Intracollisional field effect in the high-field regime of the quantum transport equation using Monte Carlo simulations

We have studied the importance of the ‘‘intracollisional field effect’’ in the quantum-mechanical transport equation derived by Khan, Davies, and Wilkins [Phys. Rev. B 36, 2578 (1987)] via Monte Carlo simulations. This equation is similar to other quantum transport equations in the literature [Barker and Ferry, Phys. Rev. Lett. 42, 1779 (1979)] and contains an electric-field-induced ‘‘broadening’’ (denoted by √‖α‖ ) of the energy-conserving δ function in semiclassical transition rates which is proportional to √‖scrE⋅q‖ , where scrE is the electric field and q is the change in electron momentum caused by scattering. We use a single parabolic band with parameters of the central valley of GaAs. The electrons are assumed to scatter with polar optical and acoustic phonons with the scattering parameters chosen to simulate GaAs. Our Monte Carlo analysis of the problem shows that intracollisional field effect is not important. This implies that in the field-dominant regime, i.e., √‖α‖ >ħ/${\tau }_{\mathrm{sc}}$, the results obtained from the quantum transport equation reduce to those obtained from the semiclassical Boltzmann equation for a single-band semiconductor of infinite width, where ${\tau }_{\mathrm{sc}{}^{\mathrm{-}1}}$ is the electron scattering-out rate.