Efficient Heat Transfer Approximation for the Chip-on-Substrate Problem
Efficient Heat Transfer Approximation for the Chip-on-Substrate Problem
复制标题
基板上芯片问题的高效传热近似
DOI：
10.1115/1.2792163
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
K. Torrance
中科院分区：
文献类型：
--
作者：
T. Fisher;F. Zell;K. Sikka;K. Torrance
本文提出了一种基于解析的近似解，用于求解安装在导电基底上的轴对称热源的热阻，该热源具有基底的底部和顶部对流冷却。该近似值与底侧对流冷却的精确解以及顶侧和两侧冷却的参考有限元解在基底厚度（10−4≤ t* ≤ 10 - 4和10−2≤ t* ≤ 102）、基底外半径（1 ≤ B* ≤ 100）和对流Blot数（10- 4至102）的宽范围内紧密匹配。通过底侧冷却，热阻的最小值可以在宽范围的基板厚度上发生。对于许多微电子应用，与精确解或计算解相比，近似解具有简单性和易于计算性。
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* ≤ 104and 10−2≤ t* ≤ 102), substrate outer radius (1 ≤ b* ≤ 100) and convective Blot numbers (10-4to 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.