Abstract
The null ellipsometry technique of generalized ellipsometry based on using a compensator-free polarizer–sample–analyzer scheme for the case of incidence of an s- or p-polarized light on an anisotropic system is analyzed. Analytical expressions establishing a relation between measured angular quantity (analyzer azimuth at minimum intensity of detected radiation) and elements of the (2 × 2) anisotropic Jones matrix are derived. The dependence of this angular quantity on sample orientation (azimuth) is proposed to be used for determining optic-geometrical parameters of studied anisotropic systems. Sensitivity of the proposed method is estimated and is found to be comparable with that of the polarizer–compensator–sample–analyzer scheme. A comparative analysis of the discussed method with the well-known photometric method of generalized ellipsometry in the polarizer–sample–analyzer scheme based on measurement of the dependence of reflected-light intensity on sample azimuth at fixed polarizer and analyzer positions is presented. It is estimated that an error of a single arc minute in the proposed method and a relative error of determining the energy reflection coefficient of 0.05% in the photometric method of the generalized ellipsometry correspond to the same sensitivity.
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REFERENCES
R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
Principles of Ellipsometry, Ed. by A. V. Rzhanov (Nauka, Novosibirsk, 1979) [in Russian].
Ellipsometry at the Nanoscale, Ed. by M. Losurdo and K. Hingerl (Springer, Berlin, 2013).
V. A. Shvets, E. V. Spesivtsev, S. V. Rykhlitskii, and N. N. Mikhailov, Nanotechnol. Russ. 4, 201 (2009). https://doi.org/10.1134/S1995078009030082
N. V. Sopinskii, Optoelectron., Instrum. Data Process., No. 1, 95 (1997).
Y. Murakami, T. Ogawa, M. Wakaki, and S. Kawabata, Jpn. J. Appl. Phys. 39, 509 (2000). https://doi.org/10.1143/JJAP.39.509
G. J. Babonas, A. Reza, R. Szymczak, M. Baran, S. Shiryaev, J. Fink-Finowicki, and H. Szymczak, Acta Phys. Polon. A 105, 197 (2004). https://doi.org/10.12693/APhysPolA.105.197
A. A. Novikov, I. A. Khramtsovskii, V. Yu. Ivanov, I. S. Fedorov, and A. Turkboev, Izv. Vyssh. Uchebn. Zaved., Priborostr. 52 (1), 62 (2009).
D. Schmidt, B. Booso, T. Hofmann, E. Schubert, A. Sarangan, and M. Schubert, Appl. Phys. Lett. 94, 011914 (2009). https://doi.org/10.1063/1.3062996
N. V. Sopinskii, V. S. Khomchenko, O. S. Litvin, A. K. Savin, N. A. Semenenko, A. A. Evtukh, V. P. Sobolevskii, and G. P. Ol’khovik, Tech. Phys. 56, 1665 (2011). https://doi.org/10.1134/S1063784211110259
M. V. Sopinskyy, N. A. Vlasenko, I. P. Lisovskyy, S. O. Zlobin, Z. F. Tsybrii, and L. I. Veligura, Nanoscale Res. Lett. 10, 232 (2015). https://doi.org/10.1186/s11671-015-0933-0
N. V. Sopinskii, Opt. Spectrosc. 123, 778 (2017). https://doi.org/10.1134/S0030400X17110212
T. Kh. Khasanov, Opt. Spectrosc. 127, 271 (2019). https://doi.org/10.1134/S0030400X19080149
R. M. A. Azzam and N. M. Bashara, J. Opt. Soc. Am. A 64, 128 (1974). https://doi.org/10.1364/JOSA.64.000128
A. Yu. Tronin, Prib. Tekh. Eksp., No. 6, 123 (1989).
J. Lee, P. I. Rovira, I. An, and R. W. Collins, J. Opt. Soc. Am. A 18, 1980 (2001). https://doi.org/10.1364/JOSAA.18.001980
N. Ya. Gorban and L. V. Poperenko, J. Appl. Specrosc. 33, 1120 (1980). https://doi.org/10.1007/BF00608389
W. Xu, L. T. Wood, and T. D. Golding, Thin Solid Films 384, 276 (2001). https://doi.org/10.1016/S0040-6090(00)01861-7
W. Xu, L. T. Wood, and T. D. Golding, Surf. Sci. 495, 153 (2001). https://doi.org/10.1016/S0039-6028(01)01559-X
S. C. Som and C. Chowdhury, J. Opt. Soc. Am. 62, 10 (1972). https://doi.org/10.1364/JOSA.62.000010
R. M. A. Azzam, J. Opt. Soc. Am. 68, 514 (1978). https://doi.org/10.1364/JOSA.68.000514
I. Z. Indutnyi, V. I. Mynko, M. V. Sopinskyy, and K. V. Svezhentsova, J. Appl. Spectrosc. 86, 1058 (2020). https://doi.org/10.1007/s10812-020-00940-4
M. V. Sopinskyy, I. Z. Indutnyi, K. V. Michailovska, P. E. Shepeliavyi, and V. M. Tkach, Semicond. Phys. Quantum. Electron. Optoelectron. 14, 273 (2011). https://doi.org/10.15407/spqeo14.03.273
J. Monin and G. A. Boutry, Nouv. Rev. Opt. 4, 159 (1973). https://doi.org/10.1088/0335-7368/4/3/305
S. A. Alekseev and V. T. Prokopenko, Meas. Tech. 27, 777 (1984). https://doi.org/10.1007/BF00863738
A. A. Tikhii, Cand. Sci. (Phys. Math.) Dissertation (Galkin Donets. Phys.-Tech. Inst., Donetsk, 2018).
T. P. Sosnowski, Opt. Commun. 4, 408 (1972). https://doi.org/10.1016/0030-4018(72)90112-5
J. Lekner, J. Phys.: Condens. Matter 3, 6121 (1991). https://doi.org/10.1088/0953-8984/3/32/017
J. Lekner, J. Opt. Soc. Am. A 10, 2059 (1993). https://doi.org/10.1364/JOSAA.10.002059
R. Bhandari, J. Opt. Soc. Am. A 26, 2368 (2009). https://doi.org/10.1364/JOSAA.26.002368
J. Lekner, J. Opt. Soc. Am. A 14, 1359 (1997). https://doi.org/10.1364/JOSAA.14.001359
D. J. de Smet, J. Opt. Soc. Am. 65, 461 (1975). https://doi.org/10.1364/JOSA.65.000461
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Sopinskyy, M.V., Ol’khovik, G.P. Generalized Null-Ellipsometry in the Polarizer–Sample–Analyzer Scheme. Opt. Spectrosc. 130, 92–101 (2022). https://doi.org/10.1134/S0030400X22010155
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DOI: https://doi.org/10.1134/S0030400X22010155