Quantitative Analysis of the Synergy of Doping and Nanostructuring of Oxide Photocatalysts

In this paper, the effect of doping and nanostructuring on the electrostatic potential across the electrochemical interface between a transition metal oxide and a water electrolyte is investigated by means of the Poisson-Boltzmann model. For spherical nanoparticles and nanorods, compact expressions for the limiting potentials at which the space charge layer includes the whole semiconductor are reported. We provide a quantitative analysis of the distribution of the potential drop between the solid and the liquid and show that the relative importance changes with doping. It is usually assumed that high doping improves charge dynamics in the semiconductor but reduces the width of the space charge layer. However, nanostructuring counterbalances the latter negative effect; we show quantitatively that in highly doped nanoparticles the space charge layer can occupy a similar volume fraction as in low-doped microparticles. Moreover, as shown by some recent experiments, under conditions of high doping the electric fields in the Helmholtz layer can be as high as 100 mV/Å, comparable to electric fields inducing freezing in water. This work provides a systematic quantitative framework for understanding the effects of doping and nanostructuring on electrochemical interfaces, and suggests that it is necessary to better characterize the interface at the atomistic level.