Modeling of ion migration depth in field-assisted ion-migration

A model for calculation of time dependence of ion migration depth in glass substrate in the process of field-assisted ion-migration (FAIM) was presented, in which glass wafer temperature rise induced by Joule heating effect was taken into consideration. In this model, glass wafer temperature rise behavior was firstly obtained by solving its thermal balance equation; after that, time dependence of electric current density, and in turn charge flux density flowing through glass wafer was calculated; finally, ion migration depth was calculated by utilizing its universally linear dependence on charge flux density. It can be observed that there exists a reasonable agreement between simulated data and experimental results in the respect of ion migration depth, for experimental conditions conventionally applied for glass-based integrated optical device fabrication. Analysis shows that this model possess wider adaptability than the conventional model in the respect of ion migration depth calculation, due to its involving of glass wafer temperature rise effect induced by Joule heating.