The Boltzmann transport equation for conduction electrons in solids is solved to third order in the applied optical fields, including nonlinearities due to the nonparabolicity of the conduction band and the momentum-dependent relaxation times. It is shown that the nonlinearity calculated from the hot-electron approximation fails to include changes described in terms of the higher-order derivatives of the distribution function. The nonlinearity arising from the momentum dependence of the relaxation times is of little importance in III-V compounds because of the predominance of the nonparabolicity effect. The relaxation-time effect should be observable in degenerate $n$-type Si and Ge samples where it exceeds the bound-electron nonlinearity, and in metals where it is expected to be larger than the nonlinearity of the electron plasma by a a factor of ${10}^3$-${10}^4$.

• Received 16 June 1969

DOI:https://doi.org/10.1103/PhysRev.188.1291