Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2022 / Paper 1 / Section B / 12 / i

For one homogeneous thermoelectric material, the dimensional thermoelectric figure of merit isThe dimensionless quantity is $ZT$. The Seebeck coefficient $S$ measures the open-circuit voltage response to a temperature difference and reflects the energy asymmetry of charge-carrier transport. The electrical conductivity $\sigma$ depends on carrier density and mobility and sets electrical loss; $\rho =1/\sigma$. The thermal conductivity is $\kappa ={\kappa }_e+{\kappa }_l$, with contributions from carriers and phonons, and represents unwanted heat leakage.

Increasing carrier concentration usually raises $\sigma$ while reducing $|S|$ once transport becomes strongly degenerate. The electronic part of $\kappa$ also tends to rise, approximately through the Wiedemann-Franz law where applicable. This competition produces an intermediate optimum, commonly in heavily doped semiconductors, rather than in a very resistive insulator or an ordinary high-carrier-density metal. The optimum depends on band structure and scattering; the schematic is not a universal measured concentration curve.