Ionized impurity scattering in quantum wells and quantum wires

Low-field mobility for scattering of electrons by ionized impurities is calculated in quantum wells and quantum wires. Analytical expressions for mobility are obtained on the basis of the quantum-kinetic approach using the quantum mechanical formalism of the dielectric function for non-interacting and interacting electrons. If the kinetic energy of electrons is much higher than their inter-particle potential energy, the electron system remains qualitatively similar to a non-interacting electron gas. The Lindhard dielectric function is used to calculate the mobility and screening factor of non-interacting electrons. If the potential energy of electrons is close to or prevails over their kinetic energy, the electron system displays a collective behavior similar to an electron liquid. In this case, electrons are considered interacting. To calculate the mobility of the interacting electrons, we have used the static local-field correction factor to the electron dielectric function. Analytical dependences of the electron mobility on dimensionality of the electron system, sizes of the quantum structures in the confining directions, temperature, forms of confining potential, electron density, and material parameters are obtained. The quantum confinement is modeled by triangular and rectangular confining potentials. The results of calculations are compared with the known experimental data.