應用熱波理論探討多層薄膜具界面熱阻效應之微觀熱傳現象

Abstract

在應用以多層薄膜組合為基礎元件的產業中，如：半導體產業、光學科技、及高溫超導體均在極端短的反應時間、極微小的尺寸、極端高的溫度或熱通量變化之條件下操作。由於物理尺寸及反應時間縮小到分別與熱載子平均自由路徑及平均自由時間同等級，使得以巨觀概念為基礎的傳統傅利葉熱傳模式的適用性受到侷限。本文以微觀概念應用非傳統傅利葉熱傳模式﹝熱波理論﹞探討雙層薄膜內的熱傳導問題。 當使用熱波理論分析熱傳導問題時發現，在短時間內熱是以波的型式傳遞，而時間漸長後則驅近於傅利葉定律的擴散效應。當熱波行進到不同薄膜材料之接觸面時，產生波的反射及穿透現象。反射波及穿透波的波型及強度取決於薄膜之間的材料性質比值及接觸面狀況。不可避免的，熱阻存在於薄膜交界面。本文以三種不同的熱阻模式，包括熱阻層模式、聲異理論模式、以及散異理論模式模擬薄膜與薄膜之間的界面熱阻。 當使用內熱阻層模擬界面熱阻時，由於波的型式亦產生於熱阻層內，而造成熱波在界面處的反射、穿透、重疊、消減之交互現象變得相當複雜。結果顯示由於內熱阻層的存在，造成原始波型改變，並且產生尾波於反射及穿透波之後。此種原始波型的改變及尾波的型態，類似於超流体實驗中的發現。另外，由於聲異理論模式、以及散異理論模式均具備輻射邊界條件。因此，當使用此兩種熱阻模式模擬界面熱阻時，特別討論不同的材料表面吸收深度不同所造成不同強度的溫度波對於系統內熱傳機制的影響。此外，本文中亦提供對應於兩層薄膜之間的材料性質比值、表面吸收深度、內熱阻層的厚度及材料性質，得以忽略界面熱阻效應的時機。 最後本文分析在應用釔鋇銅氧高溫超導薄膜配合四種常用基材之應用情況。結果顯示熱傳模式、界面熱阻、基材的材料性質、以及入射熱源時間對於高溫超導体的應用皆有相當程度的影響，據此以提供高溫超導薄膜選用基材的依據。

Heat transfer in the multi-layer thin films composite medium is a rapidly emerging area, which becomes more and more attractive in practical engineering problems. Examples include short-pulse or ultra-short pulse laser heating widely used in the electronic layers package, thermal stability of superconductors, annealing of semiconductors, measurement of thin-film properties, and surface heating and melting of metals. The heat conduction in these situations dealing with the microscale in length and time, extremely short time responses, extremely high rate change of temperature or flux. Therefore, the classical Fourier’s law which established on the macroscopic level, can not provide sufficient resolutions. This study investigates the heat transfer in the two-layered composite medium using the non-Fourier heat conduction equation (thermal wave model) which includes the time lag between heat flux and the temperature gradient. The thermal wave model predicts that the heat transfer in the medium is in wave behavior in short time scales which is significantly different with those predicted by the Fourier’s diffusion model. The differences between the Fourier’s model and thermal wave model diminish with increasing time. Reflection and transmission occur when the wave impacts the contact surface of the dissimilar material. The waves strength and feature depend on the two layers properties ratio and interface condition. Three models include interfacial layer model, acoustic mismatch model, and diffuse mismatch model are employed to predict the interface thermal resistance at the contact surface. When using the interfacial layer model to predict the interface resistance, the presentation of the wave nature in the interfacial layer deforms the initial wave feature and induces secondary wavelets behind the reflected and transmitted wave. Which are resembles that of the experimental observation in superfluid helium. In addition, due to the acoustic mismatch model, and diffuse mismatch model are in the same form as the radiation boundary condition, where the heat flow across the interface is proportional to the difference of the fourth power of the temperature on each side of the interface, the influence of absorption skin depth under a fixed incident energy is examined. The regime map for the perfect contact interface with related to the absorption skin depth, two layers properties ratios, interfacial layer thickness and properties are given. Finally, the heat transfer phenomenon for the applications of YBaCuO thin film high Tc superconductor is analysis. The results show the substrate properties, thermal boundary resistance between film and substrate, surface heat duration, and heat transfer model affect significantly the heat transfer mechanism. The results can be regarded as the design reference for the superconducting devices.