Planar Force-constant Method for Lattice Dynamics of Cubic InN
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Planar Force-constant Method for Lattice Dynamics of Cubic InN H. W. Leite Alves1, J. L. A. Alves1, L. M. R. Scolfaro2 and J. R. Leite2 1 Departamento de Ciências Naturais, FUNREI, CP 110, CEP 36.300-000, São João del Rei, MG, Brazil 2 Instituto de Física da Universidade de São Paulo, CP 66.318, CEP 05.389-970, São Paulo, SP, Brazil ABSTRACT
Using the density-functional theory within the Full Potential Linear Augmented Plane-Wave (FP-LAPW) method, we have calculated, in this work, the equation of state, the effective charges and the phonon dispersion along [100] and [111] directions for the cubic Indium Nitride(c-InN), including hydrostatic strains dependence. A good agreement with the microRaman scattering experiment is obtained for the phonon modes at Γ. Our results show that the apparent divergence between the known experimental results is a consequence of hydrostatic effects on the sample due to differences of the used Raman methods.
INTRODUCTION
The group III-nitrides(AlN, GaN, InN) and the corresponding alloys have attracted great interest due to their successful applications in the electronic and optoelectronic device technology [1]. The InN has deserved much less attention than the extensively studied AlN and GaN binary compounds. Because the light emitting media in the LEDs and lasers devices are composed by the InxGa1-xN alloys with low In contents, most of the studies carried out on the nitrides concentrate on the lower values of the alloy composition x. However, it has been demonstrated recently that nanostructures composed by nearly pure InN quantum dots play the major role on the device operating in the green-ultraviolet(UV) spectral region [2]. Moreover, it has been argued that the cubic(c-) InN inclusions in the hexagonal(h-) InGaN quantum well layer should be the devices active media [3]. Unfortunately, the amount of theoretical knowledge on cubic InN is limited to a handful of works [4-9] and, particularly, the data on phonon spectra and vibrational properties are rather scarce: only Raman scattering measurements are reported [10,11]. It is interesting to note that, despite the fact that only two different Raman spectra were reported, both were recorded on the same sample and their results agree only for the longitudinal mode at Γ. Following Ref. 11, the supposed wrong assignment for the TO(Γ) mode is probably due to the similarity of the nonresonant spectra of Ref. 10 to the second-order spectra of InAs. In the present work, we report our preliminary results for the lattice dynamics of c-InN, including hydrostatic strains, in order to clarify this controversy and to supply the missing information on the vibrational properties of this compound. The phonon frequencies at [100] and [111] directions were obtained within the planar force-constant model [12,13]: it consists in selecting one direction of the wavevector k and in representing the lattice vibrations as the 1
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motion of rigid planes of atoms perpendicular to k and connected by inter-planar forces. In order to determine these for
