  The mathematical modeling and numerical simulation of
semiconductor-electrolyte systems play important roles in the design of
high-performance semiconductor-liquid junction solar cells. In this work, we
propose a macroscopic mathematical model, a system of nonlinear partial
differential equations, for the complete description of charge transfer
dynamics in such systems. The model consists of a
reaction-drift-diffusion-Poisson system that models the transport of electrons
and holes in the semiconductor region and an equivalent system that describes
the transport of reductants and oxidants, as well as other charged species, in
the electrolyte region. The coupling between the semiconductor and the
electrolyte is modeled through a set of interfacial reaction and current
balance conditions. We present some numerical simulations to illustrate the
quantitative behavior of the semiconductor-electrolyte system in both dark and
illuminated environments. We show numerically that one can replace the
electrolyte region in the system with a Schottky contact only when the bulk
reductant-oxidant pair density is extremely high. Otherwise, such replacement
gives significantly inaccurate description of the real dynamics of the
semiconductor-electrolyte system.
