Defect Phase Diagram for Doping of Ga2O3

For the case of n-type doping of β-Ga₂O₃ by group 14 dopants (C, Si, Ge, Sn), a defect phase diagram is constructed from defect equilibria calculated over a range of temperatures (T), O partial pressures (pO₂), and dopant concentrations. The underlying defect levels and formation energies are determined from first-principles supercell calculations with GW bandgap corrections. Only Si is found to be a truly shallow donor, C is a deep DX-like (lattice relaxed donor) center, and Ge and Sn have defect levels close to the conduction band minimum. The thermodynamic modeling includes the effect of association of dopant-defect pairs and complexes, which causes the net doping to decline when exceeding a certain optimal dopant concentration. The optimal doping levels are surprisingly low, between about 0.01% and 1% of cation substitution, depending on the (T, pO₂) conditions. Considering further the stability constraints due to sublimation of molecular Ga₂O, specific predictions of optimized pO₂ and Si dopant concentrations are given. The incomplete passivation of dopant-defect complexes in β-Ga₂O₃ suggests a design rule for metastable doping above the solubility limit.