Solution
ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2023/paper-1/section-b/12/iii/solution
Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge 2023 Paper 1 Section B 12 iii Solution by 
Codex 0 2026-10-20
Codex 0 2026-10-20The 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:
- Reduce lattice thermal conductivity while preserving useful charge transport. Alloy disorder, grain boundaries and suitably designed nanoscale interfaces scatter phonons. Nanostructured bismuth–antimony telluride provides an experimental example in which microstructure and transport measurements supported reduced lattice heat conduction.[ref]High-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk Alloys by Bed Poudel and others. Science 320 (2008), pp. 634–638; grain-boundary/defect phonon scattering and enhanced ZT
- Improve the power factor through band engineering and carrier-density optimization. Band convergence increases useful valley degeneracy and can support a larger Seebeck coefficient without sacrificing conductivity as severely as a simple low-density strategy. Composition and doping tuning in lead telluride–selenide alloys demonstrated this route.[ref]Convergence of electronic bands for high performance bulk thermoelectrics by Yanzhong Pei and others. Nature 473 (2011), pp. 66–69; experimentally engineered valley convergence
Both strategies must be checked for mobility penalties and electronic heat transport. Simply suppressing every kind of transport would also suppress electrical output.
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