| 研究生: |
劉奕宏 Yi-Hong Liu |
|---|---|
| 論文名稱: |
多波長光學常數量測之研究 Optical Constant and Thickness Measurements through Multi-wavelength Interferometry |
| 指導教授: |
李正中
Cheng-Chung Lee |
| 口試委員: | |
| 學位類別: |
碩士 Master |
| 系所名稱: |
理學院 - 光電科學與工程學系 Department of Optics and Photonics |
| 畢業學年度: | 98 |
| 語文別: | 中文 |
| 論文頁數: | 72 |
| 中文關鍵詞: | 動態干涉儀,擬合,基因演算法 |
| 外文關鍵詞: | fitting, Genetic Algorithm, Dynamic interfrometer |
| 相關次數: | 點閱:20 下載:0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本研究分別利用軟體及硬體對薄膜進行光學常數的量測,軟體方面提出較新潮且實用的基因演算法;而硬體方面提出以Twyman-Green干涉儀為架構的偏極相移干涉儀,量測系統採用低同調光源廣波域之白光汞燈,加上窄帶濾光片構成光譜密度為高斯分部的光源,進而得出相位做為擬合所需之資訊。
實驗的架構對不同波長(中心波長532nm、580nm、632nm、690nm和730nm)進行量測薄膜的相位資訊,使用具四個偏極態的偏極陣列架設在CCD鏡頭前,在偏極相移干涉儀中可同時取出四個相移的值,經由電腦運算即時求解得到相位,速度快且減少環境擾動造成的誤差。
加上使用HITACHI公司製造的U4100型的光譜儀所量得的該薄膜光譜
,進一步的利用基因演算法所撰寫的程式,擬合出單層膜多波長的折射率(Refractive Index)與厚度(Thickness)。
本研究將分為兩個部份來進行,分別是只使用穿透率進行擬合、使用穿透率及相位進行擬合。此實驗只需五個波長的相位及穿透率即可推出多波斷折射率的變化。最後將擬合穿透光譜與相位資訊,所得到之光學薄膜常數與商用SOPRA公司製造之橢偏儀進行比較,結果相當吻合。
In this thesis, there were two major parts, software and the hardware parts, for measuring the optical constants and thickness of the thin film. For the software, we used novel Genetic Algorithm to design our program. For the hardware, we proposed a polarization phase shifting interferometer based on Twyman-Green interferometer structure. In our arrangement, the low coherence light source is composed of a mercury lamp, which is a polychromatic light source and covering the visible spectral range, and a narrow band pass filter to create a Gaussian power spectral density source.
We chose five color filters (532nm, 580nm, 632nm, 690nm, 730nm) for selecting wavelengths. In the polarization interferometer, a novel pixelated mask with a micro-polarizer phase shifting array was placed just in front of the CCD, so that we can use single shot to extract phase information and it is effective to reduce environmental vibration.
Then we can get the spectrums from U4100 spectrometer made by HITACHI, and use genetic algorithm to write a fitting program to get the refractive index and thickness of single-layer thin film.
We used two parts, transmittances only and transmittances plusing with phases, to process our problems. All the researches need only five phases and spectrums can derive multi-wavelength refractive index and thickness. The measurement results were compared with the results obtained by SOPRA ellipsometer. The results meet reasonable values in both refractive index and thickness.
[1] Holland J.H., “Adaptation in Natural and Artificial Systems”, Ann Arbor, MI: The University of Michigan Press, 1975.
[2] Brock N., Hayes J., Kimbrough B., Millerd J., North-Morris, Novak M. M.& Wyant J., “Dynamic interferometry”, Proc. SPIE Int. Soc. Opt. Eng., 5875, 1, 58750F, 2005.
[3] Kimbrough B., Millerd J., Wyant J. & Hayes J., “Low Coherence Vibration Insensitive Fizeau Interferometer”, Proc. of SPIE, 6292, 62920F-1,2006.
