Electronic and acoustic-phonon inter-Landau-level Raman scattering in GaAs/AlxGa1−xAs multiple quantum wells

We present an experimental study of inter-Landau-level excitations in undoped GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum wells in high magnetic fields by means of Raman scattering. The experiments were performed in Faraday backscattering geometry with the field along the growth axis, using circularly polarized light for resonant excitation of low-index magneto-optical transitions between Landau levels. We observe two types of peaks. One of them, present in both Stokes and anti-Stokes regions at a constant Raman shift, corresponds to the electron cyclotron energy. We attribute it to electronic Raman scattering from a quasistationa…

Magnetic-field-enhanced outgoing excitonic resonance in multi-phonon Raman scattering from polar semiconductors

A combined scattering mechanism involving the states of free electron-hole pairs (exciton continuum) and discrete excitons as intermediate states in the multi-phonon Raman scattering leads to (1) a strong increase of the scattering efficiency in the presence of a high magnetic field and to (2) an outgoing excitonic resonance: the two features are not compatible when only free pairs (leading to a strong increase of the scattering efficiency under the applied magnetic field) or discrete excitons (resulting in the outgoing resonance at the excitonic gap) are taken into account.

Temperature and Isotopic Mass Dependence of the Direct Band Gap in Semiconductors: LCAO Calculations

Resonant Raman scattering in quantum wells in high magnetic fields: Deformation-potential interaction.

A theoretical study of one-phonon resonant Raman scattering in a quantum well (QW) in high magnetic fields has been performed. The Raman profiles are calculated as a function of magnetic field, quantum-well thickness, and laser frequency. The basic theory is first developed assuming parabolic masses in the plane perpendicular to the growth direction of the QW. Selection rules for deformation-potential-allowed scattering are given and a compact analytical expression for the Raman-scattering efficiency is obtained for infinite barriers. The double-resonance conditions are derived as a function of the magnetic field or well thickness. In a second part of the work, the heavy-hole\char21{}light-…

Excitonic model for second-order resonant Raman scattering.

A theoretical model for second-order resonant Raman scattering is presented. The effect of Coulomb interaction between electrons and holes is fully taken into account in the framework of the effective-mass approximation. By introducing discrete and continuous excitonic intermediate states in the Raman process, an explicit expression for the Raman scattering efficiency is given for long-range Fr\"ohlich electron-phonon interaction. The model developed can be used to evaluate Raman profiles around the resonant region. A closed-form expression for all matrix elements of the exciton-phonon interaction is obtained once the Coulomb problem for the relative electron-hole motion is separated in sph…

Dependence of the lattice parameters and the energy gap of zinc-blende-type semiconductors on isotopic masses.

The dependence of the ${\mathit{E}}_{0}$ direct gap of Ge, GaAs, and ZnSe on isotopic masses at low temperatures has been investigated. Contributions of the variation of the lattice parameter to the gap shift of the binary compounds have been evaluated by using a volume-dependent lattice dynamics, while local empirical pseudopotential techniques have been employed to calculate gap shifts due to electron-phonon interaction. The dependence of these terms on the lattice-dynamical model and on the q\ensuremath{\rightarrow}0 extrapolation of the pseudopotential form factors has been investigated. The contributions of the optical and acoustical modes to the isotopic shift are analyzed. The result…

Raman studies of isotope effects in Si and GaAs

Abstract We have measured by Raman scattering changes of the optic phonon energy and line width in Si and GaAs with isotopic composition. The phonon energies of isotopically pure samples show the expected dependence on the average atomic mass in Si and the reduced mass in GaAs, respectively, as well as small anharmonic contributions. In isotopically disordered samples we find frequency shifts of 1.15(20) cm−1 for 28Si0.530Si0.5 and 0.31(20) cm−1 for the TO phonon of natGaAs, induced by mass disorder which also contributes to the line broadening. We give theoretical estimates of these effects.

Pressure measurements of TO-phonon anharmonicity in isotopic ZnS

We have measured the dependence on pressure of the line-widths of the TO and LO Raman phonons of β-ZnS. In order to enhance the phenomena observed, and to eliminate possible effects of isotopic disorder, we have measured a nearly isotopically pure crystal, 68 Zn 32 S. The strongly structured pressure effects observed are interpreted on the basis of anharmonic decay and the corresponding two-phonon density of states.

Electric-field-induced Raman scattering in GaAs: Franz-Keldysh oscillations

We have studied the influence of strong electric fields on the Raman scattering intensity from LO phonons in GaAs (100) at room temperature using laser excitation energies above the fundamental ${\mathit{E}}_{0}$ gap. Striking oscillations are found in the scattering intensity for configurations where either the deformation potential or Fr\"ohlich electron-phonon interaction contribute. The oscillations in the deformation-potential-mediated scattering intensity can be related to Franz-Keldysh oscillations derived from the ${\mathit{E}}_{0}$ gap, whereas a more complicated mechanism has to be invoked for processes where Fr\"ohlich interaction is responsible.

