Carrier density and compensation in semiconductors with multiple dopants and multiple transition energy levels: Case of Cu impurities in CdTe

Doping is one of the most important issues in semiconductor physics. In many cases, when people describe carrier concentration as a function of dopant density and Fermi energy, they usually assume only one type of dopant with single transition energy level in the system. However, in reality, the situation is often more complicated, that is, in a semiconductor device, it usually contains multidopants and each can have multitransition energy levels. In this paper, using detailed balance theory and first-principles calculated defect formation energies and transition energy levels, we derive formulas to calculate carrier density for semiconductor with multidopants and multitransition energy levels. As an example, we studied CdTe doped with Cu, in which V_Cd, Cu_Cd, and Cu_i are the dominant defects/impurities. We show that in this system, when Cu concentration increases, the doping properties of the system can change from a poor p-type, to a poorer p-type, to a better p-type, and then to poor p-type again, in good agreement with experimental observations.