Heat Conduction in Printed Circuit Boards: A Mesoscale Modeling Approach

[+] Author and Article Information
Wataru Nakayama

 ThermTech International, 920-7 Higashi Kosio, Oh-Iso, Kanagawa 255-0004, Japanwatnakayama@aol.com

J. Electron. Packag 130(4), 041106 (Nov 14, 2008) (10 pages) doi:10.1115/1.2993126 History: Revised June 03, 2008; Received September 18, 2008; Published November 14, 2008

An analytical model is developed to estimate the heat transfer performance of printed circuit board (PCBs). The PCB under study is the substrate for a ball-grid-array (BGA) package. Under the BGA, the PCB has a belt of densely populated through-vias that penetrate the laminate of horizontal copper and resin; outside the BGA-covered area the board is a copper/resin laminate and its surfaces are exposed to cooling air. Calculations are performed on a sample board having the dimensions 11×11cm2(footprint)×1.26mm (thickness). The model of the board has two internal layers of continuous copper (0.03 mm thick) and through-vias under a 4.4×4.4cm2 BGA package. The impacts of board design parameters on the temperature and the heat flow are presented; the parameters are the width of the insulation gap around the via, the area of copper coverage at the via bottom, and the population of vias.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

A PCB under study; A air-cooled area, B and C under BGA package, and B via array zone

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Figure 2

Cross section of via zone B

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Figure 3

Cross section of zone A

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Figure 4

Heat flows from the vias to the plates and the boundary condition assumed on the PCB surface

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Figure 5

Network of heat conduction paths around the via

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Figure 6

Effect of insulation gap width on temperatures

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Figure 7

Effect of Biot number on heat flow distributions (B=B1=B2)

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Figure 8

Effect of copper area coverage at the PCB bottom on temperatures (hAU=5 W/m2 K, hL=40 W/m2 K)

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Figure 9

Effect of via count on temperatures (total heat input fixed at 4 W)

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Figure 10

Zone of analysis around via element

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Figure 11

(a) Resin element connecting the hole plating and the copper plate; (b) numerically computed isotherms



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