Numerical calculations of space charge layer effects in nanocrystalline ceria. Part I: comparison with the analytical models and derivation of improved analytical solutions

Abstract

Using numerical solutions of the Poisson-equation, one dimensional space charge layer (SCL) concentration profiles in CeO₂ are calculated. The SCL conductivity effects of nanocrystalline CeO₂ are analyzed as a function of doping content (donor doped, pure and acceptor doped ceria) and SCL potential including not only the standard Gouy–Chapman and Mott–Schottky cases, but also the more complex mixed situations. The results of the numerical approach are compared with the usual analytical approximations. While for the ideal Gouy–Chapman and Mott–Schottky cases for moderate and high potentials the agreement between analytical and numerical solutions is found to be satisfactory, mixed cases and low potential situations cannot be reliably treated by using the standard analytical approaches. Finally, inspired from the numerical solutions, improved analytical equations are proposed which are found to generally yield much more precise results and are accurate even for the mixed situations and low potentials.