Conductive Bump Stress Estimation Using Analytical Propagation Formula
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Solution Overview
Problem
Current methods for estimating stress in semiconductor packaging, such as finite element simulation, are computationally intensive and time-consuming, failing to rapidly assess the stress and lifetime of conductive bumps due to thermal and mechanical fatigue caused by mismatched coefficients of thermal expansion.
Innovation Solution
A method that calculates the stress of conductive bumps using a simplified formula σ2=LD-2rσ1, where σ2 is the stress value of secondary bumps, L is the distance, D is the average pitch, and r is the radius, allowing for rapid estimation of stress propagation and lifetime without complex simulations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If finite element simulation is used to calculate stress of conductive bumps, then measurement precision is improved, but loss of time increases
Solution Approach 1:
The patent creates a simplified mathematical model that copies the essential stress propagation behavior observed in finite element simulations. By establishing an analytical formula based on stress propagation theory, the invention reproduces the key characteristics of complex simulations without requiring computational resources, thus achieving comparable accuracy with dramatically reduced calculation time.
Solution Approach 2:
The patent transforms the complex multi-parameter finite element simulation into a simplified analytical solution by identifying and focusing on the dominant parameters (stress value of reference bump, distance, pitch, radius). This parameter simplification allows direct calculation using basic mathematical operations while maintaining sufficient precision for practical applications.
2Measurement precision
If finite element simulation is used to calculate stress of conductive bumps, then measurement precision is improved, but device complexity increases
Solution Approach 1:
The patent extracts the essential stress propagation mechanism from the complex finite element simulation framework. By isolating and modeling only the critical stress transmission path from the reference bump to surrounding bumps, the invention eliminates unnecessary computational complexity while retaining the core accuracy needed for stress assessment.
Solution Approach 2:
The patent replaces the numerical computation system (finite element analysis) with an analytical mathematical model. This substitution transforms a complex iterative computational process into a direct calculation using closed-form equations, significantly simplifying the calculation procedure while maintaining measurement precision.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables rapid calculation of stress values and lifetime of conductive bumps, effectively addressing the inefficiencies of existing methods by propagating stress values from a central bump to surrounding bumps, thereby improving the estimation process without the need for extensive computational resources.
Implementation Method 1
the stresses received by the conductive bumps gradually propagate toward and are accumulated at the surrounding second conductive bumps from the first conductive bump as the center
Implementation Method 2
coefficients of thermal expansion (CTEs) of bonding surfaces are different. Thermal fatigue failure, on the other hand, is caused by poor match of coefficients of thermal expansion between two surfaces
Data Source
AI summary
A method for estimating stress of an electronic component. An electronic component including first and second elements and conductive bumps is provided. Each conductive bump has two surfaces connected to the first and second elements respectively. Two adjacent conductive bumps have a pitch therebetween. The conductive bumps includes a first conductive bump and second conductive bumps. A stress value of the first conductive bump related to a testing parameter is calculated. A stress value of each second conductive bump related to the testing parameter is calculated according to a first calculating formula. The first calculating formula isσ2=LD-2rσ1,σ2 is the stress of each second conductive bump, L is a beeline distance between each second conductive bump and the first conductive bump, D is an average value of the pitches of the conductive bumps, r is a radius of each surface, and σ1 is the stress value of the first conductive bump.