A Model for Assessing the Shape of Solder Joints in the Presence of PCB and Package Warpage

[+] Author and Article Information
Mahidhar Rayasam

School of Mechanical Engineering, Purdue University, West Lafayette, IN

Terrace B. Thompson

Department of Engineering Mechanics, USAF Academy, Colorado Springs, CO

Ganesh Subbarayan1

School of Mechanical Engineering, Purdue University, West Lafayette, IN

C. Gurumurthy2

IBM Corporation

J. R. Wilcox

IBM Corporation


Professor, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2088.


Currently at Intel Corporation.

J. Electron. Packag 128(3), 184-191 (Aug 27, 2005) (8 pages) doi:10.1115/1.2227058 History: Received August 30, 2004; Revised August 27, 2005

Our goals in this paper are to develop and demonstrate a computationally efficient methodology for assessing the effect of circuit board warpage, component warpage, and solder volume variation on the shape of the solder joints in area array packages. The effect of warpage is analyzed using a two-step procedure in the present paper. In the first step, the restoring forces and moments (in the molten state of solder droplet) that result from a given solder joint height, solder material volume, pad diameter, and pad inclination are predicted using the surface tension theory. In the second step of the analysis, the forces and moments at individual solder joints caused by varying solder heights and pad tilts are combined to predict the equilibrium configuration of the package. A program written in the MATHEMATICA® environment was developed to implement the above-described methodology. The developed procedure was validated on an experimental test vehicle with nine solder joints. The heights of solder joints computed by the program matched the experimentally measured heights to within ±5% error. Further, the general capabilities of the modeling procedure are demonstrated by assuming complex combinations of package and PCB warpage.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 2

Types of warpage

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Figure 3

Force and moment balance on the solder droplet

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Figure 4

Flow of control and data in the program

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Figure 1

Percentage change in restoring force with pad inclination for a fixed height of 0.458mm, volume of 0.368mm3, lower and upper pad radii of 0.443mm, surface tension coefficient of 350μN∕mm, and a density of 8.2242μKg∕mm3

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Figure 5

Schematic diagram of area-array test vehicle

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Figure 6

Schematic diagram of experimentally measured solder heights

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Figure 7

X-ray images of an area-array test vehicle

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Figure 8

Statistics of difference in restoring forces of solders in a symmetrically warped board and package

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Figure 9

Statistics of difference in restoring forces of solders in an unsymmetrically warped board and package



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