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Band convergence brings distinct extrema of an electronic band structure close enough in energy that several valleys contribute to charge carrier transport at the operating temperature. Increasing the effective valley degeneracy can improve the balance between Seebeck coefficient and electrical conductivity, rather than merely increasing the number of carriers in one valley. Composition and semiconductor doping can tune this energy separation. A primary example is the lead telluride-selenide alloy study that combined measured transport with a multiband model.^[ref]

The thermoelectric power factor is not determined by valley degeneracy alone. Additional inter-valley scattering can reduce charge carrier mobility, so a larger number of populated valleys need not improve transport. The spacing of the valleys in both energy and wave vector, and the relevant electron-phonon interactions, matter.^[ref]

Lead telluride is the compound semiconductor $\mathrm{PbTe}$, important in thermoelectric materials and infrared devices. Its electronic band structure and transport properties can be modified through composition and doping, while heat is carried by both charge carriers and lattice vibrations.

Thermoelectric performance is summarized by $ZT=S^2\sigma T/\kappa$, combining the Seebeck coefficient $S$, electrical conductivity $\sigma$ and thermal conductivity $\kappa$. These quantities cannot generally be tuned independently. Experiments on doped lead telluride-selenide alloys demonstrated improved performance by bringing multiple electronic valleys into closer energetic alignment, connecting band structure with measured transport.^[ref]

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.

Yanzhong Pei is the first-listed author of Convergence of electronic bands for high performance bulk thermoelectrics by Yanzhong Pei and others. The study uses convergence of electronic bands in lead telluride-based alloys to improve performance measured by the thermoelectric figure of merit. It illustrates how electronic structure can be engineered alongside heat transport when optimizing the thermoelectric figure of merit.^[ref]