臺灣博碩士論文加值系統

本研究為探討單層薄膜及多層干涉濾光片的熱應力、熱膨脹係數、以及雙軸模量的變化，並提出一個多層膜熱應力預估模型，可透過實驗方法預估多層膜的熱應力。在實驗上以改良式的Twyman-Green干涉儀，量測單層薄膜在不同溫度下的應力變化關係，並結合雙基板技術，可以檢測在不同溫度下薄膜的熱應力，進一步分析薄膜的熱膨脹係數與雙軸模量。考慮到溫度梯度的影響，採用溫度梯度分布應力修正公式，將熱膨脹係數與雙軸模量做修正，即可檢測出較為精確的薄膜熱膨脹係數與雙軸模量，藉此研究熱效應對於多層薄膜濾光片特性的影響。從實驗結果可以得知，不同高低折射率的薄膜經過堆疊後，獲得的多層膜濾光片相較於單層膜來說，它的熱膨脹係數接近於我們所使用的玻璃基板，可產生較小的熱應力。在熱應力預估模型上通過改進Vegard公式，加入熱膨脹係數以及雙軸模量的修正因子優化原先的公式，來提高熱應力預估的準確度，使得預估值與實驗值的差異降低至10%以內。

In order to investigate the thermal stress, thermal expansion coefficient, and biaxial modulus of single-layer thin films and multilayer interference filters, a thermal stress prediction model for multilayer films is proposed, which can be used to estimate the thermal stress of multilayer films through experimental methods. An improved Twyman-Green interferometer was used to measure the film residual stress change at different temperatures. Using dual-substrate method, the thermal stress of thin films at different temperatures was measured, and then the thermal expansion coefficient and biaxial modulus of thin film were analyzed. Considering the influence of temperature gradient, the modified thermal stress formula is used, both the thermal expansion coefficient and biaxial modulus of multilayer thin film filters are modified to improve the accuracy.The experimental results show that the thermal expansion coefficient of the multi-layer film filters coated with different high refractive index and low refractive index films is close to that of the substrates, which compared with the single-layer thin films. In the thermal stress prediction model, the modified Vegard formula improves the accuracy by adding a correction term. The difference between the measured and predicted values is less than 10%.

致謝
摘要
Abstract
目錄
圖目錄
表目錄
第一章 緒論
1.1研究動機
1.2研究目的
1.3文獻回顧
1.3.1薄膜和基板間的關係
1.3.2薄膜中殘留應力的問題
1.3.3薄膜彈性模量及熱膨脹係數的測量
1.3.4溫度對薄膜干涉濾光片的影響
1.3.5熱應力預估模型
1.4研究方法
第二章 基本原理
2.1薄膜殘留應力
2.2薄膜熱膨脹係數和彈性模量的檢測方法
2.2.1光學干涉法
2.2.2雙基板技術
2.3溫度梯度對薄膜表面受熱的影響
2.4熱應力預估模型
第三章 實驗方法與儀器
3.1薄膜的製備
3.2薄膜特性的量測
3.2.1薄膜應力量測系統
3.2.2紫外光/可見光分光光譜儀
3.2.3表面輪廓儀(Alpha Step)
3.2.4簡式橢圓偏光儀(Ellipsometer）
第四章 實驗結果與討論
4.1 單層膜的殘留應力及熱應力特性檢測
4.1.1 SiO2薄膜
4.1.2 MgF2薄膜
4.1.3 Nb2O5薄膜
4.1.4 TiO2薄膜
4.1.5 單層介電薄膜熱應力誤差分析
4.2 多層膜的殘留應力及熱應力特性檢測
4.2.1藍光陷波濾光片
4.2.2紅光陷波濾光片
4.2.3窄帶濾光片
4.3 多層膜熱應力預估模型
第五章 結論
5.1 研究成果
5.2 未來展望
參考文獻

[1] 林采薇， “光學薄膜各向異性殘留應力之量測分析”，逢甲大學電機工程所碩士論文（2012）。
[2] 陳文星， “透明導電氧化物薄膜溫度相關特性之檢測”，逢甲大學電機工程所碩士論文（2012）。
[3] 徐聲豪， “溫度及應力對高密度分波多工器(DWDM)濾光片中心波長飄移之研究”， 國立中央大學光電科學與工程學系碩士論文 (2008)
[4] Z. H. Jin, “Thermal stresses in a multilayered thin film thermoelectric structure,” Microelectronics Reliability, Vol.54, No.6-7, pp.1363-1368 (2014).
