Understanding the dopability of p-type Mg-2(Si,Sn) by relating hybrid-density functional calculation results to experimental data

It is crucial to reach a sufficiently high carrier concentration in order to optimize the thermoelectric (TE) material in the development of Mg-2 X (X= Si, Ge, and Sn)-based TE generators. While n-type Mg-2(Si,Sn) has excellent TE properties, p-type shows suboptimal TE performance because of insufficient carrier concentration, in particular for Mg2Si and Si-rich Mg-2(Si,Sn). A systematic investigation of Li-doped Mg2Si1-x Sn x has been performed as Li, in contrast to other typical dopants, has a high solubility in the material system and has been shown to yield the highest reported carrier concentrations. We observe that the carrier concentration increases with Li content, but the dopant efficiency decreases. With respect to the Si:Sn ratio, we find a clear increase in maximum achievable carrier concentration and dopant efficiency with increasing Sn content. The trends can be understood by employing defect formation energies obtained within the hybrid-density functional theory (DFT) for the binaries. Further, we use a linear interpolation of the hybrid-DFT results from the binaries to the ternary Mg-2(Si,Sn) compositions and a simple single parabolic band model to predict the maximal achievable carrier concentration for the solid solutions, providing a simple guideline for experimental work. Finally, we show that the approach is transferable to other material classes. This work highlights that, besides dopant solubility, the interplay between intrinsic and extrinsic defects determines the achievable carrier concentration.