Comprehensive Modeling of Ion Conduction of Nanosized CaF2/BaF2 Multilayer Heterostructures

Molecular beam epitaxy-grown CaF2/BaF2 heterolayers are a demonstration of the potential of nanoionics. It has been shown that ion conductivities both parallel and perpendicular to the interfaces increase with decrease in interfacial spacing. This size effect was attributed to the thermodynamically necessary redistribution of the mobile fluoride ions (N. Sata, K. Eberl, K. Eberman, J. Maier, Nature 2000, 408, 946; X. X. Guo, I. Matei, J.-S. Lee, J. Maier, Appl. Phys. Lett. 2007, 91, 103102). On this basis, the striking phenomenon of an upward bending in the effective parallel conductivity as a function of inverse interfacial spacing sigma(parallel to)(m)(1/l) for low temperatures (T <= 593 K) has been satisfactorily explained by application of a modified Mott-Schottky model for BaF2 (X.X. Guo, I. Matei, J. Jamnik, J.-S. Lee, J. Maier, Phys. Rev. 8 2007, 76, 125429). This model was further confirmed by measurements perpendicular to the interfaces that offer complementary information on the more resistive parts. Here a successful comprehensive modeling of parallel and perpendicular conductivities for the whole parameter range, namely for interfacial spacings ranging from 6 to 200 nm and investigated temperatures ranging from 455 to 833 K is, presented. The model is based on literature data for carrier mobilities and Frenkel reaction constants and the assumption of a pronounced F- redistribution. Given the fact that an impurity content that was experimentally supported is taken into account and apart from minor assumptions profile homogeneity, the only fit parameter is the space charge potential. In particular, it is worth mentioning that in BaF2 the low temperature Mott-Schottky space charge zone which is determined by impurities changes over, at high temperatures, into a Gouy-Chapman situation owing to increased thermal disorder. (The situation in CaF2 is of Gouy-Chapman type at all temperatures.)