Triple magnetopolarons in quantum wells

We derive the equations for eigenstates and eigenenergies of a triple magnetopolaron in quantum-well structures. An iteration procedure for obtaining the wave function and energy including the contributions of diagrams with crossing phonon lines is given. We show that under conditions of exact resonance the middle energy branch of the triply split magnetopolaron state consists of only two out of three bare states. We suggest the experimental verification of this prediction.

Resonant hyper-Raman scattering in semiconductors

A theoretical model for resonant hyper-Raman scattering by LO phonons is developed, taking into account excitonic effects. The model is valid for energies below and above an allowed absorption edge. The matrix elements corresponding to the exciton-photon and exciton-phonon interactions are derived analytically, and their contributions to the total scattering efficiency are analyzed. The two main electron-phonon interaction mechanisms present in polar semiconductors, deformation potential, and Fr\"ohlich interaction, are considered. It is shown that the one-phonon resonance hyper-Raman scattering mediated by the deformation potential interaction is dipole forbidden, whereas it is allowed whe…

Raman scattering inβ-ZnS

The first- and second-order Raman spectra of cubic ZnS $(\ensuremath{\beta}$-ZnS, zinc-blende) are revisited. We consider spectra measured with two laser lines for samples with different isotopic compositions, aiming at a definitive assignment of the observed Raman features and the mechanisms which determine the linewidth of the first order TO and LO Raman phonons. For this purpose, the dependence of the observed spectra on temperature and pressure is investigated. The linewidth of the TO phonons is found to vary strongly with pressure and isotopic masses. Pressure runs, up to 15 GPa, were performed at 16 K and 300 K. Whereas well-defined TO Raman phonons were observed at low temperature in…

Raman Scattering in CuCl under Pressure

Raman spectra of CuCl were measured under hydrostatic pressures up to 14 GPa at low temperatures (T = 5 K). The anomaly in the Raman lineshape of zincblende CuCl at frequencies near the transverse-optic (TO) mode, which consists of a broad structure with several maxima, disappears at a pressure near 3 GPa. This effect is well reproduced by a model calculation of the anharmonic coupling of the TO mode to acoustic two-phonon states (Fermi resonance). Alternative interpretations of the TO Raman anomaly in terms of local vibrational modes of Cu atoms in off-center positions are not supported by the present results. Raman spectra indicate the existence of the phase CuCl-IIa in a narrow pressure …

Lattice phonon modes of the high-pressure phase CuCl-IV

Raman spectra of isotopically pure CuCl samples ${(}^{63}\mathrm{CuCl}$ and ${}^{65}\mathrm{CuCl})$ were measured under hydrostatic pressure up to 14 GPa at low temperature $(5 \mathrm{K}).$ Up to six Raman modes were resolved for the binary BC8-analog phase CuCl-IV in the range from 4.1 to 14 GPa. The phonon dispersion relations of this phase were calculated within a rigid ion model. Based on this calculation an assignment for the observed Raman-active modes is proposed. The calculated pressure dependences of mode frequencies reproduce the experimental results. Raman spectra support the existence of the phase CuCl-IIa in a narrow pressure range from 3.3 to 4.1 GPa.

Resonant hyper-Raman scattering in semiconductors: Excitonic effects

Abstract A theoretical model of resonant hyper-Raman scattering involving two incident photons of frequency ωL is developed. The model is valid for energies 2ℏωL around the absorption edge of the semiconductor, and takes into account Wannier excitons as intermediate states in the scattering process. Both deformation potential and Frohlich interaction are included in the model: It is found that Frohlich-mediated scattering is a dipole-allowed process, in contrast to one-phonon Raman scattering, where the Frohlich mechanism is dipole-forbidden. We have performed numerical calculations of the resonance profile (hyper-Raman cross-section versus 2ℏωL) and applied our model to materials with dipo…

Electron–phonon effects on the direct band gap in semiconductors: LCAO calculations

Abstract Using a perturbative treatment of the electron–phonon interaction, we have studied the effect of phonons on the direct band gap of conventional semiconductors. Our calculations are performed in the framework of the tight-binding linear combination of atomic orbitals (LCAO) approach. Within this scheme we have calculated the temperature and isotopic mass dependence of the lowest direct band gap of several semiconductors with diamond and zincblende structure. Our results reproduce the overall trend of available experimental data for the band gap as a function of temperature, as well as give correctly the mass dependence of the band gap on isotopic. A calculation of conduction band in…

Spatial correlation of laser-generated electrons and holes in quantum wells

The spatial correlation of hot electrons and holes generated by light in a semiconductor quantum well (QW) is studied. For hot electron-hole pairs in a polar material, this correlation is determined by the interaction with LO-phonons. We analyze the distribution F N (r, K) of electrons and holes which are created in a given light absorption process, with respect to their relative separation r and total quasimomentum ħK, after the emission of a number N of LO-phonons. The relationship between the spatial distribution of electrons and holes in these intermediate states and the cross-section of multi-phonon resonant Raman scattering (MPRRS) is established. Spatial correlation effects are stron…

Tight-binding calculation of spin splittings in semiconductor superlattices