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 $\mathit{\text{ZT}}$ for $\mathit{\text{n}}$ and $\mathit{\text{p-doped}}$, 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.