Research Papers

Analytical Thermal Solution to a Nonuniformly Powered Stack Package With Contact Resistance

[+] Author and Article Information
S. Ghalambor

e-mail: Saeed.ghalambor@mavs.uta.edu

A. Haji-Sheikh

Department of Mechanical and
Aerospace Engineering,
The University of Texas at Arlington,
Arlington, TX 76019-0018

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received June 30, 2012; final manuscript received March 28, 2013; published online September 23, 2013. Assoc. Editor: Sujoy Kumar Saha.

J. Heat Transfer 135(11), 111015 (Sep 23, 2013) (9 pages) Paper No: HT-12-1332; doi: 10.1115/1.4024623 History: Received June 30, 2012; Revised March 28, 2013

The semiconductor industry, following Moore's law, has consistently followed a trajectory of miniaturization that enables design engineers to achieve greater levels of innovation in the same or smaller die footprints. According to Samsung technologists, the next generation of semiconductor technology will cost about $10 billion to create. Alternatively, improved performance through lowering of signal delays can also be achieved using stacked or 3D packaging. With this architectural achievement come cooling challenges as it is difficult to utilize conventional cooling technology and especially when stacking logic and memory processors for high end applications. The accumulation of excessive heat within the stack is a challenge that has caused thermal engineers to focus on the issue of extracting this heat from the system. Thus, one important aspect of design is the ability to obtain an accurate analytical temperature solution of the multilayer stack packages beforehand in order to sustain the reliability of the 3D stack packages albeit for a more simplified configuration. This study addresses the analytical solution of temperature distribution in multilayer bodies by using the Mathematica code developed in this study. The numerical approach using ansys Workbench is discussed, and the results are compared with the one obtained analytically.

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Fig. 1

Schematic of a multilayer body

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Fig. 2

(a) The five-layer 3D stack and (b) the surface temperature as function of x and z

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Fig. 3

The computed temperature θj(a/2,0,c/2) = Tj(a/2,0,c/2)-T∞ for a five-layer body in example 1 and a comparison with θj*(a/2,0,c/2)/4

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Fig. 4

(a) The five-layer 3D stack and (b) the wattage of each volumetric source

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Fig. 5

(a) The mesh of the model and (b) the temperature contours

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Fig. 6

The total heat flux of the package

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Fig. 7

The analytically obtained temperature profile for the first layer

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Fig. 8

Comparison of the numerically and analytically derived temperature solutions

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Fig. 9

A five-layer stack of silicon material

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Fig. 10

The four functional units in each layer

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Fig. 11

The temperature contours of the stack package

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Fig. 12

The total heat flux of the package

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Fig. 13

The comparison between the analytically and numerically derived results

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Fig. 14

The analytically obtained temperature profile for the first layer



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