Dynamical and thermodynamic properties of III-nitrides L.S. Pereira a , A.M. Santos b , J.L.A. Alves a , H.W.L. Alves a, * , J.R. Leite b a Departamento de Cie ˆncias Naturais, Universidade Federal de Sa ˜o Joa ˜o del Rei, Caixa Postal 110, 36300-000 Sa ˜o Joa ˜o del Rei, Minas Gerais, Brazil b Instituto de Fı ´sica, Universidade de Sa ˜o Paulo, Caixa Postal 66318, 05315-970 Sa ˜o Paulo, Brazil Abstract In this work, we have calculated ab initio the equation of state, the principal phonon modes, the effective charges and the temperature dependence of the specific heat for the III-Nitrides, by using the density-functional theory within the local density approximation, plane wave expansions and the pseudopotential method. A good agreement with the experiment and other calculations is obtained, whenever a comparison is possible. From our results, we speculate whether these systems undergo, by a second-order phase transition, from the wurtzite structure to the zincblende one. q 2003 Elsevier Science Ltd. All rights reserved. Keywords: III-Nitrides; Phonons; Specific heats 1. 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 optoelec- tronic device technology [1]. However, their growth in the zinc-blende structure has been a hard task to the experimentalists, once the most stable structure for these compounds is the wurtzite one. On the other hand, from the theoretical point of view, while the structural and electronic properties of III-Nitrides were extensively studied in the last years, many questions about their growth and stability in cubic modification by the epitaxial techniques are still unadressed [2] and, besides that, the amount of knowledge on their dynamical and thermodynamic properties are rather scarce: only the description of the phonon dispersion of the unstrained cubic and wurtzite modifications was done [3,4]. In order to supply the missing information on the vibrational and thermodynamical properties of III-Nitrides, we have calculated ab initio the equation of state, the principal phonon modes, the effective charges for the III- Nitrides, by using the density-functional theory within the local density approximation (LDA), plane wave expansions and the pseudopotential method (ABINIT code) [5]. We have used the Troullier-Martins pseudopotentials, following the recipe developed by Stampfl and Van de Walle [6] for the III-Nitrides, which includes the d-electrons as valence states for GaN and InN (using the fhi98PP code [7]). The phonon modes and their dispersion curves were obtained using the adiabatic perturbation theory [8]. And, with the tetrahedron approach for the density of phonon states [9], we also have calculated the temperature dependence for the free energies, entropies and specific heats. With the methods described above, we have started by checking the equilibrium properties of the III-Nitrides in both hexagonal and cubic modifications. We obtained 4.31(4.51, 4.99) A ˚ for the AlN(GaN, InN) lattice parameters in the zinc- blende structure and 2.09(1.88, 1.38) Mbar, respectively, for their Bulk Moduli. These results were converged with 55(80, 60) Hartrees of plane-wave cutoff energy and 10 k-points for the Brillouin-zone sampling in the Monkhorst-Pack scheme. Also, in the wurtzite structure, we obtained 3.04(3.18, 3.53) A ˚ for their lattice parameter, 1.638(1.643, 1.633) for the c=a ratio, 0.378(0.375, 0.377) for the internal parameter u and 2.00(1.89, 1.33) Mbar for their Bulk Moduli, respect- ively, converged with 60(85, 65) Hartrees of plane-wave cutoff energy and 6 k-points for the Brillouin-zone sampling. All these values agree very well (within 2%) with the established data for the III-Nitrides [1,3,4,6,10]. 2. Phonons and effective charges In Tables 1 and 2, we show our converged values for the zone-center phonon frequencies (in cm 21 ) for both cubic 0026-2692/03/$ - see front matter q 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0026-2692(03)00088-0 Microelectronics Journal 34 (2003) 655–657 www.elsevier.com/locate/mejo * Corresponding author. Tel.: þ55-32-3379-2489; fax: þ 55-32-3379- 2483. E-mail address: hwlalves@funrei.br (H.W.L. Alves).