An Analytical Thermal Buckling Model for Semiconductor Chips on a Substrate.
Guangping Gong1, Dian Xu1, Sijun Xiong1
1State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, International Research Center for Computational Mechanics, Dalian University of Technology, Dalian 116024, China.
Micromachines
|November 25, 2023
Summary
This study introduces a new analytical model for thermal buckling in semiconductor chips, offering accurate predictions for critical buckling temperatures and mode shapes. The developed method enhances safety designs for electronic devices facing temperature fluctuations.
Area of Science:
- Mechanical Engineering
- Materials Science
- Solid Mechanics
Background:
- Semiconductor chips are vital in electronic devices but susceptible to mechanical buckling due to environmental temperature changes.
- Existing analytical models lack the efficiency and accuracy needed for robust safety designs.
Purpose of the Study:
- To develop an efficient and accurate analytical model for thermal buckling of semiconductor chips on a substrate.
- To investigate the effects of elastic foundation moduli and geometric parameters on buckling behavior.
Main Methods:
- The study employs the Symplectic Superposition Method (SSM) within a symplectic space-based Hamiltonian system.
- The problem is divided into two subproblems solved using separation of variables and symplectic eigenvector expansion.
- This approach avoids assumptions on solution forms, differentiating it from traditional methods.
Main Results:
- Analytical solutions for thermal buckling temperatures and mode shapes were obtained using SSM.
- Results were validated against the finite element method, showing good agreement.
- The influence of elastic foundation moduli and geometric parameters on critical buckling temperatures and mode shapes was analyzed.
Conclusions:
- The SSM provides an effective and accurate method for analyzing the thermal buckling of chips on elastic foundations.
- The findings contribute to improved safety designs for electronic devices subjected to thermal stress.
