First-principles total-energy calculation of gallium nitride.

Gallium nitride (GaN) is a tetrahedrally coordinated III-V compound semiconductor which has the hexagonal wurtzite structure with a wide band gap of 3.5 eV at 300 K. It is reported that a simple-metal-insulator-n-typeGaN diode produces blue electroluminescence. ' For this reason it has been studied as a material suitable for an effective optoelectronic device such as laser and light emitting diode, but the technical difficulties are yet to be surmounted. The major difficulty has been that the concentration of free electrons is too large (10' —10 cm ) for the fabrication of a p-type crystal to be successful. It is believed that nitrogen vacancies are the source of free electrons rather than some unknown donor impurities. The growth of a GaN crystal has had other difficulties, too. The GaN substrate on sapphire has different lattice constants and luminescence characteristics depending on the direction of growth. Also there is a report about an unusually large variation of the lattice constants depending on the growth conditions, such as growth rate, lattice defects, and foreign impurities. ' Thus it is of importance to understand the energetics of the GaN crystal. A first-principles total-energy calculation can provide useful information for studying the energetics of a solid-state system. Without introducing empirical parameters, it provides a good description of the equilibrium properties such as lattice structure, lattice constant, cohesive energy, and bulk modulus. Such input from first-principles calculations can be helpful for understanding the nature of the current problem in crystal growth. We also present the electronic band structure of GaN from our calculations. Currently there are band calculations that do not agree with each other about the nature of the band gap. Although it is well known that local density approximation' (LDA) calculations usually underestimate the size of the band gap, it is accurate enough for one to determine whether the band gap is direct or not.