Models of Ionic Transport for Silicon-Glass Anodic Bonding

Abstract

We solve numerically the coupled Poisson and transport equations for the motion of ions within the glass during anodic bonding in order to obtain the external current vs time curves and the charge density profiles within the sodium-depleted zone. We consider two simple models for the mobile ions. In both, the sodium cations are assumed to be the most mobile species. In one model the only additional mobile species are anions of the same initial concentration. They represent the compensating nonbridging oxygens. The only free parameter is the relative mobility of anions and cations. In the other model we assume the presence of additional cations and anions which could model the presence of dissociated water in a leached layer. The best agreement with experimental current vs time curves is obtained with the second model, but only if the initial concentration of dissociated water is close to the initial concentration of sodium in the glass. Redistribution of ions in the “leached layer” model is essential in lowering the local electric field within the bulk sodium-depleted zone. There are significant differences in the final charge density profiles obtained from both models, and the ones in the second one are more consistent with recent measurements in the literature.