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A researcher in materials for the thermoelectric effect who coauthored a review with G. Jeffrey Snyder. Their account explains the competing requirements for a high thermoelectric figure of merit: useful electrical transport must coexist with weak heat transport. Complex crystal structures and nanoscale design offer ways to suppress the phonon contribution to thermal conductivity while retaining useful electronic behavior.^[ref]

A researcher who studies materials and devices using the thermoelectric effect. With Eric S. Toberer, he reviewed strategies for improving the thermoelectric figure of merit by controlling carrier concentration and reducing thermal conductivity. The central challenge is coupled transport: improving one property can worsen another. The material therefore has to be designed as a complete heat-and-charge transport system.^[ref]

The dimensional material figure of merit and its common dimensionless form areHere $S$ is the Seebeck coefficient, $\sigma$ the electrical conductivity, ${\rho }_e=1/\sigma$ the electrical resistivity, and $\kappa ={\kappa }_e+{\kappa }_l$ the total thermal conductivity. $Z$ has units ${\mathrm{K}}^{-1}$; $ZT$ is dimensionless.

Seek a large thermoelectric power factor $S^2\sigma$ and low thermal conductivity. Optimize carrier concentration and band structure to balance thermopower and conductivity. Alloy disorder, complex unit cells, grain boundaries or suitable nanoscale features can scatter phonons and reduce lattice heat transport.

The properties are coupled: increasing carrier density often reduces $|S|$, electronic heat conduction grows with electrical transport, and boundaries that scatter phonons may also scatter carriers. Evaluate the net change and the operating-temperature range, rather than maximizing each favorable term independently.^[ref]

Tune doping to the optimum carrier concentration; a rise in conductivity is useful only if it outweighs the accompanying loss of thermopower and extra electronic heat conduction. Band convergence, favourable density of states and energy-dependent transport can improve the power factor $S^2\sigma$, provided mobility is retained.

Reduce lattice thermal conductivity through alloy disorder, heavy or complex unit cells, grain boundaries and nanoscale inclusions that scatter phonons. Aim to scatter heat-carrying phonons much more strongly than charge carriers; indiscriminate disorder can reduce both thermal and electrical conductivity. Nanostructuring and interfaces can therefore help, but an improvement must be demonstrated in total $ZT$ at the operating temperature, not inferred from lower $\kappa$ alone.^[ref]

At low carrier concentration, $|S|$ can be large but electrical conductivity is too small. Increasing the carrier concentration usually increases $\sigma =ne\mu$, while $|S|$ decreases. Electronic thermal conductivity rises approximately as ${\kappa }_e=L\sigma T$ by the Wiedemann-Franz law; lattice conduction supplies an additional background. Thus neither an insulator nor an ordinary metal usually maximizes $Z$.

Heavily doped semiconductors and semimetals often give the useful compromise, near a maximum of $S^2\sigma /\kappa$ as doping is varied. The optimum is material- and temperature-dependent; there is no universal optimal concentration.

The dimensionless thermoelectric figure of merit compares electrical conversion with thermal leakage in a material: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.^[ref]

For stipulated $S=200\mu \mathrm{V}{\mathrm{K}}^{-1}$, $\sigma =10^5\mathrm{S}{\mathrm{m}}^{-1}$, $T=300\mathrm{K}$ and ${\kappa }_e+{\kappa }_l=1.5\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, the calculated thermoelectric power factor is $0.004\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-2}$ 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.

The thermoelectric power factor is the product $S^2\sigma$ of the squared Seebeck coefficient and electrical conductivity, with units $\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-2}$. It combines a material's voltage response to a temperature gradient with its ability to carry electric current. For example, $S=200\mu \mathrm{V}{\mathrm{K}}^{-1}$ and $\sigma =10^5\mathrm{S}{\mathrm{m}}^{-1}$ give $S^2\sigma =0.004\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-2}$.

At fixed geometry and imposed temperature difference, a constant-property thermoelectric generator behaves as a voltage source with internal electrical resistance. Matching the external electrical resistance to it maximizes output power; the material dependence of that maximum is proportional to the thermoelectric power factor. Maximizing thermal efficiency also requires controlling thermal conductivity, which is why the thermoelectric figure of merit includes the thermal denominator.^[ref]