Session: 17-01-01: Research Posters
Paper Number: 150028
150028 - A 3d Phase-Field Approach to Simulate Brittle Fracture of Single Crystal Silicon
Single crystal silicon (SCS) is extensively utilized in the design and manufacture of semiconductors due to its superior electronic properties. To enhance the understanding and prediction of its fracture behavior, a novel three-dimensional (3D) phase-field approach is proposed to simulate its brittle fracture. This research introduces a modified phase-field model that incorporates the anisotropic fracture toughness characteristic of SCS. Unlike isotropic materials, the critical energy release rate in SCS is direction-dependent, necessitating a sophisticated method to account for its anisotropic nature. The critical energy release rate is identified by determining the most probable cleavage direction, which corresponds to the principal direction of the maximum tensile principal component of the local strain tensor.
To implement this model, an iso-parametric monolithic finite element algorithm and corresponding computational codes were developed. These employ 4-node tetrahedral elements and 8-node hexahedral elements, enabling precise and efficient simulations. The accuracy of the finite element method was validated by benchmarking against analytical solutions for an SCS brick specimen subjected to uniaxial extension. The comparison showed excellent agreement, underscoring the reliability of the proposed model.
Further validation was performed through the simulation of brittle fracture in two different SCS structures: a micro-cantilever beam and a tapered double cantilever beam. For both cases, the simulation results demonstrated remarkable consistency with experimental data. Key metrics such as force versus deflection, compliance versus crack length, and the crack growth direction were closely matched, affirming the model's predictive capabilities.
This study presents a significant advancement in the simulation of brittle fracture in SCS, addressing the anisotropic properties in both elasticity and fracture toughness. The primary challenge of integrating the anisotropic fracture toughness into the phase-field simulation was effectively tackled through a modified phase-field formulation. This new approach allows for the accurate determination of the most probable cleavage direction and critical energy release rate, thus enabling precise predictions of crack initiation sites and growth directions. This is a notable improvement over existing models that define the critical cleavage plane as a plane normal to the phase-field gradient, an assumption that may lack physical justification.
The successful application of this model to the brittle fracture of SCS micro-cantilever and tapered double cantilever beams highlights its versatility and computational accuracy. The approach can be extended to other 3D fracture analyses of single-phase materials, making it a valuable tool for predicting fracture behaviors in a range of applications. This research opens avenues for further exploration into the fracture mechanics of anisotropic materials, potentially leading to more resilient and reliable semiconductor devices.
Presenting Author: Hamid Nayeb-Hashemi Northeastern University
Presenting Author Biography: Dr. Hashemi is a professor in Mechanical and Industrial department at Northeastern University for over 40 years.
He is an author of numerous technical papers.
Authors:
Yanhui Jiang School of Mechanical Engineering, Nanjing University of Science and TechnologyHamid Nayeb-Hashemi Northeastern University
Masoud Olia Wentworth Institute of Technology
A 3d Phase-Field Approach to Simulate Brittle Fracture of Single Crystal Silicon
Paper Type
Poster Presentation