R e s u m d -Les spectres de plaonons de superr6seaux SijGe dans la direction de la croissance ont kt6 calcul6s. A c6tB des modes plies et confines comme dans le cas du systeme GaAs/AlAs, dans la direction (001) les r6sultats montrent aussi des modes d'interface dans la polarisation transverse e t des modes resonants dans la polarisation longitudinale au bord de la rCgion des frhquences oii les modes de volume de Si et Ge se recouvrent. La dispersion, les vecteurs propres et la d6pendance en

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... ction de l'bpaisseur des couches de ces derniers modes ont un comportement trks semblable B celui des modes proprement confines. A b s t r a c t -The phonon spectra of SijGe superlattices are calculated along the growth direction. Besides folded and confined modes, as in the more studied case of GaAs/AlAs systems, along (001) they show interface modes in the transverse polarization and resonant modes in the longitudinal one at frequencies just below the edge where the Si and Ge bulk modes start overlapping. The thickness dependence, dispersion and displacement patterns of the latter modes show their similarities t o proper confined modes. The lattice dynamics of semiconductor SL's has been extensively studied,botli experimentally and theoretically in the last few pears [l-151 mostly for the GaAs/AlAs system, for which the concepts of folding of the acoustical branches and confinement of optical modes have been introduced. Si/Ge superlattices (SL's) are now starting to be grown with high crystalline quality 1161 despite their 4.2 % lattice mismatch. The Si/Ge (001) SL's are, on one hand, similar to GaAs/AlAs in that one component (Si) is much lighter than the other (Ge), with a consequent much higher upper edge of the frequency spectra; on the other hand there are two important differences: i ) the Ge longitudinal bulk continuum is entirely contained in the Si bulk frequency range, and ii) the bonds present a t the interface (Si-Ge) are different from those inside the layers (Si-Si and Ge-Ge). These two latter features make Si/Ge SL's much more similar t o InAs/GaSb SL's, which have recently been studied theoretically [14, 15] and where, in particular, the different bonds a t the interfaces (In-Sb or Ga-As) have been shown t o give rise t o new modes localized at the interface. It is therefore worthwhile investigating t o which extent the same behaviour can be expected for Si/Ge SL's. We calculate the phonon spectra of Si/Ge superlattices along the (001) and (111) growlh directions by means of a one-dimensional model with interplanar force constants, as done for GaAs/AlAs in 112,131. We use the interplanar force constants (extending to third neighbour planes for longitudinal and fifth neighbour planes for transverse modes), calculated for bulk Ge (171 in the local density approximation, to describe both materials, the differences in their bulk spectra being accounted for by their different masses only. In Fig.1 we compare the resulting bulk Si and Ge phonon spectra along the (001) direction with the experimental data [18, 19] . (Analogous results are obtained for dispersions along the (111) direction, for which Ge ab initio interplanar force constants are also available in Ref. 17.) The agreement is satisfactory. A further improvement could be achieved by e.g. abandoning the mass approximation and using force constants derived Article published online by EDP Sciences and available at http://dx.