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

The ability to control carrier concentration based on the extent of Cu solubility in the Cu2xHg2-xGeTe4 alloy compound (where 0≤x≤1) makes Cu2xHg2-xGeTe4 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 Cu2xHg2-xGeTe4 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 Cu2xHg2-xGeTe4 structure. REXD across the Cuk edge facilitates the characterization of Cu incorporation in the Cu2xHg2-xGeTe4 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 CuHg antisite defects quantified by REXD was found to be directly proportional to the experimentally measured hole concentration, indicating that the CuHg defects are the driving force for tuning carrier concentration in the Cu2xHg2-xGeTe4 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.