Modeling and simulation of phase transformation and crack formation during scribing of mono-crystalline silicon

This paper presents a simple two-parameter constitutive model to describe the material deformation behavior during scribing of mono-crystalline silicon (Si) - a process characterized by phase transformation and crack formation. The effect of phase transformation and volume densification of diamond-cubic Si (Si-I) to metallic Si (beta-Si) during the loading stage is described by a modified Drucker-Prager yield surface. During the unloading stage, beta-Si is completely transformed to amorphous Si (a-Si) due to the high unloading rate. The volume expansion accompanying the amorphization is described by a newly defined yield surface. The initiation and propagation of cracks are modeled using the extended finite element method (XFEM). The two constitutive model parameters, namely the cohesion parameter d and the initial yield stress p(s), are calibrated using data from nano-indentation tests. The model is shown to be capable of predicting the load-displacement curve during nano-indentation of Si, including the elbow feature experimentally observed during the unloading stage. The material model is then used in a finite element model of scribing of mono-Si, and shown to successfully predict the residual depth of the scribed groove as well as the crack formation observed at the ductile-brittle transition point.