Hot electrons under quantization conditions: I. Kinematics

Abstract

A detailed analysis of the kinematic peculiarities of the interaction of bulk acoustic phonons with confined electrons in a quantum wire is peformed for intra- and inter-sub-band transitions. Due to quantization of the electron motion in a quasi-one-dimensional wire a new parameter appears in the kinetic theory ( is the electron effective mass, s is the sound velocity, is the quantum energy of the ground state and is some numerical constant which depends upon the shape of the quantizing potential), characterizing the electron - acoustic-phonon interaction. At low lattice temperatures , when , the intra-sub-band interaction has a strong inelastic character for the majority of electrons (assuming that the mean electron energy is also less than ). In the opposite case of high lattice temperatures, , this interaction is always quasi-elastic for the majority of electrons because the mean electron energy exceeds . Inter-sub-band scattering, on the other hand, is quasi-elastic at arbitrary lattice temperatures. These kinematic peculiarities of the electron - acoustic-phonon interaction are universal and, in general, do not depend on the physical nature of the quantizing field. It can be an external quantizing magnetic field or size-quantizing electrostatic potential, resulting in the confinement of electrons in a two-dimensional sheet or in a quantum wire, or confinement can be realized due to both electrostatic and magnetic potentials combined. The discussed peculiarities manifest themselves in novel kinetic properties of low-dimensional electron systems.