Biased percolation and abrupt failure of electronic devices

Abstract

We propose a new percolation model as an aid to understand abrupt failure of electronic devices. It is called biased percolation because we assume that local Joule heating determines the probability of generating defects causing percolative breakdown of the device. We take as a simple geometry a homogeneous thin film, modelled as a two-dimensional resistor network. By carrying out Monte Carlo simulations we investigate the evolution of the system including: the damage pattern, current distribution, resistance degradation, resistance relative fluctuations and its power spectrum associated with 1/f noise. Our results show that biased percolation efficiently simulates degradation of thin films in good agreement with available experiments and predicts several features that should take place close to the abrupt failure of most devices.