Supplementary Materials: Hidden processing drivers of thermoelectric performance in tetrahedrites

Tetrahedrites are promising thermoelectric materials owing to their intrinsically low thermal conductivity and earth-abundant constituent elements. However, reported performance varies widely across the literature and shows no clear or consistent trends, hindering the development of reliable optimisation strategies. Here, we combine a large-scale meta-analysis of 276 experimental data series with targeted microstructural characterisation and first-principles calculations to decouple compositional effects from processing-induced artefacts.

After normalising the thermoelectric figure of merit, zT, for its temperature dependence, we find that most dopant classes do not produce statistically robust performance improvements over undoped tetrahedrite. Instead, processing-induced variation emerges as the dominant source of performance scatter. Our analysis identifies porosity generated by gas evolution during sintering as a major hidden variable that obscures intrinsic transport behaviour and masks dopant-specific trends. 

Because heat-carrying phonons in tetrahedrites already exhibit near-atomic-scale mean free paths, microstructural defects provide only marginal further reductions in lattice thermal conductivity, while significantly disrupting electrical connectivity. Systematic first-principles calculations further show that Fe is electronically distinct among dopants, introducing localised states near the valence-band edge, consistent with the only statistically significant doping response observed in the meta-analysis.

These findings demonstrate that thermoelectric performance in tetrahedrites is currently governed more by processing quality and the resulting microstructure than by composition. More broadly, this work redirects optimisation efforts from purely compositional fine-tuning toward rigorous processing control, quantitative microstructural characterisation, and standardised transport-property benchmarking, providing a transferable framework for thermoelectric materials development.