Dielectric breakdown in a thin oxide is presented in terms of an interacting particle system on a two-dimensional lattice. All edges in the system are initially assumed to be closed. An edge between two adjacent vertices will open according to an exponentially distributed random variable. Breakdown occurs at the time an open path connects the top layer of the lattice to the bottom layer. Using the extreme value theory, we show that the time until breakdown is asymptotically Weibull distributed.

中文翻译：

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一种稀薄氧化物分解分布的分析方法

薄氧化物中的介电击穿表示为二维晶格上的相互作用粒子系统。最初假定系统中的所有边都是闭合的。两个相邻顶点之间的边将根据指数分布的随机变量打开。击穿发生在开放路径将晶格的顶层连接到底层时。使用极值理论，我们证明了直到崩溃的时间是渐近 Weibull 分布的。