Factors Affecting the Electron Conductivity in Single Crystal Li₇La₃Zr₂O₁₂ and Li₇P₃S₁₁

One of the serious challenges in all solid-state Li ion batteries is neutral Li intrusion into the solid-state electrolyte that can ultimately cause catastrophic failure. One possibility for this is due to n-type electron conductivity that induces the reaction Li⁺ + e^- → Li⁰ at sites where the potential is less than the Li⁺/Li potential. This paper reports hybrid density functional theory calculations of the electronic conductivity in two prototype single crystalline solid-state electrolytes, cubic Li₇La₃Zr₂O₁₂ (c-LLZO) and Li₇P₃S₁₁ (LPS). The formation energies of important point defects that can affect electron conductivity are determined, and we find that the mechanism of n-type electron conductivity for both solid-state electrolytes is via “small” electron polaron hopping, where the quotes signify that substantial Li ion rearrangement is associated with the polaron formation and its migration. In both electrolytes, the formation energies for the small polarons at the Fermi energy are too high to generate measurable electron conductivity at room temperature. For c-LLZO, the concentration of electron polarons necessary to ensure charge neutrality from positively charged oxygen vacancies formed in synthesis can be significantly higher. Hence, the electron conductivity could be significant when measured with ion-blocking metal electrodes, and we discuss how the synthesis conditions could affect this magnitude. However, in the solid-state battery, these polarons are replaced by negatively charged Li vacancies so that the electron conductivity should remain minimal. For LPS single crystals, the inherent minimal electron conductivity is independent of synthesis conditions. We also show that the cost of forming Li⁰ in bulk c-LLZO is enormous due to strain effects so that it could only potentially form at voids, grain boundaries, or around vacancy defects which relax the lattice strain.