Compositional Dependence of Formation Energies of Substitutional and Interstitial Mn in Partially Compensated (Ga,Mn)As

We use the density-functional theory to calculate the total energy of mixed crystals (Ga,Mn)As with a small concentration of various donors. We find that the formation energy of Mn depends strongly on the partial concentrations of Mn in the substitutional and interstitial positions, and on the concentration of other dopants. The composition dependence of the formation energies represents an effective feedback mechanism, resulting in the self-compensation property of (Ga,Mn)As. We show that the partial concentrations of both substitutional and interstitial Mn increase proportionally to the total concentration of Mn.