Transport theory of semiconductor energy conversion

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Abstract
A systematic analysis of all the microscopic processes corresponding to macroscopic energy conversion in semiconductors is presented. Starting from the quasi-classical particle Boltzmann equations, a continuity equation for total energy is derived containing terms which can be identified with external electric power transfers. Similar continuity equations for internal energy and entropy are obtained, and from the latter, the irreversible entropy generation rate may be found. Using expressions for the particle and heat currents, the usual ohmic heating, thermoelectric and photoelectric effects are identified together with a new reversible effect whose magnitude is Ψ∇φ∇T/T, where Ψ=(σeσh/σ) T(Σh−Σe). Here σe,σh are partial electron and hole electrical conductivities, σ=σe +σh, Σe and Σh are the partial electron and hole Seebeck coefficients, φ is the difference between the electron and hole quasi-Fermi levels, and T is the temperature. Similarly, a complete account is given of the heating and refrigerating processes within the semiconductor. The analysis allows for the possibility of band structure inhomogeneities.