Effect of linear temperature dependence of thermoelectric properties on energy conversion efficiency

New thermal rate equations were developed by taking the temperature dependences of the electrical resistivity ρ and thermal conductivity κ of the thermoelectric (TE) materials into the thermal rate equations on the assumption that they vary linearly with temperature T. The relative energy conversion efficiency η/η0 for a single TE element was formulated by approximate analysis, where η and η0 are the energy conversion efficiencies derived from the new and conventional thermal rate equations, respectively. Applying it to Si–Ge alloys, the temperature dependence of ρ is stronger than that of κ, so the former has a more significant effect on η/η0 than the latter. However, the degree of contribution from both of them to η/η0 was a little lower than 1% at the temperature difference ΔT of 600 K. When the temperature dependence of κ was increased to become equal to that of ρ, however, it was found that η/η0 is increased by about 10% at ΔT = 600 K. It is clarified here that the temperature dependences of ρ and κ are also important factors for an improvement in η.