[5] B. Li, et al. “Recent progress in improving low-temperature stability of infrared thin-film interference filters,” Optics Express, Vol.13, No.17, pp. 6376-6380 (2005).
[6] H. Takahashi, “Temperature stability of thin-film narrow-bandpass filters produced by ion-assisted deposition,” Appl. Opt. Vol.34, No.4, pp.667-675 (1995).
[7] L. Xu, et al. “Tunable Coefficient of Thermal Expansion of Composite Materials for Thin-Film Coatings,” Coatings, Vol.12, No.6, pp.836 (2022).
[8] P. H. Townsend, D. M. Barnett, T. A. Baunner, “Elastic relationships in layered composite media with approximation for the case of thin films on a thick substrate,” Journal of Applied Physics, Vol.62, No.11, pp.4438-4444 (1987).
[9] M. F. Doerner, W. D. Nix, “Stresses and deformation processes in thin films on substrates,” Critical Reviews in Solid State and Material Sciences, Vol.14, No.3, pp.225-268 (1988).
[10] J. A. Thornton, D. W. Hoffman, “Stress-related effects in thin films,” Thin solid films, Vol.171, No.1, pp.5-31 (1989).
[11] H. Windischmann, “Intrinsic stress in sputter-deposited thin films,” Critical Reviews in Solid State and Material Sciences, Vol.17, No.6, pp.547-596 (1992).
[12] M. J. Huang, P. K. Chou, M. C. Lin, “Thermal and thermal stress analysis of a thin-film thermoelectric cooler under the influence of the Thomson effect,” Sensors and Actuators A: Physical, Vol.126, No.1, pp.122-128 (2006).
[13] W. R. Manning, et al. “Thermal expansion of Nb2O5,” Journal of the American Ceramic Society, Vol.55, No.7, pp.342-347 (1972).
[14] T. Shibata, “Effect of residual stress on the photochemical properties of TiO2 thin films,” The Journal of Physical Chemistry C, Vol.113, No.29, pp.12811-12817 (2009).
[15] C. C. Jaing, “Thermal expansion coefficients of obliquely deposited MgF2 thin films and their intrinsic stress,” Applied Optics, Vol.50, No.9, pp.159-163 (2011).
[16] X. Tian, et al. “Simulation of thermal stress in ion beam sputtered Ta2O5/SiO2 multilayer coatings on different substrates by finite element analysis,” Surface and Coatings Technology, Vol.362, pp.225-233 (2019).
[17] W. C. Herrmann, D. E. Morton, “Thin-film optical coating filter stability under different environmental conditions,” Applied Optics, Vol.32, No.28, pp.5673-5676 (1993).
[18] A. Zoller, et al. “Temperature-stable bandpass filters deposited with plasma ion-assisted deposition,” Applied Optics, Vol.35, No.28, pp.5609-5612 (1996).
[19] L. Scholtz, L. Ladanyi, J Mullerova, “Interfacial roughness and temperature dependence of narrow band thin film filters for the DWDM passive optical networks,” Advances in Electrical and Electronic Engineering, Vol.14, No.1, pp.75-82 (2016).
[20] T. C. Chen, W. J. Lin, D. L. Chen, “Effect of temperature gradient on simultaneously experimental determination of thermal expansion coefficients and elastic modulus of thin film materials,” Journal of Applied Physics, Vol.96, No.7, pp.3800-3806 (2004).
[21] N. H. Zhang, “Thermoelastic stresses in multilayered beams. Thin Solid Films, Vol.515, No.23, pp.8402-8406 (2007).
[22] C. Gao, Z. Zhao, X. Li, “Modeling of thermal stresses in elastic multilayer coating systems,” Journal of Applied Physics, Vol.117, No.5, pp.055305 (2015).
[23] W. Z. Yao, et al. “Modelling and analysis of the stress distribution in a multi-thin film system Pt/USG/Si,” Materials Research Express, Vol.5, No.4, pp. 046405 (2018).
[24] M. M. de Lima, Jr., R. G. Lacerda, J. Vilcarromero, and F. C. Marques, “Coefficient of thermal expansion and elastic modulus of thin films,” J. Appl. Phys., Vol. 86, No.9, pp. 61-68 (1999).
