We investigate the self-compensation mechanism in phosphorus-doped CdTe. The formation energies, charge transition levels, and defects states of several P-related point defects susceptible to cause self-compensation are addressed by first-principles calculations. Moreover, we assess the in uence of the spin-orbit coupling and supercell-size effects on the stability of AX centers donors, which are believed to be responsible for most of the self-compensation. We report an improved result for the lowest-energy configuration of the P interstitial (P$_\text{i}$) and find that the self-compensation mechanism is not due to the formation of AX centers. Under Te-rich growth conditions, (P$_\text{i}$) exhibits a formation energy lower than the substitutional acceptor (P$_\text{Te}$) when the Fermi level is near the valence band, acting as compensating donor. While, for Cd-rich growth conditions, our results suggest that p-type doping is limited by the formation of (P$_\text{Te}$-V$_\text{Te}$) complexes.
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