Confined LO Phonons Research Articles

Electron-phonon interaction and electron scattering by modified confined LO phonons in semiconductor quantum wells.

Developpement d'un modele ameliore de l'interaction electron-phonon pour les phonons longitudinaux optiques dans les puits quantiques semiconducteurs. Dans ce modele simple du continuum dielectrique modifie, les phonons LO sont des modes confines possedant des champs electriques et des champs de deplacement qui sont en accord avec les modeles electrostatique et microscopique des phonons longitudinaux optiques. Les resultats numeriques sont presentes et discutes pour les champs electriques de ces modes. Les vitesses de diffusion resultantes des electrons pour l'emission et l'absorption des phonons LO dans un puits quantique sont calculees et presentees sous forme graphique

Electron-LO-phonon scattering rates in GaAs-AlxGa1-xAs quantum wells

The authors calculate the electron-LO-phonon scattering rates for confined phonon modes associated to intrasubband and intersubband transitions for GaAs-AlxGa1-xAs quantum wells with finite depth. The Huang and Zhu approximation for the confined LO phonon modes, based on a microscopic lattice-dynamic approach, is used and the results are compared with corresponding calculations for infinitely deep quantum wells and some experimental results. The authors found a remarkably good agreement with the experimental results.

Confined LO phonons in GaAs/AlAs superlattices.

We report the observation of both GaAs and AlAs confined LO phonons in short-period GaAs/AlAs superlattices. The measured GaAs mode frequencies are found to map well onto the bulk dispersion curve with a suitable choice of an effecive wave vector, confirming the validity of this technique for determining bulk phonon dispersions over at least the first half of the bulk Brillouin zone. The frequency separation of confined AlAs LO modes is found to be consistent with a weak dispersion of this branch along the [001] direction, in agreement with recent lattice-dynamic calculations.

Phonon frequencies for Si-Ge strained-layer superlattices calculated in a three-dimensional model.

We present the results of full three-dimensional calculations of phonon frequencies in silicon-germanium strained-layer superlattices (SLS's) and compare with experimental data. We use a modified version of the six-parameter valence-force-potential model, incorporating the strained nature of the layers. We confirm that the dispersion relations for Si/Ge SLS's fall into bands closely associated with the bulk dispersion relations of silicon and germanium, as expected. Also, we find that our model precisely reproduces the predicted strain-induced frequency shifts to within one-tenth of 1% for epitaxial layers grown in the [001] direction, if longitudinal and transverse polarized phonons are considered separately. We also present analytical expressions for these frequency shifts. We find that the degree of penetration of confined LO phonons into adjacent layers is qualitatively different for growth in the [001] and [110] directions. Confined phonons in [110] superlattices have nearly zero penetration depth into adjacent layers, while the penetration depth for phonons in [001] superlattices is quite significant. This large penetration depth for [001] superlattices allows for coupling of transverse interface modes across thin layers, giving rise to a bifurcation of these otherwise degenerate modes. We also show that only transversely polarized interface modes are confined to the interface region, while longitudinally polarized modes with similar energies actually extend across the silicon layers and thus depend strongly on the width of the silicon layers. We compare our calculated results with measured Raman spectra of two typical samples and find that our model gives the correct position of the Raman peaks to within 1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, after correcting for temperature.

Interaction of electrons with the confined LO phonons of a free-standing GaAs quantum wire.

A continuum model is employed to describe the allowed longitudinal-optical phonons of a cylindrical free-standing GaAs wire. The electron-phonon interaction Hamiltonian is then obtained and used to calculate intrasubband transitions in the extreme quantum limit. The scattering rate is predicted to be markedly reduced compared with the bulk value, and compared with the value expected when the wire is not free standing. This result is due to the lack of LO interface modes in the free-standing situation.

Calculation of phonons in [001] and [110] SiGe strained-layer superlattices

Abstract In this communication, we present the results of full three dimensional calculations of phonon frequencies in silicon-germanium strained-layer superlattices. We used a modified version of the six-parameter valence force potencial model (VFPM), incorporating the strained nature of the layers. We found that the VFPM reproduces the predicted strain-induced frequency shifts for superlattices grown in the [001] direction extremely well, if longitudinal and transverse polarized phonons are considered separately. We found that the degree of penetration of confined LO phonons into adjacent layers is different for growth in [001] direction and growth in the [110] direction. Confined phonons in [110] superlattices have nearly zero penetration depth into adjacent layers, while the penetration depth for phonons in [001] superlattices is quite significant. This information is crucial when determining layer thicknesses using Raman spectroscopy. It was found that the large penetration depth for [001] superlattices allowed for coupling of interface modes across layers, giving rise to a splitting of these otherwise degenerate modes. The model was found to be unsuitable for modelling strain for superlattices grown in the [110] direction.

LO-phonon confinement and polaron effect in a quantum well.

Polaronic corrections are calculated considering electron coupling with confined LO phonons in a quantum well (QW). The electron--LO-phonon Hamiltonian for a confined electron-phonon system in a QW is taken from a previous work. The electron self-energy is calculated by use of the standard perturbation-theory treatment for the weak-coupling polaron assuming parabolic energy band structure and T=0 K. Screening effects are included along the lines of the static Thomas-Fermi approximation. Comparison with different experimental works is made and acceptable agreement is achieved. We also present comparisons with other theoretical works on the subject.

