Thermoelectric Figure of Merit of Two-Band Semiconductors

Abstract

The locus of points on the (α,κ/σT) plane for a two‐band (electrons and holes) semiconductor as the concentration of doping agent is changed, is a curve that forms a closed loop, where α is the Seebeck coefficient, κ the thermal conductivity, σ the electrical conductivity, and T the absolute temperature. The value of the dimensionless thermoelectric figure of merit ZT=α²/(κ/σT) has, in general, two maxima on this loop, either or both of whose values are determinable, in principle, from measurements of α, κ, and σ on a few specimens with different amounts of doping. The shape and size of the loop and its position on the (α,κ/σT) plane depend upon the values of two dimensionless material parameters of the Chasmar and Stratton type, one for each band, the scattering parameters for the charge carriers in each band, and the value of the band gap in kT units. The effects of these parameters on the values of the ZT maxima are considered and approximate empirical relationships for Z(max)T as a function of these parameters are developed to aid in the quantitative evaluation of these effects. The relationships between these parameters and the pertinent physical properties of the material are discussed from the viewpoints of the requirements for improved thermoelectric materials and of the possible existence of an upper limit to the thermoelectric figure of merit.