Thermal Stabilization of Defect Charge States and Finite-Temperature Charge Transition Levels

Abstract

Point defects introduce localized electronic states that critically affect carrier trapping, recombination, and transport in functional materials. The associated charge transition levels (CTLs) can depend on temperature, requiring accurate treatment of vibrational and electronic free-energy contributions. In this work, we use machine-learned interatomic potentials to efficiently compute temperature-dependent CTLs for vacancies in MgO, LiF, and CsSnBr3. Using thermodynamic integration, we quantify free-energy differences between charge states and calculate the vibrational entropy contributions at finite temperatures. We find that CTLs shift with temperature in MgO, LiF and CsSnBr3 from both entropy and electronic contributions. Notably, in CsSnBr3 a neutral charge state becomes thermodynamically stable above 60 K, introducing a temperature-dependent Fermi-level window absent at 0 K. We show that the widely used static, zero-kelvin defect formalism can miss both quantitative CTL shifts and the qualitative emergence of new stable charge states.

Figures (3)

• Figure 1: Machine-learned interatomic potential and illustrations of marked structures. (a) The MgO model performance. Six closest Mg atoms to the oxygen vacancy are marked. (b) The LiF model performance. Six closest Li atoms to the fluorine vacancy are marked. (c) The CsSnBr3 model performance. Two closest Sn atoms to the bromine vacancy are marked.
• Figure 2: Temperature-dependent for MgO, LiF, and CsSnBr3 with regard to position. Dashed lines represent the positions of the and solid vertical lines indicate and positions, colored according to the temperature they represent. (a,d) The $\varepsilon_{+2/0}$ level in MgO shifts by approximately -785 over a temperature range of 1000. (b,e) In LiF, the $\varepsilon_{+1/0}$ and $\varepsilon_{0/-1}$ levels shift by about -994 and -1035, respectively, over 500. (c,f) The exhibited a shift of roughly 111, 324 and 218 over the 300K for the transitions between $+1/0$, $0/-1$ and $+1/-1$ respectively. Notably, a region where the neutral charge state is thermodynamically favorable is introduced around 60.
• Figure 3: Configurational coordinate diagrams and temperature-dependent optical transitions for MgO, LiF, and CsSnBr3. (a--c) The energy difference at the relaxed geometry of each charge state defines the corresponding emission or absorption energy. The specific emission and absorption energies are shown as insets in the figures. (d--f) Emission and absorption energies during simulations at different temperatures. The shaded area represents the standard deviations of the sampled emission and absorption distributions.