[25] J. Thurn, M. P. Hughey, “Evaluation of film elastic modulus and coefficient of thermal expansion from thermoelastic film stress measurements,” J Appl Phys, Vol.95, No.12, pp.7892–7897 (2004).
[26] C. L. Tien, C. C. Lee, Y. L. Tsai and W. S. Sun, “Determination of the mechanical properties of thin films by digital phase shifting interferometry,” Opt. Comm., Vol.198, No.4-6, pp.325-331 (2001).
[27] C. L. Tien, H. D. Zeng, “Measuring residual stress of anisotropic thin film by fast Fourier transform,” Optics Express, Vol.18, No.16, pp.16594-16600 (2010).
[28] K. H. Raveesha, K. Kumar, B. K. Prasad, “On alternative methods of determining Radius of Curvature using Newton’s Rings set up,” International Letters of Chemistry, Physics and Astronomy, Vol.48, pp.27-31 (2015).
[29] A. Dobroiu, A. Alexandrescu, D. Apostol, V. Nascov, V. S. Damian, “Centering and profiling algorithm for processing Newton’s rings fringe patterns, ”Optical Engineering, Vol.39, No.12, pp.3201-3206 (2000).
[30] P. An, F. Z. Bai, Z. Liu, X. J. Gao, and X. Q. Wang, “Measurement to radius of Newton’s ring fringes using polar coordinate transform, ”Journal of the European Optical Society-Rapid Publications, Vol.12, No.1, pp.1-6 (2016).
[31] C. L. Tien and H. D. Zeng, “Measuring residual stress of anisotropic thin film by fast Fourier transform,” Optics Express, Vol.18, No.16, pp.16594-16600 (2010).
[32] C. Gao, Z. Zhao, X. Li, “Modeling of thermal stresses in elastic multilayer coating systems,” Journal of Applied Physics, Vol.117, No.5, pp.055305 (2015).
[33] S. Adachi, “GaAs, AlAs, and Al x Ga1− x As: Material parameters for use in research and device applications,” Journal of Applied Physics, Vol.58, No.3, pp.1-29 (1985).
[34] J.Ma, et al. “Effect of different oxide thickness on the bending Young’s modulus of SiO2@ SiC nanowires,” Scientific reports, Vol.6, No.1, pp.1-7 (2016).
[35] H. K. Pulker, J. Maser, “The origin of mechanical stress in vacuum-deposited MgF2 and ZnS films,” Thin Solid Films, Vol.59, No.1, pp.65-76 (1979).
[36] 吳偉良, “α-堇青石礦渣微晶玻璃熱處理工藝優化及氟的影響”, 中國陶瓷, Vol.54, No.10, pp.48-53 (2018).
[37] S. Dhawan, T. Dhawan, A. G. Vedeshwar, “Residual stress induced crystalline to amorphous phase transformation in Nb2O5 quantum dots,” Journal of Applied Physics, Vol.116, No.4, pp.043503(2014).
[38] Y. Dai, X. Chu, F. Gao, “Molecular dynamics simulation investigation on thermal stability and repetitive tensile performance of TiO2,” Materials Research Express, Vol.6, No.8, pp.085053 (2019).
[39] C. C. Lee, “An apparatus for the measurement of internal stress and thermal expansion coefficient of metal oxide films,” Review of Scientific Instruments, Vol.72, No.4, pp.2128-2133 (2001).
[40] J. E. Mahan, “Physical vapor deposition of thin films,” pp.336 (2000).
[41] S. M. Rossnagel, “Thin film deposition with physical vapor deposition and related technologies,” Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol.21, No.5, pp.74-87 (2003).
[42] 李正中，“薄膜光學與鍍膜技術”，第9版，藝軒出版社 (2019).
[43] P. J. Martin, R. P. Netterfield, W. G. Sainty, “Modification of the optical and structural properties of dielectric ZrO2 films by ion‐assisted deposition,” Journal of Applied Physics, Vol.55, No.1, pp.235-241 (1984).
[44] 田春林,“光學薄膜應力與熱膨脹係數量測之研究”， 國立中央大 學光電科學研究所博士論文(2000).
[45] A. Zoller, “Temperature stability of optical coatings produced by plasma and ion assisted evaporation processes,” Optical Interference Coatings, Vol.9, pp.2-4 (1998).