A MODEL FOR THE EFFECTIVE BARRIER HEIGHT OBSERVED WITH A SCANNING TUNNELING MICROSCOPE

We consider electron exchange between a metal tip and a metal electrode immersed in an aqueous solution. The tip and the substrate are modeled as jellium; the solution is treated on the Gouy-Chapman level. We construct an effective energy barrier for the tunneling electron by a superposition of its interaction with the two metals and an approximate solution of the nonlinear Poisson-Boltzmann equation. The rate of electron tunneling is calculated by solving the appropriate Schrodinger equation; the effective barrier height is then obtained by calculating the change of the tunneling current with distance.