硅薄膜导热系数微尺度效应的临界尺寸

基于灰介质假设及拟合的色散关系,采用蒙特卡洛方法对微纳米硅薄膜内的声子热输运特性进行了模拟.将3μm厚的硅薄膜导热系数的计算结果与文献结果进行了对比,二者吻合较好.分析了厚度对薄膜内温度场及导热系数的影响.结果表明,当厚度小于某一尺度时,薄膜导热系数会随着厚度的减小而降低,呈现尺度效应;薄膜内温度场也不再是线性分布,而是在边界处呈现阶跃特性,且随着厚度减小,温度阶跃增大.基于该方法求得了100~400 K温度区间内,硅薄膜法向导热系数出现明显尺度效应的临界尺寸.计算发现,随着温度的升高,临界尺寸变化范围很大,平均温度为100 K时,临界尺寸约为50μm,平均温度为400 K时,临界尺寸约为2.5μm,前后相差了一个数量级.

Critical Size for Microscale Effect of Silicon Film Thermal Conductivity

Based on the gray media approximation and the fitted dispersion relation, the phonon heat transport in micro-nano silicon films was simulated with the Monte Carlo method. The predicted thermal conductivity （TC） of silicon film with 3 μm thickness was in good agreement with literature results. The effect of the thickness on the temperature field and cross-plane TC of the silicon films was analyzed. The results show that when the thickness is less than a certain scale, the TC of the film decreases with the de- crease in thickness, which exhibits scale effect; the temperature field is not in linear distribution, but shows discontinuous characteristics at the boundary, and as the thickness decreases, the temperature dis- continuity degree increases. The critical size at which TC begins to show obvious scale effect was obtained at the temperature range between 100 K and 400 K. Calculated results show that as the temperature in- creases, the critical size decreases sharply. When the average temperature is 100 K, the critical size is about 50 μm; when the average temperature is 400 K, the critical size is about 2.5 μm, which shows a difference of an order of magnitude.