Origin of hole density pinning in group-V doped CdTe

Hole densities in group-V (P, As, and Sb) doped CdTe typically fall below ${10}^{17}c{m}^{-3}$ although sufficient group-V dopants are incorporated. Previous theoretical studies suggested that the formation of AX centers compensates the acceptors, thereby limiting $p$-type doping. However, recent calculations including spin-orbit coupling effects suggest that AX centers are unstable and thus cannot hinder $p$-type doping. Therefore, the origin of the hole density pinning issue in CdTe remains elusive. Our first-principles calculations, incorporating spin-orbit coupling, coupled with detailed balance simulations, reveal that hole doping in CdTe remains significantly limited despite the instability of the AX centers. This limitation stems from the self-compensation driven by the native vacancies and the band-edge excitations induced by free carriers. Additionally, we find that As is the most favorable dopant among group-V dopants due to its relatively low formation energy and shallow transition level. Our understanding of the hole-limiting mechanism is important for improving the dopability of CdTe solar cells. Moreover, our analysis of the band-edge excitations is critical for describing the defect properties in semiconductors.