Shell-model calculations of the zone-center phonons of InAs/GaSb superlattices reveal that their confinement characteristics depend on the direction of the atomic displacements and the relative orientation of the interface bonds. Similar behavior is found for certain modes even in the frequency range of bulk acoustic phonons. These findings are attributed to diA'erent elastic coupling between the two constituent layers. Interface modes localized at the two different interfaces Ga-As and In-Sb are discussed.The electronic properties of InAs/GaSb superlattices (SL's) have been extensively studied over the past ten years, ' while their dynamical properties are still under investigation. To our knowledge, these systems have not been studied either by infrared or Raman spectroscopy up to now. The phonon dispersion and confinement in longperiod InAs/GaSb SL's was examined by Fasolino, Molinari, and Maan, using the linear-chain model. " Similar features have been observed by Akera and Ando again using the linear-chain model but the envelopefunction formalism for long-wavelength phonons. In all these cases only one type of interface is assumed, either Ga-As or In-Sb, which corresponds to higher-symmetry SL's in three dimensions than the more natural case where both types of interfaces appear alternately. Moreover, the ambiguities in the choice of force constants in Refs. 4-6 or the approximations involved in Ref. 7 may influence the accuracy of the eigenvectors more than the calculated frequencies. In particular, confinement and/or quasiconfinement of phonons in regions where the bulk continua of frequencies overlap has not been studied in detail. Other calculations, using three-dimensional models, ' report on the phonon dispersion in short-period SL's. Their interest is mainly concentrated on the interface modes and on the anisotropy of the phonons propagating parallel and perpendicular to the SL axis.In this paper we study the confinement of phonons in an 8/8 SL, for phonons at the center of the first Brillouin zone (BZ), for both longitudinal and transverse phonons.It is found that the confinement characteristics of transverse phonons depend on the relative orientation of the atomic displacements with respect to the direction of the interface bonds. These bonds provide either a weaker or stronger coupling between the eigenmodes of the two diAerent layers, which results in a larger or smaller mutual transfer of energy, depending also on the eigenfrequencies of the modes.The calculation is based on a ten-parameter valenceoverlap shell model (VOSM), ' with a slightly modified valence force field. ' ' The model employs three electric parameters, Z, Y~, and Y2, to describe the long-range interactions, two core-shell coupling parameters, k~and k2, and five valence-force-field parameters, k, k, ,~, k', ,~, k",g, and k', ,~, to describe the short-range interactions. The values of the parameters are obtained by a least-squares fitting to the experimentally known phonon dispersion of the bulk compounds InAs (Ref. 12) and GaSb...

The lattice dynamics of (GaAs)(n)/(AlAs)(n)(001) superlattices (SLs), n = 1,2, with perfect and disordered (non-perfect) interfaces is studied in detail. The SLs with disordered interfaces are approached by primitive cells, much larger in volume than that of the perfect SL primitive cell. The dynamical matrices of the SLs have been constructed from a combination of the dynamical matrices corresponding to the bulk crystalline constituents, while the interionic forces are calculated by using a ten-parameter valence overlap shell model (VOSM). Furthermore, we calculate the Raman spectra, for both perfect and disordered superlattices by using an eight-parameter bond polarizability model (BPM). Our theoretical results are in very good agreement with the available experimental spectra. Finally, our results clearly demonstrate that intermixing of Ga and Al cations, even to a very small extent, can induce Raman activity, which although not expected in the spectra of perfect superlattices, is actually observed experimentally.

Equations with reference to the zinc blende primitive cell volume are slightly changed. (ii) On page 1522, the paragraph after Eq. (10) should be changed. The current version which reads: ''where p ij are the components of the elasto-optic tensor of the bulk crystal and e 1 , a, r 0 , V c the high frequency dielectric constant, the lattice constant, the first neighbor distance and the bond volume of the bulk crystal, respectively. (The bond volume, V c , is defined as the volume of the cube occupied by the tetrahedrally coordinated bond. This volume is equal to the zinc blend primitive cell volume.)'' should be replaced by this new paragraph: ''where p ij are the components of the elasto-optic tensor of the bulk crystal and e 1 , a, r 0 , V c the high frequency dielectric constant, the lattice constant, the first neighbor distance, and the volume of the zinc blende primitive cell, respectively.'' These corrections do not influence the results obtained in the article, since the calculations were done with the proper volume V c , which is the volume of the primitive zincblende cell.

Equations with reference to the zinc blende primitive cell volume are slightly changed.

In the present work, we study the modes of vibration of small period (GaSb)n/(AlSb)n supelattices, n=1,2,3, grown along (001) direction. Any supelattice (SL) is described by a three dimensional elementary cell several times bigger of the elementary cell of the zinc blend bulk constituents. The modes of vibration are calculated using a ten parameter (10) Valence Overlap Shell Model, with the interactions of the binaries GaSb and AlSb calculated with different parameter sets, for both short and long range forces. With the atomic displacements known, we calculated the Raman spectra, away of resonance conditions, based on the Bond Polarizability Model. Our results are in good agreement with the existing experimental data. The so restricted information on the dynamical properties of these materials was the motive for this work, which is organized in the following way. Firstly, based on a ten (10) parameter Valence Overlap Shell Model [5], [6] we calculated, the phonon dispersion curves for both bulk GaSb and AlSb crystals. The calculation of the interactions between the atoms is made with different parameter sets for each one of the constituents. Next, we construct the dynamical matrix for each SL, properly combining the elements of the dynamical matrices of the GaSb and AlSb. we present the calculated phonon dispersion curves for GaSb/AlSb SLs (001) for certain high symmetry directions.In the final step, we present Raman spectra calculations for the longitudinal modes of vibration in the long wavelength limit with wave vector propagating along the growth direction for the three cases (n = 1, 2, 3). The calculations are accomplished with the Bond Polarizability Model [7]. The results are in good agreement with the experimental data. Phonon calculations of the bulk constituentsThe calculation of the atomic force constants for each material, The first three are the electric parameters last five ones are the valence-force-field parameters, which describe the short-range interactions. The values of the model parameters are obtained by a least-squares fitting procedure of the calculated phonon frequencies to the experimentally known phonon dispersion of the bulk compounds GaSb and AlSb. The aim of this procedure is to find the proper minimum based on the relation (1) From the fitting procedure for the GaSb crystal, we found the following parameter set : Ζ= 2, Y 1 = 4.941, Y 2 = 3.56, (proton charges) k 1 = 17.19, k 2 = 4.346, λ= 1.732, k r1θ= 0.176, k' r1θ= -0.183, k r2θ = -0.0435, k' r2θ = -0.0054 (in 10 5 dyn/cm units). Τhe mean standard deviation is 3.5 cm -1 per phonon. The values of the elastic constants obtained by this parameter set are (in parenthesis the experimental ones) C 11 = 8.6 (8.9), C 12 = 4.7 (4.0), C 44 = 3.5 (4.3) (in 10 11 dyn/cm 2 units). In Fig. 1 is shown the phonon dispersion curves of the bulk GaSb crystal in the high symmetry directions Χ, Σ, L, Χ-W. The boxes are the experimental frequencies. Except from the middle of the higher frequency acoustic branch along Σ direction the overall fi...