Complexes and compensation in degenerately donor doped GaN

Gallium nitride is an increasingly technologically relevant material system. While donor doping GaN to low and intermediate dopant concentrations using silicon and germanium has become routine, compensation mechanisms activate under very high donor doping, limiting the maximum electron concentration achievable with either dopant in the degenerate doping regime. This effect, and how it differs between the two dopants, is investigated by hybrid functional density functional theory calculations and grand canonical thermodynamics models and is found to be due to the onset of multi-member Ga vacancy-donor substitutional complexes under degenerate doping conditions. The differing energetics of Ge- and Si-related complexes leads to different responses, ultimately making Ge the more effective donor in degenerate conditions.