[4] 李正中, “薄膜光學與鍍膜技術”, 第五版, 藝軒出版社, 台灣, 2006.
[5] Malacara D., “Optical shop testing”, Wiley, New York, 18-30, 1997.
[6] Zhang T., Yamaguchi I., “Three-dimensional microscopy with phase-shifting digital holography”. Opt. Let., 23, 1221-1223, 1998.
[7] 洪文明, “白光相移干涉術之三維表面量測”,國立交通大學光電所碩士班論文,2003 .
[8] Wyant J.C. “Interferometry optical metrology: basic principles and new systems”, Laser Focus, 65-71, 1982.
[9] Hariharan P., Oreb B. F. and Eiju T., “Digital Phase-Shifting Interferometry: a Simple Error-Compensating Phase Calculation Algorithm”, Appl. Opt. 13, 2504, 1987.
[10] Robinson D.W. and Reid G.T., “Interferogram Analysis”, 2nd Ed., 123-126, Institute of Physics Publishing, Bristol and Philadelphia, 1993
[11] Amnon Y. & Pochi Y., “Optical Waves in Crystals”, Mei Ya, Taipei, 121-131, 1983.
[12] Hauge P.S., “Recent Developments In Instrumentation In Ellipsometry”,Surf. Sci.96, 108, 1980.
[13] Abeles F., “Methods for determining optical parameters of thin films”, in Progress in Optics, Vol. 2, Chap. VI, ed. by Wolf E., North-Holland Publishing Company, 251-288, 1963.
[14] Manifacier J.C., Gasiot J. and Filland J.P., “Simple method for determination of the optical constant n, k and the thickness of weekly absorbing thin films”, J. Phy. E.: Sci. Inst. 9, 1002-1004, 1976.
[15] Swanepoel R., “Determination of the thickness and optical constant of amorphous silicon”, J. Phy. E.: Sci. Inst. 16, 1214-1222, 1983.
[16] 林奕德,"數值分析簡式橢偏儀中的偏光片及析光片之校正及更正",國立交通大學光電所碩士班論文,2005 .
[17] Shokooh-Saremi M., Nourian M., Mirsalehi M.M., Keshmiri S.H.,"Design of multilayer polarizing beam splitters using genetic algorithm", Optics Communications ,233,57–65, 2004.
[18] Julien Cardin, Dominique Leduc, “ Determination of refractive index, thickness, and the optical losses of thin films from prism–film coupling measurements”, Appl. Opt., Vol. 47, No. 7, March 2008.
[19] Kirkpatrick, “Optimization by Simulator Annealing: Quantitative Studies”, S.Journal of Statistical Physics, 34, 975-986, 1984.
[20] Acton F.S., “Numerical Methods That work”, corrected edition, Washington: Mathematical Association of America, 55,454-458, 1990.
[21] Gungor T., Saka B., “Calculation of the optical constants of a thin layer upon a transparent substrate from the reflection spectrum using a genetic algorithm”, Thin Solid Films, Vol.467, 319-325, NOV 2004.
[22] Kalyanmoy Deb, Associate Member, IEEE, Amrit Pratap, Sameer Agarwal, and Meyarivan T., “A fast and elitist multi objective genetic algorithm: NSGA-II”, IEEE transactions on evolutionary computation, Vol. 6, No. 2, April 2002.
[23] Stephane Guindon and Olivier Gascuel, “A Simple, Fast, and Accurate Algorithm to Estimate Large Phylogenies by Maximum Likelihood”, Syst. Biol.52 (5), 696- 704, 2003.
[24] Phillips S.J., Robert P. Anderson, Robert E. Schapire, “Maximum entropy modeling of species geographic distributions”, Ecological Modelling, 190, 231–259, 2006.
[25] Edward Collett, “Polarized Light”, Marcel Dekker, Inc. cptl, 21-89, 1993.
[26] 吳肇元, “動態干涉儀量測薄膜之光學常數”,國立中央大學光電科學研究所碩士班論文, 2009.