Temperature dependence of the high-frequency resistivity of a type-I superlattice due to impurity and phonon scatterings

A general expression is developed here for the memory function of the linear dynamical conductivity of a type-1 superlattice with impurity and phonon scatterings, taking account of the electron-electron Coulomb interaction between different quantum wells as well as within a given quantum well. The real part of the frequency-dependent resistivity of a GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum-well superlattice due to remote and background impurity scatterings and due to polar-optical-phonon couplings is calculated at several different temperatures, showing significant temperature dependence in both the bulk plasmon resonance (associated with close packing of the superlattice planes) and in the phonon resonance.