Nonequilibrium thermodynamic model of thermoelectricity and thermodiffusion in semiconductors

We present a self-consistent model rooted in nonequilibrium thermodynamics for defining concentration gradients in the electron/hole pairs and electric-field gradients in an intrinsic semiconductor created upon exposure to a temperature gradient. The model relies on the equation for entropy production expressed through phenomenological equations for the electron/hole flux, with the imposed condition that the resulting concentration profiles of the electrons and holes are identical. The chemical potentials of electrons, holes, and parent atoms of the lattice, which are contained in the flux equations, are calculated on the basis of the temperature-dependent equilibrium dissociation reaction: lattice atom ↔ electron + hole. Electron/hole concentration profiles resulting from the temperature gradient, along with the associated gradient in the electric field, are expressed through equilibrium microscopic parameters of the semiconductor, which include the effective masses of electrons and holes, the energy gap width, and the Debye temperature. The resulting expressions contain neither kinetic nor fitting parameters, and predict values in reasonable (order-of-magnitude) agreement with empirical data. Finally, the model predicts a measurable additional thermodiffusion-based Seebeck effect when the temperature difference is on the order of several tens of degrees across a nonisothermal semiconductor working as a power supply under conditions of optimal power transport.