由材料薄膜製成的的電子裝置，其薄膜與基材間的接觸或是元件與元件間薄膜的接觸都不是百分之百接觸的，也就是其微觀下真實接觸面積遠比我們在巨觀下所看到的視面積小。而其接觸面積不過是數個無規則分佈的接觸峰尖，所有的熱、電等傳遞都必須透過這些接觸峰，因此這些接觸點的分佈跟摩擦產生之熱傳遞是本研究探討的主題。
本文應用碎形理論(fractal theory)與非傅利葉(non-Fourier)熱傳導定律，探討次微米薄膜微觀接觸下其奈米摩擦熱傳導的問題。當薄膜薄到次微米甚至奈米的情況下，必須考慮熱載子(聲子)所具有的導熱性質。本文先討論由碎形理論所建構描述的表面形貌，並獲得由其理論參數所建構的真實接觸面積、最大接觸面積與總負載。接著由單一點微接觸其力學作用導致接觸面的變化進而推導摩擦所產生的熱傳導溫度分佈，再加進非傅利葉定律考慮聲子的效應，先得到單一微接觸點的溫度分佈解。之後加入碎形理論建立次微米整體薄膜表面形貌的分佈與接觸面積等參數，並結合這兩種理論推導出由這些真實接觸面積之接觸溫度，最後藉熱傳分析求得塊材之整體溫度上升量。
本論文之特色為求出了含有聲子傳熱波動效應的三維奈米溫度場，而且從分析的結果發現:(一)粗糙峰之平均溫度會隨著碎形維度 、粗糙度參數 與無因次分離距離的增加而上升。(二)薄膜鍍在塊材上其對整體塊材的溫度上升率幾乎不造成影響。(三)傅利業定律與非傅利業定律在摩擦產生熱的瞬間其溫度差異不大，其差別在微觀下熱傳遞的過程。微觀下，本身波傳遞速度較快的材料其傳熱速度較快。(四)造成各種材料溫度差異的還有材料本身的參數如熱擴散係數與熱傳導係數，而硬度與楊式模數對溫度的影響不大。

In this study, we apply fractal theory to characterize and model the roughness of surface. We also apply non-Fourier’s law to consider the heat transfer effect of heat carrier. The temperature model of the three-dimensional nano-heat transfer is established and the frictional temperature rises at the microcontacts of two sliding surfaces are analyzed by fractal surfaces and temperature model.

According to the analysis results, the average temperature rise of single asperity increase as fractal dimension, topothesy and non-dimensional separation distance increase. The difference of the Fourier’s law and non-Fourier’s law is not the temperature arising at the microcontacts, the difference of them is when heat transfer from top to bottom of the asperity. When the process of heat transport in very small distance or in very short time, heat will be transferred faster. The properties which effect temperature of material are thermal diffusivity and thermal conductivity. Temperature will increase as the ratio of thermal diffusivity and thermal conductivity increase. Other properties of material like hardness and Young’s modulus which has small influence of temperature.

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