Numerical solution of coupled steady-state hot-phonon–hot-electron Boltzmann equations in InP

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Abstract
A matrix method for the numerical determination of steady-state hot-phonon and nondegenerate hot-electron distribution functions is presented. The coupled Boltzmann equations for the longitudinal-optical phonons and for the electrons, in the Γ and L valleys of III-V semiconductor compounds, are iteratively solved with high accuracy under typical hot-electron conditions. The phonon distribution is shown to be significantly disturbed from thermal equilibrium. In turn, nonequilibrium phonons induce a substantial disturbance of the hot-electron distribution. Computations are performed for InP at 300 K, taking into account all relevant scattering mechanisms. It turns out that the electron transport parameters are strongly affected in the field range from 0 to 10 kV/cm: the drift velocity is increased by about 42% at 2 kV/cm and the Ohmic mobility by 37%. These effects are shown to be due to the drag and reduced cooling of the carriers by the nonequilibrium LO phonons.