An Efficient Numerical Homogenization Method for Multi-Scale Modeling of 2.5D Package Warpage and Thermal Analysis

Area of Science:

• Materials Science and Engineering
• Computational Mechanics
• Semiconductor Device Physics

Background:

• 2.5D packages require high interconnect density using microscale features like through-silicon vias (TSVs), microbumps, and redistribution layers (RDLs).
• The significant scale difference between microscale features and larger package components creates multi-scale challenges for traditional analysis methods.
• Finite Element Analysis (FEA) faces computational limitations and convergence issues in analyzing these complex, dense 2.5D packages.

Purpose of the Study:

• To develop an efficient numerical homogenization method for the mechanical and thermal analysis of 2.5D packages.
• To accurately determine equivalent material properties for complex multi-scale microstructures within 2.5D packages.
• To enhance the computational efficiency and accuracy of 2.5D package design and analysis.

Main Methods:

• Implementation of a numerical homogenization method using periodic boundary conditions (PBCs) and referential statistical volume elements (rSVEs).
• Treatment of microstructures (TSVs, microbumps, RDLs) as a homogeneous medium to evaluate equivalent material properties.
• Calculation of stiffness matrices, coefficients of thermal expansion, and thermal conductivity for the homogenized material.

Main Results:

• The proposed method ensures continuity of displacement, stress, strain, and heat flux across rSVE surfaces.
• Accurate determination of equivalent material properties for complex multi-scale structures, validated against experimental data and existing techniques.
• Significant improvement in computational efficiency compared to traditional methods without geometric restrictions.

Conclusions:

• The numerical homogenization method provides an accurate and computationally efficient solution for mechanical and thermal analyses of 2.5D packages.
• The method is successfully applied to wafer warpage and thermal analyses, demonstrating its practical utility.
• This approach establishes a robust foundation for the development and analysis of next-generation 2.5D semiconductor packaging.