Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2023 / Paper 1 / Section B / 12 / iii / Solution

The material figure of merit isLarge thermoelectric power factor supplies electrical output, while low thermal conductivity limits heat leaking without useful conversion. For a constant-property ideal generator, a common approximation isIncreasing the appropriately averaged figure of merit raises efficiency toward, but not beyond, the Carnot limit. Actual devices also incur contact, geometric and heat-transfer losses, and a single peak material ZT does not specify their efficiency.

The supplied trends show the trade-off with carrier density: conductivity rises, the magnitude of the Seebeck coefficient tends to fall, and electronic thermal conductivity rises approximately with conductivity through the Wiedemann-Franz law. Thus neither arbitrarily high doping nor maximization of conductivity alone gives the best ZT; the power factor and thermal terms produce an intermediate optimum.

Two complementary strategies are:

Both strategies must be checked for mobility penalties and electronic heat transport. Simply suppressing every kind of transport would also suppress electrical output.