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

Band structure parameters, such as the band gap, can be estimated using electrical transport properties. In many thermoelectric studies, the temperature dependent Seebeck coefficient is used to estimate the band gap using the Goldsmid–Sharp band gap formula: Eg 1⁄4 2eSmaxTmax. This important, fundamental parameter is useful for characterizing and understanding any semiconductor, but it is particularly critical in thermoelectric materials because the efficiency at high temperatures is limited by minority carrier excitation across the band gap. In this work, we compare this estimate to optical band gap measurements in the ZrNiSn system which highlights the limitations of the Goldsmid–Sharp band gap estimate—when electron-to-hole weighted mobility ratio, A, is large. By understanding this parameter, we show why ZrNiSn half Heusler materials are very good n-type, but inherently poor p-type materials. N-type XNiSn (X 1⁄4 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. Eg 1⁄4 2eSmaxTmax 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 Zr1 xScxNiSn 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 weightedmobility 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 1⁄4 Ti, Zr, Hf) HH compounds.