Temperature effect on charge-state transition levels of defects in semiconductors

Defects are crucial in determining the overall physical properties of semiconductors. Generally, the charge-state transition level É α(q/q'), one of the key physical quantities that determines the dopability of defects in semiconductors, is temperature dependent. However, little is known about the temperature dependence of É α(q/q') and, as a result, almost all existing defect theories in semiconductors are built on a temperature-independent approximation. In this paper, by deriving the basic formulas for temperature-dependent α(q/q'), we have established two fundamental rules for the temperature dependence of α(q/q') in semiconductors. Based on these rules, surprisingly, it is found that the temperature dependencies of α(q/q') for different defects are rather diverse: It can become shallower, deeper, or stay unchanged. This defect-specific behavior is mainly determined by the synergistic or opposing effects between free-energy corrections (determined by the local volume change around the defect during a charge-state transition) and band-edge changes (which differ for different semiconductors). These basic formulas and rules, confirmed by a large number of state-of-the-art temperature-dependent defect calculations in GaN, may potentially be widely adopted as guidelines for understanding or optimizing doping behaviors in semiconductors at finite temperatures.