Dopant-induced modulation of lithium-ion conductivity in cubic garnet solid electrolytes: a first-principles study.

Cubic garnet Li ₇ La ₃ Zr ₂ O ₁₂ (c-LLZO) is a promising solid electrolyte for all-solid-state batteries, often doped with Ga, Al, and Fe to stabilize the structure and enhance Li-ion conductivity. Despite introducing the same amount of Li vacancies, these dopants with +3 classical charge yield different Li-ion conductivities by around an order of magnitude. In this study, we used density functional theory (DFT) calculations to investigate the impact of Ga, Fe, and Al dopants on Li chemical potential and Li-ion conductivity variations. We identified the energetically favorable dopant location in c-LLZO and determined the optimal U value of 7.5 eV for DFT+ U calculations for dopant Fe in c-LLZO. Our calculations showed that Ga or Fe doping enhances the Li chemical potential by 0.05-0.08 eV, reducing Li-ion transfer barriers and increasing Li-ion conductivity, while Al doping lowers the Li chemical potential by 0.08 eV, reducing Li-ion conductivity. To determine the cause of Li chemical potential variations, we performed a combined analysis of the projected density of states, charge density, and Bader charge. The distinct charge distribution from dopant atoms to neighboring O atoms is critical for determining the Li-ion chemical potential. Ga and Fe dopants retain more electrons, which consequently makes the adjacent O atoms acquire a more positive charge that destabilizes Li ions by reducing the restraining force acting on them, thereby enhancing Li-ion conductivity. In contrast, Al doping transfers more electrons to neighboring O atoms, resulting in greater attraction forces to Li ions and reducing Li-ion conductivity. Additionally, Fe-doped LLZO exhibits extra states in the bandgap, potentially causing Fe reduction, as observed in experiments. Our findings provide valuable insights into the design of solid electrolytes and highlight the importance of the local charge distribution around the dopant and Li atoms in determining Li-ion conductivity. This insight could serve as a guiding principle for future materials design and optimization in solid-state electrolyte systems.