  Defects are crucial in determining the overall physical properties of
semiconductors. Generally, the charge-state transition level (TEL), 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 TEL, and, as a result, almost all existing defect
theories in semiconductors are built on a temperature-independent
approximation. In this article, by deriving the basic formulas for
temperature-dependent TEL, we have established two fundamental rules for the
temperature dependence of TEL in semiconductors. Based on these rules,
surprisingly, it is found that the temperature dependences of TEL 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.
