Thermoelectric performance: why the three transport properties must be read together

A practical introduction to the Seebeck coefficient, electrical conductivity, thermal conductivity, power factor and figure of merit.

THERMOELECTRIC FUNDAMENTALS · RESEARCH NOTE 01

Thermoelectric materials convert a temperature difference directly into an electrical potential. Their performance is often summarized by the dimensionless figure of merit, but understanding that number requires reading several coupled transport properties together.

The figure of merit

The conventional expression is

[ ZT = ]

where (S) is the Seebeck coefficient, () is electrical conductivity, (T) is absolute temperature, and (_{}) is total thermal conductivity.

The numerator is commonly expressed as the power factor:

[ PF = S^2 ]

The power factor describes the electrical contribution to thermoelectric performance, while the denominator captures heat transport through the material.

Why optimizing one property is not enough

SEEBECK(S)Voltage generated per temperature difference

CONDUCTIVITY()Ability to carry electrical current

THERMAL()Ability to conduct heat

A large Seebeck coefficient is not sufficient by itself. In many materials, increasing carrier concentration raises electrical conductivity but reduces the magnitude of the Seebeck coefficient. This creates a trade-off in the power factor.

Thermal conductivity introduces another constraint. Total thermal conductivity is often separated into electronic and lattice contributions:

[ _{} = _e + _L ]

The electronic contribution is linked to charge transport, whereas the lattice contribution is associated with heat carried by phonons. Strategies that strongly suppress lattice thermal conductivity can be useful, provided they do not severely damage carrier mobility.

A practical way to read transport data

1. Check units and geometry. Confirm whether conductivity is reported in S m⁻¹ or S cm⁻¹, and whether the sample dimensions and contact configuration are appropriate.
2. Inspect temperature trends. A single maximum can hide changes in carrier concentration, mobility, phase stability or measurement quality.
3. Calculate the power factor consistently. Use (PF=S^2), convert (S) to V K⁻¹ and () to S m⁻¹ before reporting SI units.
4. Separate thermal contributions when possible. State whether the reported value is total or lattice thermal conductivity and explain how the electronic part was estimated.
5. Report ZT at the same temperature. Do not combine a power factor measured at one temperature with thermal conductivity measured at another without a justified model.

What this means for oxide thermoelectrics

Oxide materials offer advantages such as chemical and thermal stability, but their transport properties can be difficult to optimize simultaneously. Composition, defect chemistry, grain boundaries, secondary phases and microstructure can all influence carrier concentration, mobility and phonon scattering.

This is why a convincing structure–property argument should combine transport measurements with phase analysis, microscopy and, where possible, defect-sensitive characterization. A lower thermal conductivity is not automatically evidence of beneficial phonon engineering if it is accompanied by a large loss in electrical conductivity.

Further reading

• G. J. Snyder and E. S. Toberer, “Complex thermoelectric materials,” Nature Materials 7, 105–114 (2008). https://doi.org/10.1038/nmat2090
• W. Kim, “Strategies for engineering phonon transport in thermoelectrics,” Journal of Materials Chemistry C 3 (2015). https://doi.org/10.1039/C5TC01670C

This note is an educational overview. Quantitative comparison between materials requires consistent measurement protocols, temperature ranges and uncertainty reporting.