Spatial confinement of percolation: Monte Carlo modeling and nanoscale laser polymerization

Abstract

Modern laser nanoprocessing technology employs the sharp, thresholdlike response of modified materials to laser exposure to create nanofeatures with sizes that are smaller than the diffraction limit. In this paper, the percolation transition is examined as a possible physical mechanism that allows such a nonlinear spatial confinement of the laser material alteration. In particular, the percolationlike transition is involved in laser polymerization techniques, including two-photon polymerization, which is capable of producing three-dimensional nanostructures with sizes of 100 nm and smaller. We perform Monte Carlo modeling of percolation with the spherically symmetric occupation probability distribution that is constrained in three dimensions. The dramatic increase in the fluctuations of the size and position of the largest connected cluster is observed when attempting to decrease its size below the critical scale. For laser polymerization, this provides the natural fluctuation-managed limitation of the minimal size of a nanofeature. We present a model that allows the analytical estimation of the critical size of the largest cluster. This analytical model fits well with the data obtained from the numerical experiments.