Electron scattering by optical phonons in ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells

The scattering of a quasi two-dimensional electron gas by optical phonons in selectively doped ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As/GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells is systematically studied in order to determine the effect of phonon confinement. The electron states are calculated solving self-consistently Schrödinger and Poisson equations to obtain an accurate dependence upon the structure parameters and the temperature. We study the way the scattering is affected by the form of the phonons calculating the mobility using three models for the phonons. They are considered:m(a) as three dimensional (3D), (b) as a set of confined and interface phonons, and (c) as the normal modes of the heterostructure. The relaxation times for the electron energy subbands are calculated solving the system of Boltzmann equations. The effect of the temperature and the well width variation is also investigated. The results are in a good agreement with experimental measurements. The agreement is only slightly dependent on the model used for the phonons and becomes best when the effect of the heterostructure on the phonon modes is taken into account.