The mathematical modeling and numerical simulation of semiconductor-electrolyte systems play important roles in the design of high-performance semiconductor-liquid junction solar cells. We discuss a macroscopic mathematical model for the complete description of charge transfer dynamics in such systems. This is a reaction-drift-diff usion-Poisson system that models the transport of electron-hole pairs in the semiconductor region and an equivalent system that describes the transport of reductant-oxidant pairs in the electrolyte region. The coupling between the semiconductor and the electrolyte is modeled through a set of interfacial reactive and current balance conditions. We present simulations that illustrate the quantitative behavior of the semiconductor-electrolyte system in both dark and illuminated environments, and compare with classical reduced models currently from electrochemistry transport. In particular we show that those reduced models yields a signi cantly inaccurate description of the real dynamics of the semiconductor-electrolyte interface. We close the discussion with open problems and future directions. This is work in collaboration with Yuan He,Heung-Chan Lee and Kui Ren.
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