Doping designed half-Heusler insulators

The 18-valence-electron 1:1:1 compounds of the type III-X-V, IV-X-IV, IV-IX-V and V-IX-IV include thermoelectric materials, topological insulators, and recently a high mobility p-type transparent conductor TaIrGe (arXiv:1406.0872), yet their intrinsic doping trends are poorly known or understood. Using the ``modern theory of doping'' that addresses via DFT and HSE the thermodynamic formation energies and the DFT-corrected transition levels in the gap, we find the following interesting trends: (1) High atomic number compounds such as TaIrGe made of metallic elements can surprisingly have a large band gap (direct) of $\sim$ 2.5 eV. (2) Half-Heusler such as A$^{\mathrm{(IV)}}$B$^{\mathrm{(X)}}$C$^{\mathrm{(IV)}}$ is naturally n-type if its DFT calculated chemical stability field resides within the A-rich or B-rich domain of the stability triangle, while it is p-type if it resides within the C-rich domain. Such calculations provide a good metric. (3) When the B atom [at (1/4,1/4,1/4)] is as large as Ir or Pt, the compound prefers p-type because the C-on-A antisite [such as Ge$_{\mathrm{Ta}}^{\mathrm{(1-)}}$] is a shallow acceptor producing holes yet the hole-killer donor of B-interstitial is unfavorable. (4) When B$=$Ni or Co, the compound favors n-type due to the dominance of B-interstitial defects (e.g. TiCoSb). We will show the calculated leading defect types and the dependence of carrier concentrations on chemical conditions for newly predicted half-Heulser insulators. This study is supported by DOE, Office of Science, Basic Energy Science, MSE division grant to CU Boulder.