Band gap renormalization effects in the BaZrO₃ electrolyte

Electrical leakage is an inherent problem in solid oxide fuel and electrolyzer cells, limiting their energy conversion efficiency. High concentrations of electrons or holes can exacerbate this issue. However, it is largely unclear how the systems’ typical high operating temperatures influence their charge carrier concentrations. In this work, we use first-principles calculations to examine how lattice vibrations impact electrical conductivity in conventional electrolytes, using BaZrO₃ as a representative material. Our analysis shows that phonon-induced shifts in the band gap and band edges lead to a dramatic increase in p-type carrier concentrations at temperatures above 600 K, compared to models that neglect temperature effects. Additionally, we reveal the importance of oxygen ion motion and volume expansion on band edge positions, which further increases charge carrier concentrations. Our study provides a protocol for calculating phonon-induced changes in similar oxides, paving the way for interrogating electrical leakage in electrolytes for high-temperature operation.