在微觀尺度下，當系統的特徵尺寸與熱載子的平均自由路徑相近或小於時，熱的傳輸不是擴散傳輸而是彈道傳輸，使用巨觀傅立葉定律分析會高估其熱傳導係數，這時需使用聲子的輻射傳輸方程式來描述微尺度下的熱傳現象。 本文利用聲子波茲曼方程式(Boltzmann transport equation,BTE)來模擬奈米尺度非均質多孔矽薄膜之熱傳性質，內容探討不同孔隙率、孔洞大小、非均質孔洞排列方式與薄膜厚度對熱傳導係數的影響。數值模擬使用COMSOL Multiphysics多重物理量耦合模擬軟體。利用有限元素法並結合分離座標法(discrete ordinate method,DOM)求解波茲曼傳輸方程式。模擬結果發現，在高孔隙率與小孔徑孔洞下，表面積與體積比(surface to volume ratio)高，增加聲子與孔洞界面散射的比例能有效降地熱傳導係數。薄膜在相同厚度與孔洞數時，總溫降是相同的，但薄膜內孔徑的大小與擺放位置會影響其中的溫度分佈，不同孔徑孔洞的排列順序會改變熱通量大小與限制其傳輸路徑而造成熱傳導係數的改變，本文透由計算不同孔徑孔洞間的界面熱阻並利用熱組串聯方式來預測其熱阻值。 As the characteristic length of a system become comparable to or smaller than the mean free path of heat carriers, the energy transport behaviors become ballistic rather than diffusive. In this case, it will overestimate the thermal conductivity of the matter by using Fourier law. The phonon radiative transfer equation can be a better way to describe the microscale heat transfer. In this study, the thermal property of inhomogeneous porous thin films are considered. The effects of porosity, pore size, thickness of the thin film, and inhomogeneous arrangements on the thermal conductivity are discussed by Boltzmann transport equation (BTE).We use the COMSOL Multiphysics software as the numerical tool to solve the BTE combined with angular discretization by the discrete ordinate method. The results shows that at high porosity and small pore size, increasing the phonon-pore’s interface scatterings can effectively decrease the thermal conductivity due to the high surface-to-volume ratio. In the case of the same film thickness and same pore number, the total temperature drops of diffenrent samples are the same, however, the temperature distribution are different for different the pore arrangements. The higher temperature gradient happens at the vicinities of the smaller pores. It is the reason for the changes of apparent thermal conductivity. The equivalent themal resistance model is also used to interpret the thermal resistance change at different inhomogeneous cases.
