First-Principle Studies of Phonons III-N Compound Semiconductors in Wurtzite Structure

Abstract

 Abstract—The phonon dispersion relations and density of states of the nitrides BN, AlN, GaN and InN in the wurtzite structure are investigated by using separately the local density approximation (LDA) and the generalized gradient approxi- mation (GGA) within the framework of density functional theory. The results show that the highest optical phonon frequency at the Brillouin zone center decreases, but the phonon band gap increases, with increasing the cation/anion mass ratio. The frequencies calculated with GGA are lower than those with LDA. The GGA is more suitable for AlN and GaN, but the LDA for BN and InN. dynamical properties of the GaN, AlN, BN and InN by the first-principle calculation based on the density functional theory. The exchange-correlation potentials in the local density approximation (LDA) (12) and the generalized gradient approximation (GGA) (13) are separately used in the calculations. The optimum plane-wave energy cut-off has been tested carefully by keeping the total energy error less than 0.001 Hartree, and is determined as 45 Ryd for all these compounds. A 3  3  3 Monkhorst-Pack mesh and ten special k point have been used to perform the Brillouin zone (BZ) integration. The self-consistent convergence of the total energy is taken to be 10 -6 eV/atom, in order to obtain accurately the phonon dispersion curves. Moreover, a 444 q mesh is employed for the force constant calculation in the first BZ by interpolation. The whole calculation is carried out by using the Quantum ESPRESSO code (14), and the calculated results of the phonon frequencies and densities of states (DOS) are shown in Fig. 1 to Fig. 4. III. RESULTS AND DISCUSSION To obtain the equilibrium lattice constant a, c and the internal geometrical constant u, we fit the energy versus volume curves to the Murnaghan equation of state. Table I lists the calculated values of the structural parameters in this work. It is seen that our results are in good agreement with the previous theoretical and experimental values.