Numerical Simulation of Delayed Fracture by Surface Reaction in Material Structures of Small Feature Sizes

Princeton University, Princeton NJ

Investigators

Abstract

9988788 Prevost Many advanced devices, such as microprocessors and Micro-Electro-Mechanical-Systems (MEMS), are material structures of small feature sizes. Because these devices are part of all major engineering systems, an ability to predict their lifetime is of great importance to both the defense and the commercial industry. The smallness of the features poses a broad challenge to scientific computation. One pervasive problem is cracking in the small dimension, driven by the combined action of residual stresses and environmental molecules. Such cracking often occurs long after the devices have been made. No method has been developed to predict the delayed cracking in such devices. The main difficulties are readily understood in the context of the lifetime prediction method established for large engineering components. For a large component such as a ceramic tile on a reentry space vehicle, the lifetime prediction relies on the crack growth model. It assumes that cracks pre-exist in the ceramic tile, and grow under the combined action of stresses and environmental molecules. To predict the lifetime requires two experimental data: the initial crack size, and the crack growth law (i.e., the crack velocity as a function of the stress intensity factor). However, both are difficult to obtain for micro devices. Fabrication processes are controlled down to the feature sizes, so that the meaning of an initial crack is ambiguous, and in any case its size will never be measured experimentally on a routine basis. Moreover, the allowable crack velocity is so small (say 0.1 micron per year) that no experimental method exists to obtain the crack growth law. This proposal proposes to address these problems via numerical simulations. This program will develop a lifetime prediction method for micro devices. The method relies on a crack nucleation model. A device initially has no sharp cracks, although stress concentration sites, such as corners, are pervasive. A solid constituent, such as silicon dioxide, loses mass to its environment by chemical reaction on the surface. The rate of the reaction depends on the local stress. Because the stress field is nonuniform, the reaction proceeds faster at a corner root than elsewhere, gradually changing the root into a sharp crack. This model was envisioned in the 1960s, and has regenerated interest in recent years. A main difficulty in using the model has been computational. Existing work has been restricted to idealized geometries and materials. The proposed work will develop a finite element method to simulate the crack nucleation process in complex structures incorporating interface models formulated by Prof. Z. Suo. The work will focus on situations where a device spends its lifetime mainly on crack nucleation rather than subsequent crack growth. Preliminary work using 2D models shows considerable promise, and this work will be further extended and address the very difficult 3D problems. An interdisciplinary research team is assembled, integrating expertise in multiphysical processes, multiprocessor finite element implementation, and mesh adaptation for large shape change and intensifying stress field. The numerical effort will be coupled with ongoing experimental works by Professor A.G. Evans and a complementary NSF-funded experimental research effort by Professor W. Soboyejo both at Princeton University. These will provide test cases that will be used to validate our computational models. ***