Understanding Cu incorporation in the Cu2xHg2−xGeTe4 structure using resonant x-ray diffraction

Abstract

The ability to control carrier concentration based on the extent of Cu solubility in the ${\mathrm{Cu}}_{2x}{\mathrm{Hg}}_{2\ensuremath{-}x}{\mathrm{GeTe}}_{4}$ alloy compound (where $0\ensuremath{\le}x\ensuremath{\le}1$) makes ${\mathrm{Cu}}_{2x}{\mathrm{Hg}}_{2\ensuremath{-}x}{\mathrm{GeTe}}_{4}$ an interesting case study in the field of thermoelectrics. While Cu clearly plays a role in this process, it is unknown exactly how Cu incorporates into the ${\mathrm{Cu}}_{2x}{\mathrm{Hg}}_{2\ensuremath{-}x}{\mathrm{GeTe}}_{4}$ crystal structure and how this affects the carrier concentration. In this work, we use a combination of resonant energy x-ray diffraction (REXD) experiments and density functional theory (DFT) calculations to elucidate the nature of Cu incorporation into the ${\mathrm{Cu}}_{2x}{\mathrm{Hg}}_{2\ensuremath{-}x}{\mathrm{GeTe}}_{4}$ structure. REXD across the ${\mathrm{Cu}}_{k}$ edge facilitates the characterization of Cu incorporation in the ${\mathrm{Cu}}_{2x}{\mathrm{Hg}}_{2\ensuremath{-}x}{\mathrm{GeTe}}_{4}$ alloy and enables direct quantification of antisite defects. We find that Cu substitutes for Hg at a 2:1 ratio, wherein Cu annihilates a vacancy and swaps with a Hg atom. DFT calculations confirm this result and further indicate that the incorporation of Cu occurs preferentially on one of the $z=1/4$ or $z=3/4$ planes before filling the other plane. Furthermore, the amount of ${\mathrm{Cu}}_{\mathrm{Hg}}$ antisite defects quantified by REXD was found to be directly proportional to the experimentally measured hole concentration, indicating that the ${\mathrm{Cu}}_{\mathrm{Hg}}$ defects are the driving force for tuning carrier concentration in the ${\mathrm{Cu}}_{2x}{\mathrm{Hg}}_{2\ensuremath{-}x}{\mathrm{GeTe}}_{4}$ alloy. The link uncovered here between crystal structure, or more specifically antisite defects, and carrier concentration can be extended to similar cation-disordered material systems and will aid the development of improved thermoelectric and other functional materials through defect engineering.