 Solution

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]