An algorithm of calculating transport parameters of thermoelectric materials using single Kane band model with Riemann integral methods

We develop an algorithm called SKBcal to conveniently calculate within minutes the thermoelectric transport parameters such as reduced Fermi level (η), electronic thermal conductivity (κ(e)), lattice thermal conductivity (κ(l)), Hall factor (A), effective mass (m(*)), quality factor (β) and theoretical zT within the framework of single Kane band (SKB) model. The generalized Fermi–Dirac integral for SKB model is integrated by left Riemann integral method. A concept of significant digits of relative error is involved to determine the accuracy of calculation. Furthermore, a combined program of "For" and "While" is coded to set up an iteration for refining the reduced Fermi level. To easily obtain the quality factor, we re-derive the expression into a formula related to carrier mobility. The results calculated by SKBcal are consistent with the data reported in the literatures.