Study of the vibrational modes of GaSb/AlSb (001) superlattices

Abstract

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...

N incorporation and associated localized vibrational modes in GaSb

“…The good agreement between our calculated phonon modes of GaSb and experiment indicates that our computational approach to determining the vibrational properties of the system gives accurate results. We note that our results also agree well with previous computational studies [82,100,101].…”

Spectroscopic Properties of AlSb Nanocrystals Using Diamondoid Structures: A Density Functional Theory Study

“…The frequency of the HFCM increases from 191.4 cm −1 for AlSbH 6 to 334.4 cm −1 for AlSb octamantane. The latter value is lower (red shifted) than bulk AlSb (337 cm −1 ) [21, 22]. The LO mode frequencies are 316.4, 330.1, 329.2 and 334.4 cm −1 for the diamondoid clusters AlSb diamantane, tetramantane, hexamantane and octamantane, respectively, which are all red shifted with respect to bulk 337 cm −1 .…”

Calculation of off‐resonance Raman scattering intensities with parametric models

“…[105] Small periods were first considered. Because of the lack of data some EOPs were transferred from AlAs to AlSb systems [106] and it was assumed that the longitudinal and transversal equilibrium parameters were equal (and therefore do not contribute to the Raman intensity).…”