Modeling ion exchange in glass with concentration‐dependent diffusion coefficients and mobilities

Abstract

Multimode buried waveguides made in silicate glass by field- assisted ion exchange present very asymmetric profiles. We show how this phenomenon originates in the large dependence of the kinetics on the local ion concentrations. For this purpose, we derive an interdiffusion equation that includes the effects of concentration-dependent diffusion coefficients and mobilities. We show how to deduce this dependence from measurements on ion-diffused samples. The maximum concentra- tion of the incoming ions is computed from surface equilibrium conditions and is used in the interdiffusion equation as a limiting parameter for coefficient variations. To control the model accuracy for surface as well as buried waveguides, we measure ion profiles with three independent methods: M-lines, scanning electron microscopy, and near-field refrac- tometry. When applied to Ag 1 -Na 1 exchange in silicate glass, the model yields theoretical estimations in good agreement with experiments. This approach underlines the fundamentally nonlinear process that takes place during ion exchange and is also valuable to properly model single- mode waveguide fabrication. © 1996 Society of Photo-Optical Instru- mentation Engineers. Subject terms: ion exchange; Boltzmann method; concentration-dependent diffu- sion coefficients; waveguides; surface ionic equilibrium.