Korean Journal of Optics and Photonics (한국광학회지)

Optical Society of Korea (한국광학회)
권호 표지
DOI QR코드

DOI QR Code

Ellipsometric Expressions of Multilayered Substrate Coated with a Uniaxially Anisotropic Alignment Layer

단축이방성 배향막이 코팅되어 있는 다층박막시료의 타원식

  • Received : 2013.08.05
  • Accepted : 2013.09.05
  • Published : 2013.10.25
Download PDF
⟨ Previous Next ⟩

Abstract

The effective reflection coefficients of an obliquely incident wave on a multi-layered substrate coated with a uniaxially anisotropic alignment layer are derived. The effective reflection coefficients as well as explicit ellipsometric expressions are provided as a function of film constants of multiple layers together with magnitude of anisotropy, direction of optic axis, and thickness of the alignment layer. It is expected that by adapting these expressions to the conventional modelling technique, the ordinary refractive index, the extra-ordinary refractive index, the azimuth angle and the tilt angle of the optic axis, and the thickness of the aligned surface can be determined simultaneously together with the thickness and volume fraction of each layer beneath the alignment layer.

다층박막이 있는 기층에 단축이방성 배향막이 코팅되어 있을 때 비스듬히 입사한 빛의 유효반사계수 표현들을 유도하였다. 유효반사계수들과 타원상수들을 다층박막의 미지상수들은 물론 단축이방성 배향막의 광학이방성의 크기와 광축의 방향 그리고 배향막의 두께로 표현하였다. 이를 바탕으로 배향막의 정상굴절률과 이상굴절률, 배향된 두께 그리고 광축의 방위각과 기울임각을 다층박막의 두께나 조성비 등과 함께 타원법이 가지고 있는 높은 수준의 측정 정밀도를 유지하며 기존의 모델링 분석방법으로 결정할 수 있도록 하였다.

