First-principles study of incorporation and migration of Sn in GaN

Abstract

We present a first-principles (density functional theory) study of the thermodynamic stability and migration of Sn-related defects in GaN. Formation energies of SnGa, VGa, and the SnGa–VGa complex were calculated under Ga-rich conditions using both generalized gradient approximation and Heyd–Scuseria–Ernzerhof exchange–correlation functionals. Vacancy-mediated migration was analyzed using the climbing-image nudged elastic band method. While diffusion along the c axis proceeds via a simple pathway with a single energy barrier, migration along the a direction follows a more complex pathway involving a local energy minimum corresponding to a metastable VGa–Sni–VGa configuration. Notably, the calculated barriers are lower than those previously reported for other group-IV donors in GaN, indicating higher diffusivity of Sn. Temperature dependence of the effective barrier was determined based on phonon calculations. Along the c direction, the energy barrier decreases with increasing temperature, whereas along the a direction, it increases. Furthermore, the effective energy of the Sn–divacancy complex decreases with temperature, allowing it to act as a weak trapping site. These findings provide microscopic insight into the anisotropic diffusion mechanism of Sn in GaN.