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.