Low electronic conductivity of Li₇La₃Zr₂O₁₂ solid electrolytes from first principles

Lithium-rich garnets such as Li₇La₃Zr₂O₁₂ (LLZO) are promising solid electrolytes with potential application in all-solid-state batteries that use lithium-metal anodes. The practical use of garnet electrolytes is limited by pervasive lithium-dendrite growth, which leads to short-circuiting and cell failure. One proposed mechanism of lithium-dendrite growth is the direct reduction of lithium ions to lithium metal within the electrolyte, and lithium garnets have been suggested to be particularly susceptible to this dendrite-growth mechanism due to high electronic conductivities relative to other solid electrolytes. The electronic conductivities of LLZO and other lithium-garnet solid electrolytes, however, are not yet well characterized. Here, we present a general scheme for calculating the intrinsic electronic conductivity of a nominally insulating material under variable synthesis conditions from first principles, and apply this to the prototypical lithium-garnet LLZO. Our model predicts that under typical battery operating conditions, electron and hole mobilities are low (<1cm²V^-1s^-1), and bulk electron and hole carrier concentrations are negligible, irrespective of initial synthesis conditions or dopant levels. These results suggest that the bulk electronic conductivity of LLZO is not sufficiently high to cause bulk lithium-dendrite growth during cell operation, and that any non-negligible electronic conductivity in lithium garnet samples is likely due to extended defects or surface contributions.