Thermoelectric efficiency has three Degrees of Freedom

Thermal energy can be directly converted to electrical energy as a result of thermoelectric effects. Because this conversion realises clean energy technology, such as waste heat recovery and energy harvesting, substantial efforts have been made to search for thermoelectric materials. Under the belief that the material figure of merit $zT$ represents the energy conversion efficiencies of thermoelectric devices, various high peak-$zT$ materials have been explored for half a century. However, thermoelectric properties vary greatly with temperature $T$, so the single value $zT$ does not represent device efficiency accurately. Here we show that the efficiency of thermoelectric conversion is completely determined by \emph{three} parameters $Z_{\mathrm{gen}}$, $\tau$, and $\beta$, which we call the \emph{thermoelectric degrees of freedom}. The $Z_{\mathrm{gen}}$, which is an average of material properties, is a generalisation of the traditional figure of merit. The $\tau$ and $\beta$, which reflect the gradients of the material properties, are proportional to escaped heat caused by the Thomson effect and asymmetric Joule heat, respectively. Our finding proposes new directions for achieving high thermoelectric efficiency; increasing one of the thermoelectric degrees of freedom results in higher efficiency. For example, thermoelectric efficiency can be enhanced up to 176\% by tuning the thermoelectric degrees of freedom in segmented legs, compared to the best efficiency of single-material legs.