Application of the Kirchhoff Transform to Thermal Spreading Problems With Convection Boundary Conditions
Application of the Kirchhoff Transform to Thermal Spreading Problems With Convection Boundary Conditions
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DOI：
10.1109/tcpmt.2013.2292584
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发表时间：
2014-03
期刊：
影响因子：
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通讯作者：
K. Bagnall;Y. Muzychka;E. Wang
中科院分区：
文献类型：
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作者：
K. Bagnall;Y. Muzychka;E. Wang
微电子器件和封装的热管理和热分析对于确保当今电子系统的性能、可靠性和寿命至关重要。当半导体或封装材料的热导率强烈依赖于温度时，使用恒定的热导率值可能会大大低估温升和热阻。基尔霍夫变换提供了一种将热传导方程线性化的方便方法，以使用计算上有效的解析解来计算器件或封装温度。在过去，基尔霍夫变换的应用一直局限于温度和热流边界条件的热扩散问题。在本文中，我们开发了一个近似的解决方案的应用基尔霍夫变换的热扩散问题，在汇平面对流，并显示该技术是准确的设备级热分析的相关问题在1%以内。所提出的技术相结合，最近开发的复杂的多层结构，其中需要考虑在散热器平面的有限传热系数的温度上升的解析解。这些解析表达式和基尔霍夫变换是精确预测高功率宽带隙电子器件（如氮化镓功率放大器）温度的宝贵工具。
Thermal management and thermal analysis of microelectronic devices and packages are critical in ensuring the performance, reliability, and lifetime of today's electronic systems. When the thermal conductivity of a semiconductor or packaging material depends strongly on temperature, the use of a constant thermal conductivity value may significantly underestimate the temperature rise and thermal resistance. The Kirchhoff transform provides a convenient way of linearizing the heat conduction equation to use computationally efficient analytical solutions to calculate the device or package temperature. In the past, the application of the Kirchhoff transform has been restricted to temperature and heat flux boundary conditions in thermal spreading problems. In this paper, we developed an approximate solution for the application of the Kirchhoff transform to thermal spreading problems with convection in the sink plane and show the technique to be accurate to within 1% for relevant problems in device-level thermal analysis. The proposed technique is combined with a recently developed analytical solution for temperature rise in complex, multilayered structures in which a finite heat transfer coefficient in the sink plane needs to be considered. These analytical expressions and the Kirchhoff transform are valuable tools for accurately predicting the temperature in high-power, wide bandgap electronics, such as gallium nitride power amplifiers.