Frank Prengel

Hot Electrons in Quantum Wires: Intersubband Impact Ionization and Relaxation

Mensch & Buch Verlag Berlin, 1998
ISBN 3-933346-21-5

The optical properties of semiconductor quantum wires are strongly influenced by scattering processes between their conduction subbands. Two important scattering mechanisms, electron-electron interaction and electron-LO-phonon interaction, are theoretically and numerically studied in detail in this work.
We first derive quantum kinetic equations for Coulomb electron-electron interaction in quasi one-dimensional systems. Our multi-subband density matrix approach treats both one-particle matrices and two-particle density correlations as independent dynamic variables.
Numerical simulations of intra- and intersubband Coulomb scattering  in non-degenerate electron gases show that on short time scales,  the strong restrictions on the available phase space for semiclassical  scattering processes in one dimension are relaxed due to quantum-mechanical energy-time uncertainty. This leads to a broadening of peak structures in the electron distribution which is semiclassically impossible.
The intersubband impact ionization rate can be significantly enhanced, compared to the semiclassical case, when electrons are optically generated in the lowest subband below the subband splitting. This is due to both a softening of the impact ionization threshold, and intrasubband broadening of the distribution function.
In the second part of this work we investigate intersubband relaxation  and intrasubband thermalization and cooling. Electron scattering by  polar optical phonons is semiclassically incorporated into the set of dynamic equations because we intend to focus on quantum kinetic effects which are induced by Coulomb scattering in conjunction with electron-phonon interaction.
We find that this model can properly describe the intrasubband  thermalization and cooling (down to lattice temperature) of hot electrons.  Also intersubband relaxation of electrons from the second to the first subband can be quantitatively analyzed. It is shown that simpler approaches, without Coulomb scattering or with semiclassical Coulomb scattering, fail to describe both intersubband relaxation and intrasubband thermalization in a satisfactory manner.