The half-Heusler filled tetrahedral structures (FTSs) are zinc-blende-like compounds, where an additional atom is filling its previously empty interstitial site. The FTSs having 18 valence electrons per formula unit are an emerging family of functional materials, whose intrinsic doping trends underlying a wide range of electronic functionalities are yet to be understood. Interestingly, even pristine compounds without any attempt at impurity/chemical doping exhibit intriguing trends in the free carriers they exhibit. Applying the first principles theory of doping to a few prototype compounds in the $A^{\mathrm{IV}}{B}^{\mathrm{X}}{C}^{\mathrm{IV}}$ and $A^{\mathrm{IV}}{B}^{\mathrm{IX}}{C}^{\mathrm{V}}$ groups, we describe the key ingredients controlling the materials’ propensity for both intrinsic and extrinsic doping: (a) The spontaneous deviations from 1:1:1 stoichiometry reflect predictable thermodynamic stability of specific competing phases. (b) Bulk ABC compounds containing $3d$ elements in the $B$ position (ZrNiSn and ZrCoSb) are predicted to be naturally $3d$ rich. The $B=3d$ interstitials are the prevailing shallow donors, whereas the potential acceptors (e.g., Zr vacancy and Sn-on-Zr antisite) are ineffective electron killers, resulting in an overall uncompensated $n$-type character, even without any chemical doping. In these materials, the band edges are “natural impurity bands” due to non-Daltonian off-stoichiometry, such as $B$ interstitials, not intrinsic bulk controlled states as in a perfect crystal. (c) Bulk ABC compounds containing $5d$ elements in the $B$ position (ZrPtSn, ZrIrSb, and TaIrGe) are predicted to be naturally $C$ rich and $A$ poor. This promotes the hole-producing $C$-on-$A$ antisite defects rather than $B$-interstitial donors. The resultant $p$-type character (without chemical doping) therein is “latent” for $C=\mathrm{Sn}$ and Sb; however, as the $C$-on-$A$ hole-producing acceptors are rather deep and $p$ typeness is manifest only at high temperature or via impurity doping. In contrast, in TaIrGe $(B=\mathrm{Ir},5d)$, the prevailing hole-producing Ge-on-Ta antisite ($C$-on-$A$) is shallow, making it a real $p$-type compound. This general physical picture establishes the basic trends of carriers in this group of materials.

• Received 16 August 2016

DOI:https://doi.org/10.1103/PhysRevB.95.085201