Polaron and Strain Effects on Ion Migration in WO$_3$

Abstract

Ion migration in WO$_3$ is a critical process for various technological applications, such as in batteries, electrochromic devices and energy-efficient brain-inspired computing devices. In this study, we investigate the migration mechanisms of H$^+$, Li$^+$, and Mg$^{2+}$ ions in monoclinic WO$_3$, and how energy barriers are affected by the presence of electron polarons and by lattice strain. Our approach in calculating the migration paths and barriers is based on density functional theory methods. The results show that the presence of polarons leads to association effects and lattice deformations that increase ion migration barriers. Therefore, the consideration of polarons is critical to accurately predict activation energies of ion migration. We further show that lattice strain modulates ion migration barriers, however, the impact of strain depends on the migrating ion. For protons that are embedded in the oxygen ion electronic shells and hop from donor to acceptor oxygens, compressive lattice strain accelerates migration by reducing the donor-acceptor distance. In contrast, the migration barriers of larger ions decrease with tensile lattice strain that increases the free space for the ion in the transition state. These insights into the effects of polarons and lattice strain are important for understanding and tuning properties of WO$_3$ when aiming for optimized device characteristics.