PHYSICAL REVIEW B VOLUME 49, NUMBER 8 15 FEBRUARY 1994-II In-plane Raman scattering of (001)-Si/Ge snperlattices: Theory anti experiment R. Schorer and G. Abstreiter Walter Schottky Institut, Technische Universitat Munchen, D-85748 Garching, Germany S. de Gironcoli INFM Institute of Condensed Matter Theory (FOR UM1, Scuola Normale Superiore, Piazza dei Cavalieri 7, I 5610-0 Pisa, Italy E. Molinari Dipartimento di Fisica, Universita di Modena, Via Campi 213/a, I-41100 Modena, Italy H. Kibbel and H. Presting Daimler-Benz AG, Research Center Ulm, Wilhelm-Runge-Strasse 11, D-89081 Ulm, Germany (Received 13 September 1993) Using a micro-Raman setup, in-plane Raman scattering was performed on short-period (001)-Si/Ge superlattices, and the complete phonon spectrum (longitudinal and transverse, optical and acoustic modes) could be studied. In the relevant wave-vector range, the in-plane dispersion was found to affect the frequencies of folded-acoustic modes, while being negligible for confined optical modes. The com- parison with theoretical spectra, calculated by means of first-principles interatomic force constants, shows that the observed deviations of "unfolded" confined optical modes from the bulk dispersions can be attributed to interface roughness and is well described by a simple alloy layer model (2-3 intermixed SiGe atomic layers at interfaces). I. INTRODUCTION In recent years there has been considerable interest in Si/Ge superlattices (SL's) since they provide a possibility to overcome the restrictions in the optical and electronic properties of bulk Si as compared to III-V semiconduc- tors. ' Short-period Si/Ge SL's have proven to be promising candidates for quasidirect band-gap lumines- cence. Raman spectroscopy is a useful tool for charac- terizing short-period SL s, since their vibrational proper- ties depend strongly on their microscopic structure. Conventionally, Raman scattering is performed in backscattering from the growth direction (usually the [001] direction). In this case, from the (001) surface only longitudinal modes are observable off resonance. In or- der to establish a full picture of the vibrational modes of SL s, their symmetry, and their coupling to light, it is necessary to perform Raman scattering along each primi- tive axis of the SL crystal. Such a full analysis was re- cently presented for the optical-phonon modes of (001)- GaAs/A1As SL's, ' where in-plane studies were shown to be possible by reducing the probe laster spot to a sub- pm focus (micro-Raman scattering). Using this ap- proach, we are now able to study the quantized longitudinal-optical (LO) and transverse-optical (TO) modes, as well as the folded longitudinal-acoustic (LA) and transverse-acoustic (TA) ones in our Si/Ge struc- tures. A similar improvement has recently taken place on the theoretical side. Earlier ab initio treatments of the pho- non spectra were limited to modes with wave vectors along the growth direction, for which one-dimensional approaches could successfully be adopted. Just recently we have been able to extend first-principles studies to three-dimensional SL dispersions by using higher-order interatomic force constants which allow us to account for both strain and interface intermixing. ' The aim of this paper is to describe the features found in the experimental Raman spectra, and to compare them with theoretical predictions. In particular, we shall focus on the confinement properties of Si-like longitudinal and transverse vibrations, and on the behavior of higher- order acoustic modes. The specific properties of the Si- Ge-like interface mode have been reported elsewhere and will be only briefly summarized here. We will show that experimental spectra deviate significantly from the theoretical spectra expected for abrupt-interface geometries. On the other hand, by taking into account interface intermixing (2 — 3 monolayers of SiGe alloy at the interfaces) a general agreement between theory and experiments is recovered. The paper is organized as follows. Section II gives a brief illustration of the sample preparation and the exper- imental technique, while Sec. III summarizes the essential features of our theoretical approach. Section IV presents our results for the optical frequency range: We first re- call the general features of the LO- and TO-phonon spec- tra of ideal SL's, and discuss the reliability of simple "un- folding" rules for confined SL modes. Systematic experi- mental results for a series of (001)-Si„/Ge„SL's are re- ported and discussed in terms of these "unfolding" rules. The analysis of the observed deviations is then performed on the basis of a detailed treatment of disorder effects. Section V is devoted to acoustic modes, while Sec. VI contains a general discussion and comparison with GaAs/A1As SL's, together with our conclusions. 0163-1829/94/49(8)/5406(9)/$06. 00 49 5406 1994 The American Physical Society