Observation of Standing Acoustic Waves by Resonant Raman Scattering

Abstract

Resonant Raman measurements on GaAsyGaP quantum wells, as thin as one monolayer, are reported. The work is focused on the low-frequency scattering range, which exhibits a continuous emission and periodic oscillations that have never been observed up to now. It is shown that spatial localization of electrons leads to Raman scattering processes for which momentum is not conserved, and hence to the activation of the density of states of acoustic phonons. A model, based on electron-acoustic phonon interaction, is developed and used for calculations of the resonant Raman efficiency. A good agreement with measured spectra is obtained. The origin of the observed periodic oscillations is interpreted by considering standing acoustic waves. [S0031-9007(97)03207-9] During the last decade considerable interest has been devoted to the vibrational properties of semiconductor superlattices (SL’s) and multiple quantum wells (QW’s), leading to a detailed understanding of phonons and their coupling with electrons [1,2]. It is now well established that, in these structures, vibrational excitations could be confined [3 ‐ 5] (optical phonons), localized [6,7] (interface phonons), or folded [8] (acoustic phonons) depending on the energy range and on the elastic and dielectric properties of the constituents. Almost all of these features were pointed out by means of Raman scattering measurements. In contrast, only a few results [9,10] are available for single QW’s (or even for a small number of QW’s), because the associated scattering volume is considerably reduced, leading to a serious experimental limitation. Beyond the experimental challenge, the study of such structures is of particular interest with regard to both vibrational and electronic properties. Indeed, in single quantum wells electrons are localized in real space which leads to a breakdown of the translational symmetry along the growth axis. In the acoustic frequency range this effect results in a strongly resonant continuous scattering [11,12]. In a previous work [10], we showed that frequency location, line shape, and intensity of the continuous scattering is mainly determined by the form factor associated with localized electron-acoustic phonon interaction. In this Letter, we report on resonant Raman measurements on GaAsyGaP quantum wells as thin as one monolayer. In this extreme situation of electron localization, a strong continuous emission appears again in the low-frequency range. In addition, periodic oscillations of the continuous scattering are observed. The origin of the continuous scattering and its oscillatory behavior is discussed and analyzed by taking into account both spatial localization of electrons and possible existence of standing acoustic waves. A model based on electron-acoustic phonon interaction in a single quantum well is developed, and a comparison between calculated and measured Raman spectra is presented. Our most exciting findings are as follows: (i) electronic wave functions can be obtained from low-frequency resonant Raman spectra; (ii) for the first time, standing acoustic waves could be observed. The structures investigated were grown by atomic layer molecular beam epitaxy (ALMBE) on a (001) oriented GaP substrate. The samples consist of three GaAs QW’s separated by wide (38 nm) GaP barriers. The first QW is at 80 nm underneath the sample surface. The GaAs QW’s are of equal thickness ranging from 1 to 4 monolayers (ML) in steps of 1 ML. Only the results obtained from 1 ML GaAs QW’s are presented here, since the other samples showed very similar features. The lattice mismatch between GaAs and GaP is about 4% (with respect to GaP), and the critical thickness for dislocation formation (and strain relaxation) is around 6 ML [13]. So, the GaAs QW’s are biaxially strained and fully matched to GaP. As a matter of fact, the high energy electron diffraction patterns showed neither threedimensional growth nor appreciable roughness. Calculation of the band structure of GaAs strained to GaP was performed according to the deformation potential theory [14]. It was found that the GaAs layer is indirect in k space. Indeed, due to strain, the lowest energy conduction states are of Xxy type. For G-band electrons, the GaAs layer forms a well which is 0.5 eV deep. The energy of transition between confined heavy hole (hh) and G-electron states was determined by electroreflectance spectroscopy performed at liquid nitrogen temperature. It was found at 2.73 eV, for the 1 ML GaAs QW’s. Raman experiments were performed at liquid nitrogen temperature and in near-backscattering configuration. The spectra were excited using the output lines of an Ar laser. The scattered light was analyzed using a triple spectrometer and detected with a conventional photon