Estudio mecano-cuántico del Nitruro de Galio desde primeros principios

Abstract

For the last few decades quantum-mechanical studies of materials have contributed to great advances in materials science and its applications, facilitating the obtention of results in a less complex way than experimentally. In this report Galium Nitride has been studied in order to understand its behavior when being affected by high pressures. To perform the ab initio simulation of the Gallium Nitride it is needed to explain the theoretical background in which it is based. As it is in the quantum mechanical frame, the total energy Hamiltonian must be solved, but to do so, it is necessary to bring out some approximations. The first one is the Born-Oppenheimer or adiabatic approximation, in which the problem is reduced to a system of electron in a frozen-in configuration of the nucleus. [1] After that, the density functional theory is considered, which stablishes that the system is formed by non-interacting electrons in an external potential and that the energy of the system is a functional of the density of states. This theory was proposed by Kohn & Hohenberg, who also described the energy functional as a sum of two contributions: one related to the external potential and the other one related to a universal functional. The form of the last one was given by Kohn & Shan. They established that the functional was composed of the kinetic energy of the electrons and the exchange-correlation energy. They also proposed a set of equations to be solved by self-consistent methods that can be used to obtain the density of states and the external potential that solve the energy equation. By obtaining the total energy of the system, it is possible to obtain other variables and parameters of it, such as the pressure, the enthalpy, structural parameters, etc. The energies and volumes obtained by the ab initio simulation can be adjusted to the Birch-Murnaghan equation of state. By doing that, the equilibrium constants can be obtained. In this work, the ab initio simulation was performed to study the evolution of the GaN at high pressures, where a transition phase can be observed. This transition takes place from a wurtzite phase to the rock salt, at 45 GPa, according to the calculations of this work carried out with VASP (Vienna Ab initio Simulation Package). The wurtzite phase has two structural parameters, c/a and u. At equilibrium, the obtained values were a0 = 3.179˚A and c0 = 5.179˚A, which are in accordance with the bibliography. The rock-salt structure only has one parameter, a0 = 4.217˚A. The other equilibrium constants are collected in the tables 2 and 3. It is also possible to calculate the electronical band structures for both phases, in which a band gap of 1.63 eV was obtained for the wurtzite (at p=0) , and one of 1.21 eV for the rock-salt at the transition pressure. The values are smaller than the experimental ones as the use of GGA underestimates the energy gap. All these calculations were done using an energy cutoff of 600 eV and Rk = 24 for the construction of the k-points grid.