Irreversible thermodynamics and Shockley recombination velocity: Application to photoabsorption near a surface
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2018 American Physical Society. We apply the method of irreversible thermodynamics to obtain, for a semiconductor with electron and hole carriers adjacent to a single-carrier material, the recombination velocity and the rate of surface heating. The lack of equilibrium across the interface drives both a charged number current flux (the difference between electron and hole fluxes) and an uncharged number current flux (the sum of electron and hole fluxes). The latter provides a generalization of Shockley's recombination velocity. There are two contributions to the surface heating rate, one proportional to the charged number current flux times a difference in electrochemical potentials across the interface, and the other proportional to the uncharged number current flux times its associated difference in electrochemical potential. We apply our results to photoabsorption at a uniform volume rate G within a distance d of a vacuum semiconductor surface, finding the distributions of number current density, charge, and voltage as a function of position.