Electron Relaxation in Multisubband GaAs Quantum Wire
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ELECTRON RELAXATION IN MULTISUBBAND GaAs QUANTUM WIRE
SALVIANO A. LEAO*, OSCAR HIPOLITO* AND FRANQOIS M. PEETERS** * Departamento de Fisica e Ci6ncia dos Materiais, Instituto de Fisica e Quimica de Siio
Carlos, Universidade de Sio Paulo, Caixa Postal 369, 13560-970, Sio Carlos, SP, Brazil ** Department of Physics, University of Antwerp (UIA), B-2610 Antwerp, Belgium
ABSTRACT The intra- and intersubband scattering rates for emission and absorption of longitudinal optical (LO) phonons by electrons confined in a cylindrical GaAs-GaAlAs quantum wire are calculated. Multiple peaks due to intersubband transitions appeared on the total scattering rate as a function of the electron energy. In the last two decades the progress in semiconductor technology has been achieved in the fabrication and characterization of microstructures in which the confinement of the electron motion in two directions results in quasi-one-dimensional behavior and leads to a wealth of interesting physics [1]. In such systems, the electrons are confined to move along the length of the wire while the motion is quantised in the two transverse directions. High-mobility GaAs/AlGaAs quantum wires, in which the elastic scattering by ionized impurities is suppressed due to remote doping, have become the system of choice for various transport experiments. Recently there has been increasing interest to understand the behavior of electrons in such quasi-one-dimensional semiconductor structures, by investigating the static and dynamical conductivity, collective excitations, mobility limited by impurities as well as by optical and acoustic phonons, binding energies of hydrogenic impurities and excitons, which all showed significant size effects [2-7]. However, most of the transport models assume the electron gas confined to the lowest quantum subband. This is certainly a drastic oversimplification in most of the typical experiments where the Fermi energy is such that several subbands are occupied. In this case one cannot expect reliable theoretical results for the transport and optical properties of quantum wires. The inclusion of multisubbands is necessary. In this paper we investigate phonon scattering in a quasi-onedimensional semiconductor GaAs/GaAlAs multisubband structures. We will assume that the phonon spectrum is essentially that of the bulk of the relevant semiconductor material. In the corresponding two dimensional system it was pointed out by Degani and Hip6lito that this approximation works very well [8]. The aim of the present paper is to calculate the intra and intersubband scattering rates for emission and absorption of optical phonons by electrons confined in a cylindrical GaAs wire. We will show that size effects have important consequences and are more pronounced than in 2D-systems. In the quasi-lD electron system under study the electrons are free to move along the direction of a cylinder, of length L, and radius R which is composed of GaAs embedded in Gao. 7A10 .3As. In the effective mass approximation, the electron wave function for the
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