volume | PIER Journals

Abstract

The reflection of linearly polarized light from an ultrathin biaxially anisotropic dielectric film on an isotropic transparent material is investigated in the long-wavelength limit. The approximate expressions for the reflection characteristics of s- and p-polarized electromagnetic plane waves are obtained. The analytical approach developed in this paper not only provides insight into the nature of reflection problem for biaxially anisotropic ultrathin films but also furnishes the methods for resolving the inverse problem for such anisotropic layers. It is shown that a key capability of the developed analytical method is to decouple the usual correlations in the index and the thickness of ultrathin films.

1. Yeh, P., Optical Waves in Layered Media, John Wiley & Sons, New York, 2005.

2. Hodgkinson, I. J. and Q. H. Wu, Birefringent Thin Films and Polarizing Elements, World Scientific, Singapore, 1997.
doi:10.1142/9789812817198

3. Robertson, J. "High dielectric constant gate oxides for metal oxide Si transistors," Rep. Prog. Phys., Vol. 69, 327-396, 2006.
doi:10.1088/0034-4885/69/2/R02

4. Zhang, H., R. Solanki, B. Roberds, G. Bai, and I. Banerjee, "High permittivity thin film nanolaminates," J. Appl. Phys., Vol. 87, 1921-1924, 2000.
doi:10.1063/1.372113

5. Adamson, P., "Reflection of light in a long-wavelength approximation from an N-layer system of inhomogeneous dielectric films and optical diagnostics of ultrathin layers. I. Absorbing substrate," J. Opt. Soc. Am. B, Vol. 20, 752-759, 2003.
doi:10.1364/JOSAB.20.000752

6. Adamson, P., "Reflection of light in a long-wavelength approximation from an N-layer system of inhomogeneous dielectric films and optical diagnostics of ultrathin layers. II. Transparent substrate," J. Opt. Soc. Am. B, Vol. 21, 645-654, 2004.
doi:10.1364/JOSAB.21.000645

7. Landry, J. P., J. Gray, M. K. O'Toole, and X. D. Zhu, "Incidence-angle dependence of optical reflectivity difference from an ultrathin film on solid surface," Opt. Lett., Vol. 31, 531-533, 2006.
doi:10.1364/OL.31.000531

8. Kim, I. K. and D. E. Aspnes, "Analytic determination of n, κ, and d of an absorbing film from polarimetric data in the thin-film limit," J. Appl. Phys., Vol. 101, 033109, 2007.
doi:10.1063/1.2434004

9. Lekner, J., Theory of Reflection of Electromagnetic and Particle Waves, Dordrecht, Martinus Nijhoff, 1987.

10. Hingerl, K., D. E. Aspnes, and I. Kamiya, "Comparison of reflectance difference spectroscopy and surface photoabsorption used for the investigation of anisotropic surfaces," Surf. Sci., Vol. 287/288, 686-692, 1993.
doi:10.1016/0039-6028(93)91054-S

11. Adamson, P., "Reflection of electromagnetic plane waves in a long-wavelength approximation from a multilayer system of anisotropic transparent films on absorbing medium," Waves in Random and Complex Media, Vol. 18, 651-668, 2008.
doi:10.1080/17455030802302142

12. Adamson, P., "Laser probing of anisotropic ultrathin dielectric films on absorbing materials via differential reflection characteristics," Opt. Laser Technol., Vol. 41, 424-430, 2009.
doi:10.1016/j.optlastec.2008.08.006

13. Adamson, P., "Reflection of electromagnetic plane waves in a long-wavelength approximation from a multilayer system of anisotropic transparent films on non-absorbing medium," Waves in Random and Complex Media, Vol. 20, 443-471, 2010.
doi:10.1080/17455030.2010.482572

14. Adamson, P., "Optical diagnostics of anisotropic nanoscale films on transparent isotropic materials by integrating reflectivity and ellipsometry," Appl. Opt., Vol. 48, 5906-5916, 2009.
doi:10.1364/AO.48.005906

15. Goldstein, H., Classical Mechanics, Addison-Wesley, Reading, 1965.

16. Azzam, R. M. A. and N. M. Bashara, Ellipsometry and Polarized Light, Amsterdam, North-Holland, 1977.

17. Xu, W., L. T. Wood, and T. D. Golding, "Optical degeneracies in anisotropic layered media: Treatment of singularities in a 4×4 matrix formalism," Phys. Rev. B, Vol. 61, 1740-1743, 2000.
doi:10.1103/PhysRevB.61.1740

Dr. Peep Adamson