Analytical results for semiconductor quantum-well wire: Plasmons, shallow impurity states, and mobility

We present a theoretical investigation of the electronic properties of a quasi-one-dimensional electron system at very low temperature. For a cylindrical quantum wire the electron-impurity interaction and the electron-electron interaction is calculated for a two-subband model. Our analytical results for the electron-impurity and the electron-electron interaction are in good agreement with the exact results for our model. Analytical results for the band bending due to the filling of the lowest subband are evaluated. Within our analytical results we discuss various aspects of the electronic properties of the semiconductor quantum wire: screening (intrasubband and intersubband plasmons), shallow impurity states (screened and unscreened), and mobility (ionized-impurity scattering and interface-roughness scattering). Analytical expressions are given for the dispersion of plasmons, the binding energies of shallow impurities, and the mobility. Our results on intersubband plasmons are compared with experiments.