The importance of temperature dependent energy gap in the understanding of high temperature thermoelectric properties

In the present work, we show the importance of temperature dependent energy band gap, E$_{g}$(T), in understanding the high temperature thermoelectric (TE) properties of material by considering LaCoO$_{3}$ (LCO) and ZnV$_{2}$O$_{4}$ (ZVO) compounds as a case study. For the fix value of band gap, E$_{g}$, deviation in the values of $\alpha$ has been observed above 360 K and 400 K for LCO and ZVO compounds, respectively. These deviation can be overcomed by consideration of temperature dependent band gap. The change in used value of E$_{g}$ with respect to temperature is $\sim$4 times larger than that of InAs. This large temperature dependence variation in E$_{g}$ can be attributed to decrement in the effective on-site Coulomb interaction due to lattice expansion. At 600 K, the value of \textit{ZT} for \textit{n} and \textit{p-doped}, LCO is $\sim$0.35 which suggest that it can be a used as a potential material for TE device. This work clearly suggest that one should consider the temperature dependent band gap in predicting the high temperature TE properties of insulating materials.