薄膜之熱傳導係數量測方法研究

Abstract

本論文利用二維穩態熱傳模型之解析解，在考慮薄膜內熱流擴散的前提下，設計薄膜熱傳導係數之量測方法。試片配置為在矽基板上沉積待測介電材質(dielectric)薄膜，接著在薄膜上沉積金屬線以作為加熱與感溫線。 大部分的薄膜量測方法，在理論分析時皆忽略薄膜內橫向熱流擴散，此假設導致其無法適用於較大的膜厚(約微米等級)。本研究利用二維熱傳模型之溫度分佈解析解，探討擴散熱阻與橫向熱傳量和各項參數的關聯，並藉此設計有考慮薄膜內橫向擴散的熱傳導係數量測方法，以增加量測方法的適用範圍。 本論文研發有兩種不同的量測方法，一為雙線量測法，其在加熱線旁平行設置另一條金屬線用以量測溫度，以加熱線與感溫線溫差推算薄膜的熱傳導係數。此方法適用於膜厚10nm ~ 1um、熱傳導係數小於10 W/mK的薄膜，此參數範圍內本方法與理論解的誤差小於3.5%。另一量測方法為膜厚差異法，此法利用兩組膜厚不同、其他參數皆相同的試片，兩組試片各別量測加熱線溫度，以兩加熱線之溫差推算薄膜的熱傳導係數。此方法適用於膜厚10um ~ 1000um、熱傳導係數小於10 W/mK的薄膜，在此參數範圍本方法誤差在5%以內。

By using the exact solution of a 2-layer, 2-dimensional steady state heat transport model, methods of measuring thermal conductivity of thin film are developed, while considering heat spreading effects in thin film layer. These methods are used for testing samples of dielectric thin film deposit on silicon substrate, with metal lines served as heater/thermometer deposit on it. Most other measurements for thin film ignore effect of in-plane heat flow in the film area in their theories. This assumption will cause a large error when film thickness gets thicker, especially when it’s larger than micrometer. Base on the 2-dimensional exact solution, we discuss relations between spreading resistance and ratio of heat flux in film area and parameters of the model are made. From this, measurements with larger suitable range of film thickness are developed. Two different measurements will be introduced in this thesis. One is the parallel line method which set another metal line parallel to heater line for thermometer. Thermal conductivity of the film is calculated by temperature difference between the two lines.The error of this method is less than 3.5% in range of film thickness 10nm ~ 1 and thermal conductivity lower than 10 W/mK. Another measurement is the thickness difference method. This method needs two sets of samples which have different film thickness while all other parameters are the same. Thermal conductivity is calculated by the difference of heating line temperature on the two samples. The error of this method is less than 5% in range of film thickness 10 ~ 1000 and thermal conductivity lower than 10 W/mK.