An analytical model of reactive diffusion for transient electronics with thick encapsulation layer

Transient electronic systems are engineered to physically disappear after a predetermined period. Such systems hold significant promise for environmental sustainability and medical applications. The transient behavior relies on the interplay between water diffusion and the hydrolysis reaction of the device components, with the thickness of the encapsulation layer serving as a crucial parameter for controlling the lifetime of the device. The established analytical model for reactive diffusion, however, is limited to relatively thin encapsulation layers. We extend the analytical model to thick encapsulation layers in order to predict transient electronics' lifetimes for both thin and thick encapsulation layers, broadening its applicability. Furthermore, we obtain a scaling law between the dissolution time and the dissolved thickness of transient electronics for the limit of a thick encapsulation layer with no reaction. This scaling law offers a robust way for calculating the dissolution time across different device configurations.