Dielectric function and impurity-limited mobility of semiconductor quantum wires: effects of dielectric mismatch and finite confining potential

The dielectric response function of the electron system in a cylindrical semiconductor quantum wire (QWR) embedded in a dielectric material is derived within the random phase approximation in the quantum limit when only the lowest electron subband is considered. The wire is studied in both finite and infinite confining potential models. It is shown that the dielectric mismatch strongly affects the collective excitations of the electron system and the electrostatic interaction between charged particles in the wire. The electron screening is greatly enhanced in thin QWRs with low-kappa dielectric surroundings and weakened for high-kappa dielectric environment. Thus, the impurity-limited electron mobility can be improved in small-radius semiconductor QWRs coated with a material having a dielectric constant smaller than that of the semiconductor, as opposed to a number of previous reports. The calculations also indicate that the model of infinite potential barrier for thin QWRs underestimates the impurity electron mobility compared to the finite barrier model and can be used in the case of QWRs with large radii.