Effects of co-doping in semiconductors: CdTe

Co-doping is an important method to improve doping properties in semiconductors, which is expected to lower the defect formation energy through the Coulomb interaction or covalent coupling between co-dopants and reduce the transition energy level through the level repulsions. However, the effectiveness of co-doping is sensitive to the type of co-dopants, and in some cases, negative effects can exist. Here, using $p$-type doping in CdTe as an example, we systematically investigate different dopant combinations based on first-principles hybrid functional calculations. We show that the complex of one donor + one double acceptor, e.g., ${\mathrm{Cl}}_{\mathrm{Te}}+{\mathrm{V}}_{\mathrm{Cd}}$, can cause a decrease in defect formation energy and a reduction in acceptor level, thus improving the dopability, especially when the Cl treatment is done at low temperature. The combination of two acceptors + one donor, e.g., ${\mathrm{Cl}}_{\mathrm{Te}}+2{\mathrm{Cu}}_{\mathrm{Cd}}$, has little or even negative effects because of the coexistence of the acceptor-acceptor and donor-acceptor coupling. More importantly, we show that the combination of one deep acceptor + one shallow acceptor, e.g., ${\mathrm{Sb}}_{\mathrm{Te}}+{\mathrm{P}}_{\mathrm{Te}}$, produces a much deeper acceptor level because the nominal deep acceptor ${\mathrm{Sb}}_{\mathrm{Te}}$ acts as a donor with respect to the shallow one, and then the deep acceptor state will be pushed even deeper due to the level repulsion. Thus, we should avoid this type of acceptor-acceptor co-doping to achieve high hole concentration. Our general understanding of the co-doping approach, therefore, provides a guideline for the future design of shallow defect complexes in CdTe and other semiconductors.