Model of the erbium ion exchange process in lithium niobate crystals

A model based on the Nernst-Planck equations is discussed for the trivalent ion exchange process in lithium niobate crystals. Due to the material anisotropy and the different valence state of the exchanged species, a correction to the ion flux expression is considered to include the strain effects. The model is then used to describe the erbium ion exchange in both X- and Z-cut lithium niobate crystals. In this case, the dopant in-depth profiles measured by secondary ion mass spectrometry are well fitted by the theoretical profiles predicted by the model, supporting its validity. Since the model allows to predict the dopant profile into the substrate, it can be used to tailor the process parameters.