Optimization of Doping $\mathrm{Cd}\mathrm{Te}$ with Group-V Elements: A First-Principles Study

Group-V substitution at the $\mathrm{Te}$ site, $X_{\mathrm{Te}}$ (X = $\mathrm{P}$, $\mathrm{As}$, $\mathrm{Sb}$), under $\mathrm{Cd}$-rich conditions is an effective way to enhance the hole density and, in the meantime, suppresses the dominant nonradiative carrier recombination center in $\mathrm{Cd}\mathrm{Te}$, thus, improving the performance of $\mathrm{Cd}\mathrm{Te}$ thin-film solar cells. However, it is not clear which group-V dopant, X, is the most effective dopant, because it is expected that ${\mathrm{P}}_{\mathrm{Te}}$ will have the shallowest acceptor level due to its high electronegativity, whereas ${\mathrm{Sb}}_{\mathrm{Te}}$ will have the smallest formation energy due to its small size mismatch with $\mathrm{Te}$. Our systematic first-principles study shows that the hole concentration contributed by the acceptor $X_{\mathrm{Te}}^{-}$ is limited by the related compensating $A{X}^{+}$ center that increases simultaneously with $X_{\mathrm{Te}}^{-}$ as the chemical potential of dopant X increases. However, the ratio of $X_{\mathrm{Te}}^{-}$ acceptors to the $A{X}^{+}$ donors can be significantly increased if the sample is grown at high temperature and then annealed to room temperature, achieving a high hole density and low Fermi level $(E_F)$. We find that all group-V ($\mathrm{P}$, $\mathrm{As}$, and $\mathrm{Sb}$) dopings can achieve maximum hole densities of about ${10}^{17}{\mathrm{cm}}^{-3}$, which are consistent with previous experimental results. Despite the relatively deep acceptor level of 150 meV, $\mathrm{Sb}$ doping can achieve a considerable hole density due to the low formation energy of substituting $\mathrm{Sb}$ for $\mathrm{Te}$ with similar atomic radii. $\mathrm{P}$ doping can achieve a higher hole density than that of $\mathrm{Sb}$ due to its shallow transition energy at ε(0/−) = 70 meV. However, the highest hole density is achieved through $\mathrm{As}$ doping, which is attributed to its balanced defect level at ε(0/−) = 80 meV and relatively small formation energy.

Figure 1

Calculated chemical-potential region for $\mathrm{As}$ doping in $\mathrm{Cd}\mathrm{Te}$ under equilibrium growth conditions, which is marked in light blue. Green area is excluded because it can form the binary competitive phase ${\mathrm{Cd}}_3{\mathrm{As}}_2$.

Figure 2

Schematic diagrams of (a) the bond-breaking model for the formation of the AX⁺ center, and (b) the stabilization mechanism of the AX⁺ center by lowering the electronic energy. X atom marked in red is $\mathrm{P}$, $\mathrm{As}$, or $\mathrm{Sb}$.

Figure 3

(a) Calculated formation energies of ${\mathrm{P}}_{\mathrm{Te}}$, ${\mathrm{As}}_{\mathrm{Te}},$ and ${\mathrm{Sb}}_{\mathrm{Te}}$ (acceptors and AX⁺ centers) as functions of the Fermi levels under $\mathrm{Te}$-rich conditions and $\mathrm{Cd}$-rich conditions, respectively. Lines with negative slope represent acceptors and positive slope represent AX⁺ centers. (b) Calculated formation energies of ${\mathrm{P}}_{\mathrm{Te}}$, ${\mathrm{As}}_{\mathrm{Te}},$ and ${\mathrm{Sb}}_{\mathrm{Te}}$ in the neutral charge state, as functions of ${\mu }_{\mathrm{Cd}}$ for the A-B-C lines shown in Fig. 1.

Figure 4

(a),(c) $E_F$, hole density (HD), and dopant concentration (DC), and (b),(d) +1, 0, and −1 charged defect concentrations of group-V-doped $\mathrm{Cd}\mathrm{Te}$ when (a),(b) T = 850 K and (c),(d) is quenched to 300 K, as functions of ${\mu }_{\mathrm{Cd}}$. HD and DC are given in cm^–3.

Figure 5

(a) $E_F$, HD, and DC, and (b) +1, 0, and −1 charged defect concentrations of group-V-doped $\mathrm{Cd}\mathrm{Te}$ at T = 300 K, as functions of ${\mu }_{\mathrm{Cd}}$.

Figure 6

(a),(c) $E_F$, HD, and DC, and (b),(d) +1, 0, and −1 charged defect concentrations of group-V-doped $\mathrm{Cd}\mathrm{Te}$ when (a),(b) T = 1000 K and (c),(d) is quenched to 300 K, as functions of ${\mu }_{\mathrm{Cd}}$.

Figure 7

(a),(c) $E_F$, HD, and DC, and (b),(d) +1, 0, and −1 charged defect concentrations of group-V-doped $\mathrm{Cd}\mathrm{Te}$ when (a),(b) T = 1300 K and (c),(d) is quenched to 300 K, as functions of ${\mu }_{\mathrm{Cd}}$.