Statistics of Critical Load in Arrays of Nanopillars on Nonrigid Substrates

Abstract

Multicomponent systems are commonly used in nano-scale technology. Specifically, arrays of nanopillars are encountered in electro-mechanical sense devices. Under a growing load weak pillars crush. When the load exceeds a certain critical value the system fails completely. In this work we explore distributions of such a critical load in overloaded arrays of nanopillars with identically distributed random strength-thresholds ($\sigma _{th}$). Applying a Fibre Bundle Model with so-called local load transfer we analyse how statistics of critical load are related to statistics of pillar-strength-thresholds. Based on extensive numerical experiments we show that when the $\sigma _{th}$ are distributed according to the Weibull distribution, with shape and scale parameters k, and $\lambda = 1$, respectively, then the critical load can be approximated by the same probability distribution. The corresponding, shape and scale, parameters K and $\varLambda$ are functions of k.