Phonon confinement in InAs/GaSb superlattices

Abstract

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...

Lattice vibration modes in type-II superlattice InAs/GaSb with no-common-atom interface and overlapping vibration spectra

“…The lower frequency mode can be assigned as an InAs QC-TO mode based on its frequency in the SL sample on InAs, as well as its intensity being lower than the bulk InAs. The higher frequency mode should be assigned as an EX-TO mode rather than an expected GaSb C-TO, [13,16] based on two considerations: (1) its intensity is about 1/8 of the bulk GaSb, while the GaSb volume fraction is about 1/3; and (2) the frequency difference with respect to the bulk GaSb TO for the SL sample on GaSb is significantly larger than those of calculated GaSb QC or C modes. [7,10] Here again we observe the strain effect: for the SL on InAs, the EX-TO mode is blue-shifted (incidentally matching the TO mode of the bulk GaSb) due to the compressive strain; for the SL on GaSb, the InAs QC-TO mode is red-shifted due to the tensile strain.…”

“…However, given the larger width of the peak and the enhanced relative intensity when compared to the primary LO mode, in particular for the SL on GaSb, this peak might also contain unresolved EX modes. The predicted InAs confined modes [15,16] are not observed, likely due to the small RC of InAs bulk. We also examined the potential anisotropy between x'…”

“…[14,16] For the SL on InAs, despite being close to the InAs LO, the SL mode is in fact the same GaSb QC-LO mode but blue shifted due to the compressive strain. Furthermore, the SL mode in the InAs-substrate sample shows an intensity between those of the bulk GaSb and InAs, which is consistent with its assignment as a GaSb QC-LO mode, because the lowest order consideration based on the volume would suggest the intensity to be simply determined by the fraction of GaSb in the SL.…”

“…The phonon spectrum of the T2SL has been predicated to have four types of modes: confined (C), quasi-confined (QC), extended (EX), and interface (IF) modes. [13][14][15][16] No-common-element interface has two consequences: (1) two IF modes, GaAs-like (IF1) and InSb-like (IF2), locating above and below the general SL modes; [13,16] and (2) the reduction of the SL symmetry from D 2d for GaAs/AlAs SL to C 2v for InAs/GaSb SL. [16] One important point not previously received attention is that the Raman cross-sections (RCs) of the two constituents are very different for the T2SL, which turns out to be pivotal for understanding its Raman spectrum.…”

Trapping of free electrons in III-V superlattices

“…In superlattices like InAs/GaSb, there exist also a kind of interface phonons coming from specific composition of the interface itself: InSb or GaSb. 19,20 Their dispersion can be evaluated with the help of continuum model replacing interfaces between two different materials of the superlattice with layers of another material. Rather cumbersome calculations that are beyond the scope of the present paper show that when the width of these layers goes to zero spectrum of phonons originated from interfaces between different materials splits in three modes: superlattice phonons described by Eq.…”