Resolving the true band gap of ZrNiSn half-Heusler thermoelectric materials

N-type XNiSn (X = Ti, Zr, Hf) half-Heusler (HH) compounds possess excellent thermoelectric properties, which are believed to be attributed to their relatively high mobility. However, p-type XNiSn HH compounds have poor figures of merit, zT, compared to XCoSb compounds. This can be traced to the suppression of the magnitude of the thermopower at high temperatures. E_g = 2eS_maxT_max relates the band gap to the thermopower peak. However, from this formula, one would conclude that the band gap of p-type XNiSn solid solutions is only one-third that of n-type XNiSn, which effectively prevents p-type XNiSn HHs from being useful thermoelectric materials. The study of p-type HH Zr_1-xSc_xNiSn solid solutions show that the large mobility difference between electrons and holes in XNiSn results in a significant correction to the Goldsmid-Sharp formula. This finding explains the difference in the thermopower band gap between n-type and p-type HH. The high electron-to-hole weighted mobility ratio leads to an effective suppression of the bipolar effect in the thermoelectric transport properties which is essential for high zT values in n-type XNiSn (X = Ti, Zr, Hf) HH compounds.