= Thermoelectric figure of merit
{title2=$ZT$}
The dimensionless <thermoelectric figure of merit> compares electrical conversion with thermal leakage in a material:
$$
ZT=\frac{S^2\sigma T}{\kappa_e+\kappa_l}.
$$
Here $S$ is the <Seebeck coefficient>, $\sigma$ the <electrical conductivity>, $T$ the absolute <temperature>, and $\kappa_e,\kappa_l$ the electronic and lattice contributions to <thermal conductivity>. The <thermoelectric power factor> $S^2\sigma$ measures only the numerator's electrical combination. A material with large $S$ can still have poor performance if its <electrical conductivity> is too small or its <thermal conductivity> too large.<Complex thermoelectric materials by G. Jeffrey Snyder and Eric S. Toberer>[pp. 105–107, definition of zT and carrier-concentration trade-offs]{ref}
For stipulated $S=200\,\mathrm{\mu V\,K^{-1}}$, $\sigma=10^5\,\mathrm{S\,m^{-1}}$, $T=300\,\mathrm K$ and $\kappa_e+\kappa_l=1.5\,\mathrm{W\,m^{-1}\,K^{-1}}$, the calculated <thermoelectric power factor> is $0.004\,\mathrm{W\,m^{-1}\,K^{-2}}$ and $ZT=0.8$. Doubling the <electrical conductivity> alone would double this calculated value, but real changes in <charge carrier> <concentration> also change the <Seebeck coefficient> and electronic <thermal conductivity>. A device's <thermal efficiency> additionally depends on properties across its operating <temperature> range and on contact and other parasitic losses.
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