Eur. Phys. J. B 74, 409–413 (2010) DOI: 10.1140/epjb/e2010-00082-9 Regular Article T HE EUROPEAN P HYSICAL JOURNAL B Theoretical and experimental Raman study of superlattices with GeSi quantum dots V.O. Yukhymchuk, V.M. Dzhagan a , A.M. Yaremko, and M.Ya. Valakh V. Lashkaryov Institute of Semiconductor Physics, National Acad. Sci. of Ukraine, 03028 Kyiv, Ukraine Received 26 August 2009 / Received in final form 23 November 2009 Published online 9 March 2010 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2010 Abstract. The results of the theoretical and experimental study of Raman scattering in the quantum dot (QD) multilayers are reported. In order to obtain an adequate description of the structure with QDs and correctly explain the experimental Raman spectra, a model is proposed which takes into account the real crystal structure of both the QD and surrounding matrix, as well as the QD-matrix interaction. The secondary quantisation and Green function method were used in the theoretical calculation model. The results obtained show that crystal structures with matrix-embedded QDs can be described as a mixed crystal with specific distribution of “impurities” organised in large “molecules”. A qualitative agreement in position and intensity of bands between the calculated and experimental Raman spectra for multilayer Ge/Si QD crystal structure is observed, the doublet character of the bands is explained. 1 Introduction Study of optical properties of artificially made quantum- sized crystal structures began just after their fabrication more than twenty years ago. First such structures were quantum wells (QW) and superlattices (SL). Experimen- tal and theoretical investigations examining these struc- tures were performed very intensively [1–14]. Already in the first theoretical works [1,5] it was shown (by using the simple linear chain model) that the appearance of a num- ber of additional bands in Raman scattering (RS) spectra in the region of acoustical vibrations is due to the effect of increasing crystal unit cell size and corresponding “fold- ing” of the bulk phonon branches. Numerical calculations of dispersion phonon branches (both acoustic and optic) in SL were made in [2]. The authors of [2] performed the cal- culation in two steps. First, in the framework of adiabatic bond-charge model, they included the interaction between the neighbuoring layers only, and then, other interactions were included as the first-order perturbations. Several ex- periments [3,6,9] confirmed the main conclusions of the theory [1,2]. However, the numerical calculations for SLs (A m B n ) were made with a rather small number of iden- tical layers (n, m ∼ 5) [8]. To obtain a more general con- clusion about the optical properties of SLs, an analyti- cal description based on the Rytov‘s approach [15] was made [3–7]. In his work Rytov studied the propagation of acoustic waves in the layer of isotropic (non-crystalline) media. Therefore, it was not clear under what conditions his final equation could be applied to a layered crystal structure. In particular, it was shown by the linear chain a e-mail: dzhagan@isp.kiev.ua model calculations [5] that Rytov‘s formalism is only ap- plicable to crystalline SLs at long-wavelength vibrations, when the lattice can be considered as a continuum and the dispersion law for acoustic branches, ω = v ac q, is lin- ear. In [11,12], a more complex situation was considered, though SL vibrations were described macroscopically by a periodic variation of density and elastic constants of me- dia. Besides, it was noted that if the disturbance of trans- lation invariance along the growth direction of SL occurs due to layer thickness fluctuations and interface rough- ness, the wave vector q of phonons is not conserved and new features in RS may appear. In the early 90s new crystal structures with QDs were intensely created and investigated, both experimentally and theoretically [16–23]. One can note that two models dominate in theoretical investigations of the vibrational spectra of QDs. One group of studies [19–22] considered QDs as spherical homogenous media, the Navier equations were used for description of movement in this media, and special boundary conditions were applied. In this case, two types of modes, spheroidal and torsional, were obtained. In [19], the properties of these modes and selection rules were studied by using group theory. Another approach to the problem was proposed in [23,24]. In particular, in [23], QDs were considered as homogenous cylindrical disks with an ellipsoidal (or circular) cross section, whose vertical size was much smaller than the lateral size (special boundary conditions were used too). This model of QD shows con- tinuation in the studies of an ensemble of QD interacting with one another via acoustic vibrations [25–28], although RS by an ensemble of spherical dots was studied too [29]. In experiments made on disk-like QD models, the periodic oscillations were observed in the low-frequency region of