Abstract

The rapid development of electronics is leading to the creation and use of small electronic components, including nanoelements of a complex layered structure. The search for effective methods for cooling electronic systems dictates the need for the development of methods for the numerical analysis of heat transfer in nanostructures. A characteristic feature of the energy transfer in such systems is the dominant role of contact thermal resistance at interlayer interfaces. Since the contact resistance depends on a number of factors associated with the manufacturing technology of heterostructures, it is of great importance to determine the corresponding coefficients from the results of temperature measurements. The purpose of this paper is to evaluate the possibility of reconstructing the thermal resistance coefficients at the interfaces between layers by solving the inverse problem of heat transfer. The complex of algorithms includes two major blocks: a block for solving the direct heat transfer problem in a layered nanostructure and an optimization block for solving the inverse problem. The direct problem is formulated in an algebraic (finite difference) form under the assumption of a constant temperature within each layer due to their small thickness. The inverse problem is solved in the extreme formulation and optimized using zero-order methods that do not require calculating the derivatives of the optimized function. As a basic optimization algorithm, the Nelder–Mead method is used in combination with random restarts to search for the global minimum. The results of identifying the contact thermal resistance coefficients obtained in the context of a quasi-real experiment are presented. The accuracy of the solution of the identification problem is estimated as a function of the number of layers in the heterostructure and the measurement error. The results are planned to be used in the new technique of multiscale modeling of thermal regimes of the electronic component base of the microwave range, when identifying the thermal conductivity coefficients of the heterostructure.

中文翻译：

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层状纳米结构中传热的反系数问题

摘要

电子技术的飞速发展正导致创建和使用小型电子组件，包括复杂的分层结构的纳米元素。对用于冷却电子系统的有效方法的探索表明需要开发用于对纳米结构中的热传递进行数值分析的方法。在这样的系统中，能量传递的特征是层间界面处接触热阻的主要作用。由于接触电阻取决于与异质结构的制造技术相关的许多因素，因此从温度测量结果确定相应的系数非常重要。本文的目的是通过解决传热问题来评估重建层间界面热阻系数的可能性。算法的复杂性包括两个主要模块：一个用于解决层状纳米结构中直接传热问题的模块和一个用于解决逆问题的优化模块。由于每一层的厚度较小，因此在假设每一层内温度恒定的情况下，直接问题以代数形式（有限差分）表示。反问题可以通过极端公式解决，并且可以使用零阶方法进行优化，而无需计算优化函数的导数。作为基本的优化算法，Nelder–Mead方法与随机重新启动结合使用以搜索全局最小值。给出了在准真实实验的背景下获得的确定接触热阻系数的结果。根据异质结构中的层数和测量误差估计识别问题的解决方案的准确性。当确定异质结构的热导率系数时，该结果计划用于多尺度建模微波范围电子元件基座热态的新技术。根据异质结构中的层数和测量误差估计识别问题的解决方案的准确性。当确定异质结构的热导率系数时，该结果计划用于多尺度建模微波范围电子元件基座热态的新技术。根据异质结构中的层数和测量误差估计识别问题的解决方案的准确性。当确定异质结构的热导率系数时，该结果计划用于多尺度建模微波范围电子元件基座热态的新技术。