First-principles density functional study of dopant elements at grain boundaries in ZnO

Abstract

We present a first-principles density functional theory study of doped ZnO with focus on its application as a transparent conducting oxide, having both high optical transparency and high electrical conductivity. Investigated is the impact of grain boundaries on the physics of atomic defects, and especially the formation energies of oxygen vacancies, cation dopants Al and Ga, and anion dopants N and P are determined. The main goal is to obtain information about the positions of the defect levels generated by the different dopants in the electronic band gap. Because of the known deficiency of the local density approximation (LDA) to yield accurate values for band gap energies for insulators such as ZnO a self-interaction correction (SIC) to the LDA is employed. As atomistic supercell models which contain grain boundaries and dopants are quite large in size we implemented the SIC by means of SIC pseudopotentials which merely increase the computational costs, as compared to the LDA. The main result of our study is that grain boundaries do affect the formation energies for substitutional dopants significantly. Furthermore the position and shape of dopant-induced electronic energy levels at the grain boundaries are changed considerably with respect to the single crystal. This may help us to explain, for example, why N doping can lead to $p$ conductivity at room temperature or why Al or Ga doping can increase the transparency.