First-principles calculations of the phase equilibrium of Be<i>x</i>Zn1−<i>x</i>O alloys

Abstract

Bandgap engineering of ZnO is crucial towards its practical applications. Due to their wide bandgap, BexZn1−xO alloys are promising materials for making optoelectronic devices that function in the solar-blind wavelength region. In this study, a theoretical investigation of the thermodynamics of these BexZn1−xO alloys is carried out using both first-principles calculations and the cluster expansion method. The cluster expansion method is used to describe the disordered alloys. It is revealed that, for both wurtzite (WZ) and zincblende (ZB) phase BexZn1−xO alloys, the formation enthalpies of all structures are positive for the whole range of composition. This implies the occurrence of miscibility gap when BeO and ZnO form alloys. A good comparison between the density functional theory used and the effective cluster interaction fitted formation enthalpies validates the cluster expansion method in the calculation of the formation enthalpies. The phase diagram of BexZn1−xO has been derived based on the theoretical calculations. It turns out that the inclusion of phonon contributions into the cluster expansion Hamiltonian affects markedly the substituent solubility of Be- and Zn-rich alloys. When lattice vibrations are considered, the solubility limits of Be in WZ-ZnO and Zn in WZ-BeO at 2000 K increase from 5.9% to 12.7% and from 0.7% to 3.8%, respectively, while the solubility limit of Be in ZB-ZnO reduces from 5.7% to 0.4% and that of Zn in ZB-BeO increases from 1.3% to 32.4%. A phase transition of BexZn1−xO from wurtzite to zincblende is predicted to occur around 1000 K.