Self-compensation in phosphorus-doped CdTe

We investigate the self-compensation mechanism in phosphorus-doped CdTe. The formation energies, charge transition levels, and defect states of several P-related point defects susceptible to cause self-compensation are addressed by first-principles calculations. Moreover, we assess the influence of the spin-orbit coupling and supercell-size effects on the stability of AX centers, 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 $\left({\text{P}}_{\text{i}}\right)$ and find that the self-compensation mechanism is not due to the formation of AX centers. Under Te-rich growth conditions, $\left({\text{P}}_{\text{i}}\right)$ exhibits a formation energy lower than the substitutional acceptor $\left({\text{P}}_{\text{Te}}\right)$ 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 $({\text{P}}_{\text{Te}}-{\text{V}}_{\text{Te}})$ complexes.

Figure 1

Left: Electronic band structure of ${\left({\text{P}}_{\text{Te}}\right)}^{+1}$ in the AX configuration. Right: Squared wave function corresponding to the antibonding $a_1$ level plotted in the range of $0–4\times {10}^{-3}{\mathrm{bohr}}^{-3}$. Dark and light spheres represent Te and Cd atoms, respectively, and the yellow sphere represents the phosphorus impurity. The calculations were performed in a 250-atom supercell.

Figure 2

Left: Electronic band structure of ${\left({\text{P}}_{\text{i}}\right)}^{+1}$. Right: Squared wave function corresponding to the $a_1$ level below the VBM, plotted in the range of $0–4\times {10}^{-3}{\mathrm{bohr}}^{-3}$. Dark and light spheres represent Te and Cd atoms, respectively, and the yellow sphere represents the phosphorus impurity. The calculations were performed in a 250-atom supercell.

Figure 3

Calculated defect formation energies of ${\left({\text{P}}_{\text{Te}}\right)}^{-1}, {\left({\text{P}}_{\text{i}}\right)}^{+1}$, and ${({\text{P}}_{\text{Te}}-{\text{V}}_{\text{Te}})}^{+1}$ as a function of the Fermi level inside the band gap under (a) Te-rich condition and (b) Cd-rich condition. The formation energy of the AX configuration obtained from the DFT+$GW$ scheme is also included.