介電薄膜在MEMS元件設計中的應用層面非常廣泛，因此介電薄膜的熱物理特性對於產品的性能預估與設計分析十分重要，而在熱物理特性當中，熱傳導性質占了很重要的一環。然而由於尺寸效應的影響，當薄膜材料熱傳導係數值會與塊材有所不同，因此必須要利用適合此種薄膜特性之量測實驗架構，將薄膜材料之熱傳導係數值求取出來。本實驗使用3ω量測方法針對不同製程下的二氧化矽薄膜來進行量測，並結合真空低溫系統對其進行低溫的量測，量測溫度的範圍為(83K~293K)，經由實驗結果發現，由於Thermal oxide薄膜孔洞率較低的緣故，其熱傳導係數在相同條件下比PECVD oxide還低。除此之外，進行在不同溫度下，對於二氧化矽薄膜其熱傳導係數是否會造成影響?結果發現熱傳導係數會隨著溫度降低而降低，這是因為溫度越低，導致尺寸效應也就會越明顯，最後將所得到的量測數據透過計算，可以得出邊界熱阻和薄膜本質熱傳導係數的數值。經由結果發現，3ω 量測方法結合真空低溫系統，不但可以精確量測二氧化矽薄膜的熱傳導係數，也能針對在不同溫度下對於熱傳導係數是否會造成影響，未來將可以拓展其應用層面對於其他的介電薄膜進行量測。

Heat transport in 30–300 nm thick dielectric films is characterized in the temperature range of 74–300 K using the 3ω method, which is a simple method to measure the cross-plane thermal conductivity of dielectric thin films. Dielectric film samples of two kinds, deposited on Si substrates using plasma enhanced chemical vapor deposition (PECVD) and grown by thermal oxidation, were measured in the cryogenics system. The apparent thermal conductivity, intrinsic thermal conductivity, and interface resistance have been analyzed in different environment temperature. The measured data with this method were verified with the measurement results from published data, which showed satisfactory agreement.
For this experiment, we discovered the thermal conductivity of PECVD SiO2 films was smaller than the conductivity of SiO2 grown by thermal oxidation, because the porosity of thermal SiO2 is smaller than PECVD SiO2. The apparent thermal conductivity of SiO2 films decreases with film thickness. The thickness dependent thermal conductivity is interpreted in terms of a small interface thermal resistance RI. For SiO2 films, the thermal conductivity decreases if the temperature decreases, because the mean free path of heater carriers increases.
3ω method combined with the cryogenics system could not only measure the thermal conductivity of SiO2 accurately, but also treat the influence of thermal conductivity on different temperature environment. In the future, we could broaden the use of this combination to measure other thin films.

[1]D.G.Cahill, "Thermometry and thermal transport in micro/nanoscale solid-state devices and structures". Journal of Heat Transfer, 2002. 124(2): p. 223~241.
[2]劉靜, "微米奈米尺度傳熱學". 2004: 五南出版社. 271~273.
[3]D.G.Cahill, "Heat transport in dielectric thin films and at solid-solid interfaces". Microscale Thermophysical Engineering, 1997. 1: p. 85~109.
[4]N.Taketoshi, T.Baba, and A.Ono, "Development of a thermal diffusivity measurement system for metal thin films using a picosecond thermoreflectance technique". Meas. Sci. Technol, 2001. 12(10): p. 2064~2073.
[5]D.McConnell and K.E.Goodson, "Thermal conductivity of doped polysilicon layers". Journal of Microelectromechanical systems, 2001. 10(3): p. 360~369.
[6]K.Kurabayashi, "Measurement of the thermal conductivity anisotropy in polyimide films". Journal of Microelectromechanical systems, 1999. 8(2): p. 180~191.
[7]T.Borca-Tasciuc and G.Chen, "Experimental techniques for thin film thermal conductivity chracterization". Physics of Solids and Liquids. Vol. 2. 2004: Springer US. 205~237.
[8]T.Yao, "Thermal properties of AlAs/GaAs superlattices". Applied Physical Letters, 1987. 51(22): p. 1798~1800.
[9]G.Chen, et al., "Thermal diffusivity measurement of GaAs/AlGaAs thin-film structures". ASME Journal of Heat Transfer, 1994. 116(2): p. 325~331.
[10]E.Jansen and E.Obermeier, "Thermal Conductivity Measurements on Thin Films Based on Micromechanical Devices". J. Micromech. Microeng., 1996. 6(1): p. 118~121.
