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Defects responsible for abnormal n-type conductivity in Ag-excess doped PbTe thermoelectrics

We find that Ag-interstitial ($Ag_I$) acts as an electron donor and plays an important role in Ag-excess doped polycrystalline PbTe thermoelectric materials. When Ag is heavily doped in PbTe, the neutral (Ag-Ag) dimer defect is formed at the Pb-site and the environment becomes Pb-rich/Te-poor condition. Then the positively ionized Ag interstitial ($Ag_I^+$) defect becomes the major defect under Pb-rich condition. Due to the small formation energy and small diffusion barrier of $Ag_I^+$, Ag can be easily dissolved into the PbTe matrix. The temperature behavior of the Ag defect formation energy well explains the $Ag_I^+$ solubility, the electron carrier generation, and the increasing electrical conductivity in Ag-excess doped polycrystalline PbTe at high temperature. This abnormal doping behavior by forming interstitial defects is also found for Au-doped PbTe.