Assessing the identifiability in isotope exchange depth profiling measurements

Accurate identification of the physical parameters describing the surface exchange kinetic coefficient k and oxygen diffusion coefficient D is key in solid state ionics, because the performance of many ionic devices is connected to such quantities. In this work we extend and generalize the concept of identifiability in Isotope Exchange Depth Profiling (IEDP), an important characterization tool in the ionics field, by exploring the measurability of k and D as a function of two dimensionless quantities, the Biot number, and the annealing time divided by the diffusional time scale. In addition, we show a novel approximate computation for the confidence intervals of the experimentally estimated k and D. In particular, if the measurement points are equally spaced, then the estimation error is inversely proportional to the number of measurement points and to the sensitivity of the experiment and directly proportional to measurement error.