[11]O.W.Käding, H.Shurk, and K.E.Goodson, "Thermal Conduction in Metallized Silicon-Dioxide Layers on Silicon". Appl.Phys. Lett., 1994. 65(13): p. 1629~1631.
[12]D.G.Cahill, "Thermal conductivity measurement from 30 to 750K:the 3ω method". Rev.Sci.Instrum., 1990. 61(2): p. 802~808.
[13]D.G.Cahill and J.R.Abelson, "Thermal conductivity of a-Si:H thin films". Phys.Rev.B, 1994. 50(9): p. 6077~6081.
[14]C.L.Tien and G.Chen, "Challenges in Microscale Conductive and Radiative Heat Transfer". Journal of Heat Transfer 1994. 116(4): p. 799~807.
[15]D.G.Cahill, W.K.Ford, and K.E.Goodson, "Nanoscale Thermal Transport". Applied Physics, 2003. 93(2): p. 793~818.
[16]D.G.Cahill, "Heat Transport in Dielectric Thin Films and at Solid-Solid Interfaces". Microscale Thermophysical Engineering. Vol. 1. 1997: Taylor and Francis Ltd. 85~109.
[17]E.T.Swartz and R.O.Pohl, "Thermal Resistance at Interfaces". Appl.Phys.Lett. , 1987. 51(26): p. 2200~2202.
[18]R.S.Prasher and P.E.Phelan, "A scattering mediated acoustic mismatch model for the prediction of thermal boundary resistance". Journal of Heat Transfer ASME, 2001. 123(1): p. 105~111.
[19]饒達仁, 邱亮維, and 簡恆傑, "金屬薄膜之熱傳導係數值量測". in 中華民國第二十九屆全國力學會議(The 29th Conference on Theoretical and Applied Mechanics). 2005. Hsinchu, Taiwan, R.O.C.
[20]N.O.Birge, S.R.N., "Wide-frequency specific heat spectrometer". Rev.Sci.Instrum., 1987. 58: p. 1464 ~ 1470.
[21]A.Jacquot, et al., "Numerical simulation of the 3ω method for measuring the thermal conductivity". Journal of Applied Physics, 2002. 91(7): p. 4733~4738.
[22]S.-M.Lee and D.G.Cahill, "Heat transport in thin dielectric films". J. Appl. Phys., 1996. 81(6): p. 2590~2595.
[23]饒達仁, et al., "薄膜熱傳導性能量測方法研究- 3ω method". in 中華民國第二十七屆全國力學會議(The 27th Conference on Theoretical and Applied Mechanics). 2003. Tainan,Taiwan,R.O.C.
[24]饒達仁, 簡恆傑, and 陳昭榮, "金屬電阻溫度係數量測之自我加熱效應探討". in 中華民國第二十八屆全國力學會議(The 28th Conference on Theoretical and Applied Mechanics). 2004. Taipei, Taiwan, R.O.C.
[25]劉勇志, "3ω方法量測熱傳導係數之溫度效應". 2004, 國立清華大學.
[26]邱亮維, "金屬薄膜之熱傳導係數量測". 2005, 國立清華大學.
[27]饒達仁, 賴威志, and 簡恆傑, "二氧化矽薄膜之熱傳導係數與邊界熱阻之量測研究". in 中華民國第三十屆全國力學會議(The 30th Conference on Theoretical and Applied Mechanics). 2006. ChangHua, Taiwan, R.O.C.
[28]T.Yamane, N.Nagai, and S.Katayama, "Measurement of thermal conductivity of silicon dioxide thin films using a 3w method". J. Appl. Phys., 2002. 91(12): p. 9772~9776.
[29]Y.S.Touloukian, et al., "Thermal Conductivity TPRC Data Series". Vol. 1. 1970, New York: IFI/Plenum. 177~209.
[30]J.Griffin, F.R.Brotzen, and P.J.Loos, "Effect of thickness on the transverse thermal conductivity of thin dielectric films". J. Appl. Phys., 1994. 75(8): p. 3761~3764.
[31]J.H.Kim, A.Feldman, and D.Novotny, "Application of the three omega thermal conductivity measurement method to a film on a substrate of finite thickness". J. Appl. Phys., 1999. 86(7): p. 3959~3963.
[32]S.Govorkov, et al., "A New Method for Measuring Thermal Conductivity of Thin Films". Rev. Sci. Instrum., 1997. 68(10): p. 3828~3834.