Revisiting Theoretical Modeling of Seebeck Coefficient of Semiconductors

Abstract

We revisit the closed-form models of Seebeck coefficient, and identify the thermodynamic flaws in those extensively-used methodologies, essentially including the confusion of electrochemical potential and electrical potential within the definition, arbitrarily neglecting the dependence on conduction band bottom and Fermi level when calculating distribution function spatial gradient, and the improper heat flux presentation. Here, an alternative methodology is presented, which derives the Seebeck coefficient model based on the drift-diffusion equation with the Soret effect in the open circuit condition. The reversible model that eliminates the electron velocity and relaxation terms in the formulation is recovered for the band term in the near-equilibrium case, and it can give the lower bound of Seebeck coefficient in theory, while the phonon-drag term is of the identical form to the Boltzmann transport equation(BTE)-based one. A case study is performed for highly-n-doped Silicon, where the reversible, ballistic(based on Landauer formulation) and BTE models are compared with each other and with the experimental data. The reversible model gives the fairly-good predictions for the experiments. Given its theoretical-soundness, simple form and low computation cost, the reversible model can serve as a concise alternative for evaluating thermoelectric properties in both the reversible and near-equilibrium cases.