Quantifying the subsurface damage and residual stress in ground silicon wafer using laser ultrasonic technology: A Bayesian approach

Abstract

Dispersion nature of surface acoustic waves (SAWs) propagating along the machined surface contains key information about the elastic properties and stress state of the subsurface damage (SSD) layer. This enables the acoustical characterization of SSD. In this paper, we develop a mechanical properties and residual stress estimation technology for the machined surfaces, especially for ground silicon wafer, based on laser-excited surface acoustic waves (LSAWs). Bayesian inversion is applied to quantify nine orthotropic elastic constants and one residual stress parameter of the SSD layer together with the corresponding uncertainty estimates from dispersion data. The forward model of SAW propagation is derived based on Biot’s theory of small deformations influenced by initial stress. The solution of the inverse problem is given in terms of the posterior probability density (PPD) of the SSD model parameters. Markov chain Monte Carlo (MCMC) method is used to generate posterior samples by repeatedly solving the forward model to compute parameter uncertainties and inter-relationships. Laser ultrasonic experiments have been performed on two typical areas of the ground silicon wafer to determine the ability of the technology to characterize SSD and residual stress and the effect of grinding direction on the damage degree of SSD. The elastic constant values estimated by the proposed method can be reasonably explained by the fracture properties of single-crystal silicon. The reliability of the results is further verified via nanoindentation and micro-Raman spectroscopy.