The Structure of Oxide Film on the Porous Silicon Surface
A prolonged stay of porous silicon in the air environment gives rise to structural changes in its surface layer, and the standard single-layer model is not sufficiently accurate to describe them. In this work, the structure of the near-surface layer in porous silicon is studied using the polygonal ellipsometry method. A combined approach is proposed to analyze the angular ellipsometry data for the parameters ф and Δ. It consists in the application of the multilayer medium model and the matrix method, while simulating the propagation of optical radiation in this medium in order to obtain the theoretical angular dependences of tan ф and cosΔ. In this method, the dependence of the sought optical profile on the specimen depth is an additional condition imposed on the multilayer model. Evolutionary numerical methods are used for finding the global minimum of the mean squared error (MSE) between the corresponding theoretical and experimental dependences, and the parameters of an optical profile are determined. A model in which the inner non-oxidized layer of porous silicon is homogeneous, whereas the refractive index in the outer oxidized layer has a linear profile, is analyzed. It is shown that the linear and two-step models for the refractive index of an oxidized film provided the best agreement with the experimental ellipsometric functions. The adequacy of the theoretical model is also confirmed by determining the color coordinates of the specimen.
T. Lohner, D.J. Wentink, E. Varsonyi, M. Fried. In Proceeding of the 2nd Japan-Central Europe Joint Workshop "Modeling of Materials and Combustion" (Budapest, November 7-9, 1996). Edited by I. Vajda (Technical University of Budapest, 1997), p. 66.
M. Fried, T. Lohner, O. Polgar, P. Petric, E. Vazsonyi, I. Barsony, J.P. Piel, J. L. Stehle. Characterization of different porous silicon structures by spectroscopic ellipsometry. Thin Solid Films 276, 223 (1996). https://doi.org/10.1016/0040-6090(95)08058-9
C. Robert, L. Bideux, B. Gruzza, M. Cadoret, T. Lohner, M. Fried, E. Vazsonyi, G. Gergely. Spectroellipsometry and electron spectroscopy of porous Si thin films on p+ substrates. Thin Solid Films 317, 210 (1998). https://doi.org/10.1016/S0040-6090(97)00517-8
V.A. Makara, V.A. Odarych, O.V. Vakulenko, O.I. Dacenco. Ellipsometric studies of porous silicon. Thin Solid Films 342, 230 (1999). https://doi.org/10.1016/S0040-6090(98)01163-8
V.A. Odarych. Applied Photometric Ellipsometry ("Pulsary" Kyiv Univ. Publ., 2017) (in Ukrainian).
Porous Silicon: From Formation to Application. Vol. 2: Biomedical and Sensor Applications. Edited by G. Korotcenkov (Taylor and Francis Group, 2016).
A.L. Yampolskiy, O.V. Makarenko, L.V. Poperenko, V.O. Lysiuk. Ellipsometry of hybrid noble metal-dielectric nanostructures. Semicond. Phys. Quant. Electron. Optoelectron. 21, 412 (2018). https://doi.org/10.15407/spqeo21.04.412
P.H. Berning. Theory and calculations of optical thin films. In Physics of Thin Films, Vol. 1. Edited by G. Hass (Academic Press, 1963), p. 69.
L.N. Acquaroli. Matrix method for thin film optics. e-print arXiv:1809.07708v1 (2018).
R. Storn, K. Price. Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341 (1997). https://doi.org/10.1023/A:1008202821328
Colorimetry: Understanding the CIE System. Edited by J. Schanda (Wiley, 2007).
O.V. Makarenko, L.V. Poperenko, O.I. Zavalistyi, A.L. Yampolskiy. Ellipsometric diagnostics of a transient surface layer in optical glass. Ukr. J. Phys. 64, 442 (2019). https://doi.org/10.15407/ujpe64.5.442