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.

中文翻译：

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厚封装层瞬态电子学的反应扩散分析模型

瞬态电子系统被设计为在预定时间后物理消失。此类系统对于环境可持续性和医疗应用具有重大前景。瞬态行为依赖于水扩散和器件组件水解反应之间的相互作用，封装层的厚度是控制器件寿命的关键参数。然而，已建立的反应扩散分析模型仅限于相对较薄的封装层。我们将分析模型扩展到厚封装层，以预测薄封装层和厚封装层的瞬态电子器件的寿命，从而拓宽了其适用性。此外，我们在无反应的厚封装层的限制下获得了瞬态电子的溶解时间和溶解厚度之间的比例定律。这种比例定律提供了一种计算不同设备配置的溶解时间的可靠方法。