Efficient Heat Transfer Approximation for the Chip-on-Substrate Problem

[+] Author and Article Information
Timothy S. Fisher, Kamal K. Sikka, Kenneth E. Torrance

Sibley School of Mechanical and Aerospace Engineering, Upson Hall, Cornell University, Ithaca, NY 14853

F. A. Zell

The Carborundum Company Microelectronics Division, 10409 South 50th Place, Phoenix, AZ 85044

J. Electron. Packag 118(4), 271-279 (Dec 01, 1996) (9 pages) doi:10.1115/1.2792163 History: Received November 19, 1994; Revised April 26, 1995; Online December 05, 2007


An analytically based approximate solution is presented for the thermal resistance of an axisymmetric heat source mounted on a conductive substrate with bottom- and top-side convective cooling of the substrate. The approximation closely matches an exact solution for bottom-side convective cooling and reference finite element solutions for top-side and both-side cooling over broad ranges of substrate thickness (10−4 ≤ t* ≤ 104 and 10−2 ≤ t* ≤ 102 ), substrate outer radius (1 ≤ b* ≤ 100) and convective Blot numbers (10-4 to 102 ). With bottom-side cooling, a minimum in the thermal resistance can occur over a wide range of substrate thicknesses. The approximate solution possesses simplicity and ease of computation as compared to exact or computational solutions for many microelectronic applications.

Copyright © 1996 by The American Society of Mechanical Engineers
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