Nanowires can increase by reducing lattice heat conduction more strongly than they degrade useful electronic transport. A wire diameter comparable to important phonon mean free paths introduces boundary scattering and reduces the lattice part of thermal conductivity. Interfaces, surface roughness and suitable nanostructure can suppress long-mean-free-path phonons while preserving shorter-mean-free-path carrier transport.
Electronic confinement or energy-dependent scattering can also change the Seebeck coefficient and thermoelectric power factor, but neither improvement is automatic. Surface depletion, disorder and contact resistance may instead reduce electrical conductivity; a smaller wire is not necessarily better. The necessary comparison is the complete ratio over the operating temperature range. The experimentally established benefit of nanostructuring is especially clear when it suppresses phonon heat conduction while retaining a useful power factor.[ref]
The material figure of merit is
Large 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 is
Increasing 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.