Interface roughness and confined LO phonons in quantum wells

We report Raman measurements of the LO phonon modes confined in GaAs/AlAs quantum wells grown by refined MBE with and without growth interruption and by migration enhanced epitaxy (MEE). The energies of the confined LO phonon modes lie close to the values expected from the bulk GaAs phonon dispersion. We show that the higher order confined phonon modes are more sensitive to roughness than the lower order modes.

A Study of Interfaces in GaAs/AlAs Superlatyices Using Phonons

ABSTRACTVibrational Raman scattering has been used in conjunction with luminescence, luminescence excitation spectroscopy, and x-ray diffraction to study the interfaces of GaAs/AlAs superlattices grown by MBE with and without growth interruptions at the interfaces. The confined LO phonon spectra clearly indicate that in the sample grown with growth interrupts at least one of the interfaces in each GaAs layer is truly smooth. In addition it is shown that the intensity of the interface phonons probed via Raman scattering is sensitive to the state of the interface.

On the Scattering of Electrons by Confined LO Phonons in a Semiconductor Quantum Well

AbstractScattering and momentum‐relaxation rates are calculated for a semiconductor quantum well (QW) considering electron scattering by confined LO phonons. Electron coupling with confined LO phonons is treated on the basis of an interaction Hamiltonian deduced in a previous work, while both electrons and LO phonons are assumed to be completely confined to the QW active layer. Besides the exact results, results are reported in the so‐called momentum‐conservation approximation (MCA) and the fractional error implied in the MCA is calculated. Detailed comparison with previous works (in the non‐confined phonon case) is made.

Interface roughness and the dispersion of confined LO phonons in GaAs/AlAs quantum wells.

We report the energies of the confined LO phonon modes in the GaAs wells of GaAs/AlAs superlattices with well widths between 10 and 18 monolayers. We observe confined LO-phonon modes up to 12th order. The measurements were performed on sample structures obtained by two different growth techniques [molecular-beam epitaxy (MBE) with growth interruption and migration-enhanced epitaxy (MEE)], which favor the smoothness of the GaAs/AlAs and the AlAs/GaAs interfaces. Measurements on a sample, where the ``normal'' GaAs/AlAs interfaces were grown on purpose without growth interruption, show weaker Raman signals and confined phonon modes up to lower order than observable for samples with growth interruption. The energies of the confined LO phonons as a function of the confinement wave vector lie close to recent neutron results for the LO-phonon dispersion in bulk GaAs. We suggest that previously reported discrepancies are due to stronger interface roughness than in the present samples. We show that the high-order confined phonons are considerably more sensitive to roughness than the low-order confined LO phonons. Therefore the former and not the latter should be used for characterization of interface roughness. For determination of the phonon dispersion, on the other hand, the uncertainties are higher for the higher-order confined modes. We observe discrete confined modes corresponding to sections of the quantum well with thicknesses differing by one monolayer.

Raman scattering from confined LO phonons and dispersion relation in GaAs/AlAs superlattices

The Raman scattering from both GaAs and AlAs confined LO phonons for several GaAs/AlAs superlattices is presented. The GaAs confined LO phonons were observed for two narrow GaAs layer samples at room temperature. The frequencies of observed phonons fit fairly well with the theoretical dispersion curves.

Magnetophonon resonance of a two-dimensional electron gas in a quantum well

Magnetophonon resonance of the transverse magnetoresistance is investigated theoretically and experimentally in AlGaAs/GaAs/AlGaAs quantum wells. The interaction Hamiltonian of the two-dimensional electron gas (2DEG) is derived for the scattering by the LO phonons confined in the quantum wells, which reveals that the inter-sub-band transition of the 2DEG plays an important role in the magnetophonon resonance. The authors evaluated the magnetoconductivity of the 2DEG in a quantum well using the Kubo formula. The calculated magnetoresistance exhibits oscillations arising from both the intra-sub-band and inter-sub-band transitions of the 2DEG induced by the scattering of confined LO phonon, resulting in the periods of oscillations in reciprocal magnetic fields, 24 and 41 T, which are in good agreement with the present observation in an AlGaAs/GaAs/AlGaAs quantum well with a GaAs well width of 100 AA (24 and 45 T). The present results indicate that the magnetophonon resonance in a quantum well arises from the scattering of the 2DEG by the LO phonons whose mode is confined in the well region.

Landau damped collective excitations of the quasi-two-dimensional polaron gas in double heterostructures

The spectrum of the collective and single-particle excitations of the quasi-two-dimensional polaron gas of a modulation doped GaAs-Ga 1- x Al x As double heterostructure is analyzed using the random-phase approximation for the electron gas. Caused by the plasmon-phonon coupling the long-wave optical phonons of the double heterostructure, the confined LO phonons and the interface phonons, become Landau damped in the regions of the single-particle intra- and intersubband continuum. Numerical results are presented for the dispersion curves and the energy-loss function. We have found additional non-phonon-like modes existing within the single-particle intra- and intersubband continuum.

Raman scattering of (GaAs) n(AlAs) n superlattices

All of GaAs-like and AlAs-like LO confined modes in (GaAs) n (AlAs) n short period superlattices are reported, to acknowledge, for the first time at room temperature and off-resonance conditions. It is shown that the Raman activity of confined LO modes is dependent on the scattering configuration. For the orientation x = (110), y = (110) and z = (001), the complete modes of confined LO phonons are observed in z( xx) z̄ configuration, and no modes in z( xy) z̄ configuration.

Raman study of the effects of annealing on folded LA and confined LO phonons in GaAs-AlAs superlattices.

Raman study of the effects of annealing on folded LA and confined LO phonons in GaAs-AlAs superlattices.