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We have coupled electron microscopy and energy dispersive spectroscopyexperiments with \textit{ab-initio} modeling to study the solubility anddiffusion of Au in Bi$_2$Te$_3$. We found that thermal annealing of Au filmsresults in Au concentrations in Bi$_2$Te$_3$ above the previously reportedsolubility limit. The time scale of Au diffusion into Bi$_2$Te$_3$ is also muchgreater than expected. To explain our observations, we calculate defectformation energies and diffusion barriers within DFT. We identify aninterstitial mechanism consistent with the previously observed low solubilityand (rapid) anisotropic diffusion. However, the lower formation energies ofsubstitutional defects suggest that they may be active in our experiments andexplain the high observed concentrations.

Energetics and diffusion of gold in bismuth telluride