current-voltage characteristic curve even when the electron mobility is independent of the electron temperature. These latter contributions in the nonlinear theory of hot electrons are exemplified by an attractive potential of the impurity potential in semiconductors.