Electron structure and charge-carrier effective masses in In$_x$Ga$_{1-x}$N ($x$ = 0.25, 0.5, and 0.75) cubic systems

The band structure of cubic Group-III nitride ternary compounds In$_x$Ga$_{1-x}$N ($x$ = 0.25, 0.5, and 0.75) is calculated within the context of density functional theory in the pseudopotential approximation. It is for the first time established that, in In$_x$Ga$_{1-x}$N cubic systems, the effect of charge transfer from metal atoms to nitrogen atoms per In–N bond is 20–30% more profound than the corresponding effect per Ga–N bond. This effect is a consequence of the difference between In and Ga in electronegativity as well as of the structural relaxation of bond lengths. It is for the first time shown that, in In$_x$Ga$_{1-x}$N systems, there exist both light and heavy holes, with the corresponding effective masses [(0.04–0.12)$m_0$] and [(0.72–0.97)$m_0$], and the electron effective masses are in the range (0.04–0.13)$m_0$ ($m_0$ is the free electron mass). It is shown that, in a In$_x$Ga$_{1-x}$N system with a high In content, the charge-carrier mobility is an order of magnitude higher than that in the GaN binary crystal.