Open AccessInfluence of cross-correlation effects on the optical quantities of rough films
Author(s) -
Daniel Franta,
Ivan Ohlı́dal,
David Nečas
Publication year - 2008
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.16.007789
Subject(s) - optics , surface finish , silicon , boundary (topology) , rayleigh scattering , surface roughness , inverse , refractive index , physics , mathematical analysis , materials science , mathematics , computational physics , geometry , thermodynamics , optoelectronics , composite material
Within the Rayleigh-Rice theory the influence of layer boundary roughness on coherently reflected light is expressed using very complex formulae. Therefore we deal with the simplification of these formulae by employing an approximation based on neglecting cross-correlation effects between both the rough boundaries. It is shown that if the mean distance of the boundaries (mean thickness) is sufficiently large in comparison with the lateral dimensions of the roughness it is possible to describe the individual boundaries of the layers by matrices corresponding to isolated rough surfaces. This fact enables us to simplify the formulae for the optical quantities in a substantial way, which also simplifies the numerical calculation needed for the inverse problem. This statement is illustrated by means of a numerical analysis simulating ellipsometric and reflectometric data of rough silicon dioxide layers placed onto silicon single crystal substrates.