Numerical Calculation of the Conditions for Photochemical Subnanopolishing of a Rough Quartz Surface under Illumination from Quartz Side

V. I. Grigoruk$^{1}$, V. I. Kanevskii$^{2}$, S. O. Kolienov$^{1}$

$^{1}$Taras Shevchenko National University of Kyiv, 60 Volodymyrska Str., UA-01033 Kyiv, Ukraine
$^{2}$O. O. Chuiko Institute of Surface Chemistry, NAS of Ukraine, 17 General Naumov Str., UA-03164 Kyiv, Ukraine

Received: 02.07.2019; final version - 28.11.2019. Download: PDF

The numerical procedure for calculation of light scattering on a rough surface of quartz is described. The profile of this surface has a Gaussian spatial correlation function. The finite-element approach is used to solve the Helmholtz two-dimensional vector equation. At the illumination of such surface from quartz side, when the angle of incidence of a beam is equal to a critical angle and when the mean square deviation $\delta$ of roughness is negligible ($\delta$ < 10 nm), the following results are obtained: (a) depending on the phase of the incident wave, its crest changes its position along the interface region; (b) the value of this crest in the regions of surface peaks is much greater than in the regions of the valleys, that creates optimal conditions for sub-nano-polishing of this surface; (c) the contrast of the field along the above surface decreases when the length of the correlation of quartz rough surface increases, and it practically does not depend on the length of the incident wave.

Key words: surface plasmon resonance, scattering of plane electromagnetic waves, Helmholtz vector equation.



PACS: 41.20.Jb, 42.25.Bs, 42.25.Fx, 42.25.Gy, 73.20.Mf, 78.66.-w, 81.65.Ps

Citation: V. I. Grigoruk, V. I. Kanevskii, and S. O. Kolienov, Numerical Calculation of the Conditions for Photochemical Subnanopolishing of a Rough Quartz Surface under Illumination from Quartz Side, Metallofiz. Noveishie Tekhnol., 42, No. 1: 105—121 (2020) (in Ukrainian)

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