Research Papers

Modeling Simplification for Thermal Mechanical Analysis of High Density Chip-to-Substrate Connections

[+] Author and Article Information
Ping Nicole An

 Peking University, Institute of Microelectronics, No. 5, Yiheyuan Road Haidian District, Beijing 100871, P. R. China

Paul A. Kohl

 Georgia Institute of Technology, School of Chemical and Biomolecular Engineering, 311 Ferst Dr, Atlanta, GA 30332-0100 kohl@gatech.edu

J. Electron. Packag 133(4), 041004 (Dec 09, 2011) (7 pages) doi:10.1115/1.4005289 History: Received May 28, 2010; Revised August 24, 2011; Published December 09, 2011; Online December 09, 2011

Finite element modeling (FEM) is an important component in the design of reliable chip-to-substrate connections. However, FEM can quickly become complex as the number of input/output connections increases. Three-dimensional (3D) chip-substrate models are usually simplified where only portions of the chip-substrate structure is considered in order to conserve computer resources and time. Chip symmetry is often used to simplify the models from full-chip structures to quarter or octant models. Recently, an even simpler 3D model, general plane deformation (GPD) slice model, has been used to characterize the properties of the full-chip and local regions on the structures, such as in the structures for solder ball fatigue. In this study, the accuracy of the GPD model is examined by comparing the mechanical behavior of a flip-chip, copper pillar package from various full and partial chip models to that of the GDP model. In addition, it is shown that the GPD model can be further simplified to a half-GPD model by using the symmetry plane in the middle of the slice and choosing the proper boundary conditions. The number of nodes required for each model and the accuracy of the different FEM models are compared. Analysis of the maximum stress in the silicon chip shows that the full-chip model, quarter model, and octant model all convergence to the same result. However, the GPD and half-GPD models, with the previously used boundary conditions, converge to a different stress values from that of the full-chip models. The error in the GPD models for small, 36 I/O package was 4.7% compared to the more complete, full-chip FEM models. The displacement error in the GPD models was more than 50%, compared to the full-chip models, and increased with larger structures. The high displacement error of the GPD models was due to the ordinarily used boundary conditions which neglect the effect from adjacent I/O on the sidewall of the GPD slice. An optimization equation is proposed to account for the spatial variation in the stress on the GPD sidewall. The GPD displacement error was reduced from 50% to 3.3% for the 36 pillar array.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Specifications of a unit of I/O

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Figure 2

Models and relative boundary conditions (a) Total-chip model; (a’) Boundary conditions for the total-chip model; (b) Quarter model; (b’) Boundary conditions for the quarter model; (c) Octant model; (c’) Boundary conditions for the octant model; (d)GPD model; (d’) Boundary conditions for the GPD model; (e) Half-GPD model; and (e’) Boundary conditions for the half-GPD model

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Figure 3

The vector sum of displacement result of (a) the octant model; and (b) the half-GPD model (μm)

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Figure 4

The Von Mises stress contour plot of (a) the octant model; and (b) the half-GPD model (MPa)

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Figure 5

Element independence curves

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Figure 6

Schematic diagram of deformed half-GPD model under at high temperature



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