An analytical model of reactive diffusion for transient electronics

Transient electronics is a class of technology that involves components which physically disappear, in whole or in part, at prescribed rates and at programmed times. Enabled devices include medical monitors that fully resorb when implanted into the human body ("bio-resorbable") to avoid long-term adverse effects, or environmental monitors that dissolve when exposed to water ("eco-resorbable") to eliminate the need for collection and recovery. Analytical models for dissolution of the constituent materials represent important design tools for transient electronic systems that are configured to disappear in water or biofluids. Here, solutions for reactive-diffusion are presented in single- and double-layered structures, in which the remaining thicknesses and electrical resistances are obtained analytically. The dissolution time and rate are defined in terms of the reaction constants and diffusivities of the materials, the thicknesses of the layer, and other properties of materials and solution. These models agree well with the experiments for single layers of Mg and SiO₂, and double layers of Mg/MgO. The underlying physical constants extracted from analysis fall within a broad range previously reported in other studies; these constants can be extremely sensitive to the morphologies of the materials, temperature, and the PH value, concentration, and properties of the surrounding liquid.