where σ is the electrical conductivity, S is the Seebeck coefficient, κ is the thermal conductivity and T is temperature.8,9
Although the optimal properties may be different for differentoperating conditions and device designs, the figure of merit providesa basis for comparing materials. One of the challengesin increasing the figure of merit is that improvements resulting from changes in one property are often offset by changes in another property. For example, metals have high electrical conductivity, but small Seebeck coefficients and high thermal conductivity, while thermal insulators are typically also electrical insulators. In particular, heat is conducted through a solid by electron conduction and lattice phonon conduction. The electron contribution (κe) is related directly to the electronic conductivity (σ) according to the Wiedemann–Franz relationship which indicates that the ratio of the two properties is constant at a given temperature according to the following relation,10