Keywords

References

  1. C. Yu, J. Bae, C. M. Keum, and S. D. Lee, "Optical anisotropy of aligned pentacene molecules on a rubbed polymer corresponding to the electrical anisotropy," Current Applied Physics 10, 64-67 (2010). https://doi.org/10.1016/j.cap.2009.04.013
  2. C. Benecke, H. Seiberle, and M. Schadt, "Determination of director distribution in liquid crystal polymer-films by means of generalized anisotropic ellipsometry," Jpn. J. Appl. Phys. 39, 525-531 (2000). https://doi.org/10.1143/JJAP.39.525
  3. J. A. Ekhoff, M. J. Farrow, D. M. Walba, and K. L. Rowlen, "Molecular orientation of a model liquid crystal alignment layer," Talanta 60, 801-808 (2003). https://doi.org/10.1016/S0039-9140(03)00141-3
  4. M. Yamahara, M. Nakamura, N. Koide, and T. Sasaki, "Influence of rubbing conditions of polyimide alignment layer on optical anisotropy of immobilized liquid crystal film," Liquid Crystals 34, 381-387 (2007). https://doi.org/10.1080/02678290601097334
  5. A. Martino, Y.-K. Kim, E. Garcia-Caurel, B. Laude, and B. Drevillon, "Optimized Mueller polarimeter with liquid crystals," Opt. Lett. 28, 616-618 (2003). https://doi.org/10.1364/OL.28.000616
  6. M. Schubert, R. Rheinlander, J. A. Woollam, B. Johs, and C. M. Herzinger, "Extension of rotating-analyzer ellipsometry to generalized ellipsometry: determination of the dielectric function tensor from uniaxial $TiO_{2}$," J. Opt. Soc. Am. A 13, 875-883 (1996). https://doi.org/10.1364/JOSAA.13.000875
  7. W. Xu, L. T. Wood, and T. D. Golding, "An ellipsometric method for the determination of the dielectric tensor of an optically uniaxial material suited for in-situ measurements," Thin Solid Films 384, 276-281 (2001). https://doi.org/10.1016/S0040-6090(00)01861-7
  8. G. E. Jellison, "Generalized ellipsometry for materials characterization," Thin Solid Films 450, 42-50 (2004). https://doi.org/10.1016/j.tsf.2003.10.148
  9. K. H. Lyum, S. U. Park, S. M. Yang, H. K. Yoon, and S. Y. Kim, "Precise measurement of ultra small retardation of LCD alignment layer using improved transmission ellipsometry," Korean J. Opt. Photon. 24, 77-85 (2013). https://doi.org/10.3807/KJOP.2013.24.2.077
  10. G. Fang, J. Maclennan, and N. Clark, "High extinction polarimeter for the precision measurement of the in-plane optical anisotropy of molecular monolayers," Langmuir 26, 11686-11689 (2010). https://doi.org/10.1021/la101117n
  11. K. H. Lyum, H. K. Yoon, S. J. Kim, and S. Y. Kim, "Study on ultra-small optical anisotropy profile of LCD alignment layer by using transmission ellipsometry," in Proc. the 6th International Conference on Spectroscopic Ellipsometry (Kyoto Research Park, 2013), p. 102.
  12. I. Hirosawa, "Method of characterizating rubbed polyimide film for liquid crystal display devices using reflection ellipsometry," Jpn. J. Appl. Phys. 35, 5873-5875 (1996). https://doi.org/10.1143/JJAP.35.5873
  13. I. Hirosawa and N. Sasaki, "Influence of annealing on molecular orientation of rubbed polyimide film observed by reflection ellipsometry," Jpn. J. Appl. Phys. 36, 6953-6956 (1997). https://doi.org/10.1143/JJAP.36.6953
  14. I. Hirosawa, H. Miyairi, T. Matsushita, and S. Satio, "The relation between pretilt angle of liquid crystal and optical anisotropy of alignment film," Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals 368, 565-571 (2001). https://doi.org/10.1080/10587250108029989
  15. S. Itoh and I. Hirosawa, "Observation of an optical anisotropy of rubbed polyimide film on actual LCD panel," Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals 367, 745-752 (2001). https://doi.org/10.1080/10587250108028696
  16. D. W. Berreman, "Optics in stratified and anisotropic media: 4x4-matrix formalism," J. Opt. Soc. Am. 62, 502-510 (1972). https://doi.org/10.1364/JOSA.62.000502
  17. A. Lien, "Extended Jones matrix representation for the twisted nematic liquid-crystal display at oblique incidence," Appl. Phys. Lett. 57, 2767-2969 (1990). https://doi.org/10.1063/1.103781
  18. C. Gu and P. Yeh, "Extended Jones matrix method and its application in the analysis of compensator for liquid crystal displays," Displays 20, 237-257 (1999). https://doi.org/10.1016/S0141-9382(99)00028-1
  19. J. W. Ryu and S. Y. Kim, "Analysis of effective optic axis and equivalent retardation of composite optically anisotropic film by using transmission ellipsometry," Korean J. Opt. Photon. 20, 288-293 (2009). https://doi.org/10.3807/KJOP.2009.20.5.288
  20. J. W. Ryu, S. Y. Kim, and Y. K. Kim, "Determination of the optic axis distribution of a hybridly aligned discotic material for wide-view films," J. Korean Phys. Soc. 57, 233-239 (2010). https://doi.org/10.3938/jkps.57.233
  21. J. Lekner, "Reflection and refraction by uniaxial crystals," J. Phys.:Condens. Matter 3, 6121-6133 (1991). https://doi.org/10.1088/0953-8984/3/32/017
  22. J. W. Ryu, Ph. D. Thesis, Ajou University, Suwon (2010).
  23. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987), Chapter 3.
  24. R. H. W. Graves, "Determination of the optical constants of anisotropic crystals," J. Opt. Soc. Am. 59, 1225-1227 (1969). https://doi.org/10.1364/JOSA.59.001225
  25. S. Y. Kim, Ellipsometry (Ajou University Press, Gyeonggi, Korea, 2000), Chapter 3-4.
  26. O. S. Heaven, Optical Properties of Thin Films (Dover Publication, Inc., 1955).

Cited by

  1. Ellipsometric Expressions for a Sample Coated with Uniaxially Anisotropic Layers vol.26, pp.5, 2015, https://doi.org/10.3807/KJOP.2015.26.5.275
  2. Ellipsometric Expressions for Two Uniaxially Anisotropic Layers Coated on a Multilayered Substrate vol.26, pp.2, 2015, https://doi.org/10.3807/KJOP.2015.26.2.115
  3. Precise Measurement of the Ultrasmall Optical Anisotropy of Rubbed Polyimide Using an Improved Reflection Ellipsometer vol.26, pp.4, 2015, https://doi.org/10.3807/KJOP.2015.26.4.195