Transient and steady-state electron transport in GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterojunctions at low temperatures: The effects of electron-electron interactions

We have performed theoretical studies of transient and steady-state low-temperature transport for electrons in GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As single-well heterojunction structures. Polar-optical-phonon–acoustic-phonon scattering (coupled by the deformation potential or piezoelectrically) and ionized impurity scattering are taken into consideration. The interactions of the electrons among themselves are also accounted for through the effect of plasmons and single pair collisions. All the rates are calculated using self-consistent envelope wave functions for up to five electronic subbands. Ensemble Monte Carlo simulations which incorporate the effect of degeneracy have been used to study the dynamics of the electrons for values of the electric field in the Ohmic to hot-electron range. The temperature dependence of the low-field mobility is analyzed and its dependence on the value of the deformation-potential constant D is shown in detail. The results are in overall agreement with experimental findings but do not confirm other theoretical ideas such as scattering-induced negative differential resistance.