微系統之熱物理特性及性質之精密估測

Abstract

摘 要 本文探討微系統的熱物理特徵及物理參數的精密量測，對於微尺寸系統，我們考慮介電材料微管內徑向熱傳導，運用聲子輻射傳遞方程式配合節點近似法來解得微管內熱傳導，並計算其等效熱傳導係數，結果顯示，微管內能量分佈決定於外壁激發的聲子能量，因此，微管外壁溫度影響其內部溫度分佈甚鉅。除了微管管壁厚度 R2 - R1 外，微管的曲率也是影響熱通量及等效熱傳導係數的重要參數，透過一簡單的關係式，等效熱傳導係數可寫成管壁厚度以及曲率的函數。 對於微時間系統，本文進行雷射脈衝加工金屬薄膜過程中，金屬熱傳導係數以及電子-聲子連結因子 ( the electron-phonon coupling factor ) 的逆運算量測分析，對敏感係數的理論分析顯示，用於逆運算的電子溫度最佳量測點應選取：在雷射脈衝加熱表面選取溫度到達最高值後的電子溫度；在雷射脈衝加熱背面則應選取整個未平衡時間的電子溫度變化。文中並透過統計理論分析逆運算模式的準確度，並運用文獻中對金薄膜受雷射脈衝加熱的實驗結果，進行金薄膜的熱傳導係數以及電子-聲子連結因子之估算，結果顯示熱傳導係數與電子-聲子連結因子兩者皆與金薄膜厚度有關。 在探討微系統之熱物理特性時，系統的熱物理性質影響相當大，熱卡計法 ( ac calorimetric method ) 具有量測沿薄膜平面以及垂直薄膜平面熱擴散係數之潛能。本文針對以雷射加熱之熱卡計法量測熱擴散係數分量時，材料不等向性 ( anisotropy ) 以及透光度 ( transparency ) 的影響。結果顯示在量測沿薄膜平面方向熱擴散係數時，二維溫度分佈影響的區域隨著材料的熱擴散係數分量比值 κ ( = Dy /Dx ) 減小而增大；同時，此二維溫度分佈影響的區域隨材料的光學厚度減小而縮小。在量測垂直薄膜平面方向的熱擴散係數時，當材料的光學厚度薄時，文獻中用以決定熱擴散係數的直線關係將不復存在；當材料的光學厚度大時，只要量測點在加熱區下，材料不等向性以及二維溫度分佈效應將不影響垂直薄膜平面的熱擴散係數的量測值。

ABSTRACT This thesis studies both microlength and microtime effects on the thermophysical characteristics. To investigate the microlength scale effect, the radial heat conduction in the tube wall of dielectric thin tubes is studied in this work. An equation of phonon radiative transfer (EPRT) is used in association with nodal approximation technique for examining the heat transport in thin tubes. The effective thermal conductivity of thin tubes is calculated based on the heat flux in the middle surface of the tubes. Results indicate that the energy distribution in the annulus is dominated by phonons excited by outer surface. Consequently, the temperature distribution is considerably affected by the temperature of outer surface. In addition to tube wall thickness, R2-R1, which was usually considered as the size effect on heat conduction, the curvature effect would significantly change the heat flux across the tube wall and consequently affect the effective thermal conductivity. A correlation for the effective thermal conductivity of thin tubes as a function of wall thickness and curvature is also derived. While focusing on the microtime scale effect , an inverse analysis is performed for simultaneous estimation of both thermal conductivity and the electron-phonon coupling factor of thin metal films during nonequilibrium laser heating of metals. Theoretical analyses on the sensitivity coefficients illustrate that optimal choices of measurements would include temperature variations at the front surface over the time interval after the electron temperature reaches its maximum, combined with measurements of temperature variations at the rear surface for the whole thermalization time. Statistical analyses are performed to depict the accuracy of the inverse schemes. Experimental data taken from the literature are used to estimate thermal conductivity and the electron-phonon coupling factor for the gold film. Results show that both thermal conductivity and the electron-phonon coupling factor are size dependent. To analysis the thermal characteristics of the microscale system, an accurate knowledge of their thermophysical properties are required. The ac calorimetric method has great potential in measuring thermal diffusivity in both in-plane and cross-plane directions. An analysis is also presented for examining the effects of anisotropy and transparency on measurements of thermal diffusivity components with ac calorimetric method associated with laser heating. Numerical results show that in the determination of in-plane thermal diffusivity the region where the two-dimensional effect occurs increases with the ratio of two thermal diffusivity components, ( =Dy/Dx) decreased. Besides, this region decreases with the optical depth of the sample. As in the measurement of cross-plane thermal diffusivity, it is shown that linear relations indicating constant slope of phase versus square root of frequency from which thermal diffusivity is deduced can not be obtained when both optically moderate and thin media are considered. Provided that the optical depth is sufficiently large, anisotropic and two-dimensional effects on the determination of cross-plane thermal diffusivity are found insignificant when the detector is located within the heating beam.