Size effect in parabolic GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells

We report the results of experimental and theoretical studies of the electron mobility in remotely doped, quasi-three-dimensional GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As parabolic wells. We show that the electron mobility in such structures is strongly reduced by a size effect due to nonspecular scattering of electrons from rough walls confining the electron gas. The roughness of the walls results from random fluctuations of the remote-ionized-impurity concentration and/or the alloy composition. Incorporation of the size effect allows for a quantitative description of the electron mobility in these parabolic wells.