臺灣博碩士論文加值系統

奈米檢測儀器多是利用柵距標準片來確認其尺寸量測準確度。本研究以Littrow架構的雷射繞射儀量測柵距標準片，由測得的繞射角度及雷射波長，可快速決定奈米柵距與二維標準片的正交性，為了驗證此自製系統的特性，分別對一維與二維奈米光柵進行量測，實驗結果顯示288 nm與700 nm的一維光柵，其量測偏差分別為0.41 nm與0.76 nm。而292 nm及700 nm的二維奈米光柵其量測偏差分別為0.073 nm與0.908 nm。而二維光柵正交性偏差的量測結果為0.01°。
除此之外，本研究針對原有雷射繞射儀量測限制，提出稜鏡耦合式浸潤繞射術量測小於半波長的柵距，因為提高待測光柵週遭的折射率，所以具備更小柵距的量測能力。以此新型繞射儀搭配633 nm He-Ne雷射，量測287 nm光柵，結果顯示偏差小於0.04 nm。本研究並使用此液體浸潤繞射的概念來測量液體折射率，實驗結果顯示相對準確度約為0.0015。
最後為了達到光柵自動化量測與減少人為誤差，本研究自行設計軟體來控制量測系統，實驗結果顯示，的確有改善系統對於繞射角度的判讀能力與大大地縮減實驗上繁瑣的步驟。

Reference standards of grating structure are widely used to assure the accuracy of nanometrological instruments. This research presents a laser diffractometer based on Littrow configuration to determine the pitches and angular orthogonalities of grating standards. Two one-dimensional gratings of periods of 288 nm and 700 nm, and two two-dimensional gratings of pitches of 292 nm and 700 nm were measured to realize the capability of the diffractometer. Comparing the measured and nominal values, the maximum pitch difference is below one nanometer, and the orthogonality error is around 0.01 degree.
This study also proposes a new method, called immersion diffractometry, to reduce the pitch measurement limit from one-half wavelength to one-third wavelength. A 287 nm grating were measured by the immersion diffractometer with a red HeNe laser and the conventional diffractometer with a green HeNe laser. The deviation between the measured pitches obtained by these two methods is less than 0.04 nm. Besides, the immersion diffractometry can be applied to measure the refractive index of liquid. Experimental results show that the relative accuracy is about 0.0015.

誌謝 i
摘要 ii
Abstract iii
目錄 iv
圖索引 v
表索引 vii
第一章 緒論 1
1.1前言 1
1.2 研究動機 2
第二章 量測原理 5
2.1 繞射光柵 5
2.2 光柵方程式 8
2.3 Littrow架構 9
2.4 浸潤繞射 10
2.4.1稜鏡耦合式浸潤繞射 10
2.4.2液體浸潤繞射 12
2.5繞射效率理論 13
2.5.1 向量繞射 13
2.5.2 繞射效率模擬 16
第三章 系統架構與實驗方法 18
3.1 一維奈米光柵量測 18
3.2 二維奈米光柵量測 23
3.3 小於半波長柵距量測 26
3.4　液體折射率量測 27
3.5 光柵自動化量測 29
第四章 實驗數據分析 33
4.1 系統量測結果 33
4.1.1 一維奈米光柵量測 33
4.1.2 二維奈米光柵量測 36
4.1.3 小於半波長柵距量測 41
4.1.4. 液體折射率量測 42
4.1.5 光柵自動化量測 44
4.2 誤差分析 45
第五章 結論與未來展望 48
5.1 結論 48
5.2未來展望 48
參考文獻 50

1.Y. Nakayama and S. Okazaki, “Proposal for a new submicron dimension reference for an electron beam metrology system,” J. Vac. Sci. Technol. B 6, 1930-1933 (1988).
2.I. Misumi et al., “Submicrometre-pitch intercomparison between optical diffraction, scanning electron microscope and atomic force microscope,” Meas. Sci. Technol. 14, 2065-2074 (2003).
3.V. I. Korotkov, S. A. Pulkin, and A. L. Vitushkin, “Laser interferometric diffractometry for measurements of diffraction grating spacing,” Appl. Opt. 35, 4782-4786 (1996).
4.H. P. Kleinknecht, H. Meier, “Linewidth measurement on IC masks and wafers by grating test patterns,” Appl. Opt. 19, 525-533 (1980).
5.S. Sohail H. Naqvi et al., “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377-1384 (1992).
6.Wang Lin et al., “Calibration of standards for precision pitch measurement in the nanometre region by combined scanning tunnelling microscopy and x-ray interferometry,” Nanotechnology 10, 412-417 (1999).
7.S. Gonda et al., “Real-time, interferometrically measuring atomic force microscope for direct calibration of standards,” Rev. Sci. Instrum. 70, 3362-3368 (1999).
8.Ichiko Misumi et al., “Uncertainty in pitch measurements of one-dimensional grating standards using a nanometrological atomic force microscpe,” Meas. Sci. Technol. 14, 463-471 (2003).
9.F. Meli and R. Thalmann, “Long-range AFM profiler used for accurate pitch measurements,” Meas. Sci. Technol. 9, 1087-1092 (1998).
10.T. H. Yoon, C. I. Eom, M. S. Chung and H. J. Kong, “Diffractometric methods for absolute measurement of diffraction-grating spacing,” Opt. Lett. 24, 107-109 (1999).
11.F.Meli, “Nano4: 1D gratings Final Report Draft,” CCL-S1, November (2000).
12.Soichi Owa and Hiroyuki Nagasaka, “Immersion lithography; its potential performance and issues,” Proc. SPIE 5040, 724-733 (2003).
13.J. Strong, “The John Hopkins University and diffraction gratings,” J. Opt. Soc. Am. 50, 1148-1152 (1960).
14.C. Palmer, Diffraction Grating Handbook, 5th ed., Richardson Grating Laboratory, Rochester, NY (2002).
15.M. G. Moharam et al, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077-1086 (1995).
16.N. Chateau and J. P. Hugonin, “Algorithm for the rigorous coupled-wave analysis of grating diffraction,” J. Opt. Soc. Am. A 11, 1321-1331 (1994).
17.E. Moreels, C. de Greef, and R. Finsy, "Laser light refractometer, " Appl. Opt. 23, pp.3010-3013 (1984)
18.Guide to the Expression of Uncertainty in Measurement, ISO (1995).
19.潘善鵬, 陳朝榮, “線距量測系統評估報告-雷射繞射儀,” 07-3-93-0068, 初版, 工研院量測技術發展中心, 民國93年.
20.B. EDLÉN, “The Refractive Index of Air,” Metrologia 2, 71-80 (1966).
21.K. P. Birch and M. J. Downs, “An Updated Edlén Equation for the Refractive Index of Air,” Metrologia 30, 155-162 (1993).
22.K. P. Birch and M. J. Downs, “Correction to the Updated Edlén Equation for the Refractive Index of Air,” Metrologia 31, 315-316 (1994).