Understanding the dopability of p-type Mg₂(Si,Sn) by relating hybrid-density functional calculation results to experimental data

Abstract

Reaching a sufficiently high carrier concentration is crucial for thermoelectric material optimization in developing Mg2X (X = Si, Ge, and Sn)-based thermoelectric generators (TEGs). While n-type Mg2(Si,Sn) has excellent thermoelectric properties, p-type shows suboptimal thermoelectric performance because of insufficient carrier concentration, in particular for Mg2Si and Si-rich Mg2(Si,Sn). A systematic investigation of Li-doped Mg2Si1-xSnx 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 employing defect formation energies obtained within the hybrid-density functional theory (DFT) for the binaries. We furthermore use a linear interpolation of the hybrid-DFT results from the binaries to the ternary Mg2(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.

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“…[ 29 ] This is a complexity that is not taken into account in this work, but can be understood by analyzing the defect formation energies calculated from a more suitable reference states with respect to these phases and not the atomic chemical potentials used in our hybrid‐DFT calculations. [ 30 ] Among the shown defects, Ag Mg and Zn Mg are expected to cause the most charge compensation in the studied system as their formation energies, and therefore densities, [ 20 ] are the closest to the main n‐type dopants (Bi X and Sb X ).…”

“…However, the Mg 2 X system has been intensively studied and Li and Bi/Sb are the best so far reported dopants. [30,32]…”