Temperature Effect on Charge-state Transition Levels of Defects in Semiconductors

TL;DR

This paper derives formulas for how defect charge-state transition levels in semiconductors depend on temperature, revealing diverse behaviors that influence doping strategies and material properties.

Contribution

It introduces fundamental formulas and rules for the temperature dependence of defect transition levels, a topic previously underexplored in semiconductor physics.

Findings

Temperature dependence of TEL varies across defects: shallower, deeper, or unchanged.

The behavior is influenced by free energy corrections and band edge shifts.

Formulas are validated with calculations in GaN, aiding defect engineering.

Abstract

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.