  We have coupled electron microscopy and energy dispersive spectroscopy
experiments with \textit{ab-initio} modeling to study the solubility and
diffusion of Au in Bi$_2$Te$_3$. We found that thermal annealing of Au films
results in Au concentrations in Bi$_2$Te$_3$ above the previously reported
solubility limit. The time scale of Au diffusion into Bi$_2$Te$_3$ is also much
greater than expected. To explain our observations, we calculate defect
formation energies and diffusion barriers within DFT. We identify an
interstitial mechanism consistent with the previously observed low solubility
and (rapid) anisotropic diffusion. However, the lower formation energies of
substitutional defects suggest that they may be active in our experiments and
explain the high observed concentrations.
