Redox properties of small semiconductor particles

In this paper we study the equilibrium properties of semiconductor particles of intermediate sizes (≥Debye length) in contact with an electrolyte solution containing a given redox pair. We focus on the size dependence of electrical and thermodynamical quantities associated with such particles. The equilibrium distribution of the potential and of the charge in the particle and in the surrounding electrolyte is obtained analytically in limiting cases and computed in the general case using the nonlinear Poisson-Boltzmann equation, assuming Boltzmann statistics for carrier distributions in the semiconductor. A simple relation for the size-dependent redox potential of a semiconductor sphere characterized by its radius and charge is proposed and is found to provide a good approximation for a broad range of electrolyte concentrations. This leads to an expression for the "equilibrium constant" for the semiconductor/electrolyte system, which relates the concentrations of the electrolytic redox components to the concentration, size, and charge of the semiconductor particles.