Long‐Wavelength Optical Phonons in GaAsAlAs Superlattices

Abstract

Optical phonons in polar semiconductor superlattices near the zone center are studied. The microscopic theory based on a rigid-ion model is simplified by restriction to one elastic force constant per material and spatial average of the long-range electric field. The theory allows much insight into the mode structure, particularly anisotropy and layer thickness dependence of frequencies, atomic displacements, and accompanying electric fields. Explicit results are given for short-period GaAs-A1As superlattices. The relationship of confined and interface modes is discussed.

Relationship of Microscopic and Macroscopic Theories for Long‐Wavelength Optical Phonons in GaAs‐AlAs Superlattices

“…3). The reasons for such drastic changes going from 8 = 0 to 8 + 0 have been discussed in a previous paper [25]. We note that all other wave vectors are shifted to higher values in the same manner.…”

“…Generally we do this numerically. Thereby we neglect the difference of the ion charges in GaAs and &As, setting el" = and f2 and this ion charge e* are adjusted to fit the experimental values wTol, wLol and wTO2 of the bulk zone-center optical phonons [25]. An analytical solution can be tried to find if the wave-vector dispersion of the bulk branches is omitted.…”

A Unified Approach to Interface and Confined Bulk Optical Phonons in Quantum Wells and Superlattices

“…Optical phonon modes in quantum wells (QW) and superlattices (SL) have been calculated by several authors [1][2][3][4][5][6][7][8][9][10][11][12][13] on the basis of classical theory of phonon modes for bulk materials and the electrodynamics. The equation of motion is where u , E, and M are the mechanical displacement field, the long-range electric field and the reduced mass of the unit cell, respectively.…”

Macroscopic behaviour of longitudinal optical phonons in a AlAs/GaAs/AlAs quantum well

“…Microscopic models of the behaviour of optical phonons in semiconductor heterostructures necessarily involve extensive numerical calculations [1][2][3][4][5][6][7][8]. A simple macroscopic model giving analytical results close to those of microscopic models would be useful in studies of the interaction of phonons with electrons and light.…”