A detailed analysis of ambipolar diffusion in nanostructured metal oxide films

Abstract

In this paper a transport equation is derived which describes the behaviour of the nanostructured metal oxide films in a photoelectrochemical cell. It is shown that a detailed analysis of the charge compensation mechanism necessarily leads to a transport equation with characteristics similar to but logically distinct from the pure diffusion equation. The studied phenomenon was named ambipolar diffusion in the early 1950s. It takes into account the fact that the diffusion processes of ions and electrons occur at different speeds. A weak electric field therefore couples the processes together to preserve charge neutrality. The electric field in turn affects the transport resulting in a deviation from purely diffusive behaviour. However, this has not been widely recognised in the literature for nanostructured semiconductor films until very recently. In this paper a detailed analysis is presented. It is based on the assumption that the current density is solenoidal. It is shown that application of the ambipolar diffusion model to a photoelectrochemical cell based on a nanostructured metal oxide film leads to an additional term in the transport equation, rather than only a new diffusion coefficient as in earlier work. It is also shown that the boundary conditions interact closely with the equation to form a transport model.