Morphology and plasmonic properties of self-organized arrays of ...

76 CHAPTER 5. MODELLING AND ANALYSIS OF THE OPT. PROP. [deg]8.07.57.06.5Surf. rough. layerCauchy layerexperimentalmodel [deg]182180experimentalmodel123a. E [eV]b.45123E [eV]45Figure 5.1: Red lines: Ψ (left panel) and ∆ (right panel) spectra measured at incidenceθ = 50 ◦ onLiF(110)crystalsintheas-receivedstate. Blacklines: correspondingcalculatedcurves, fitted using the model sketched in the inset.roughness; in fact, AFM analysis of the substrates revealed a mean RMS roughness ofabout 6÷9 nm (see §3.1, fig. 3.2), and, given the high sensibility of ellipsometry, this isalso expected to affect the spectra, mostly ∆. Since roughness is a standard element inellipsometric analysis, the software already provides the appropriate methods to accountfor it.AsketchoftheoverallmodelandthecorrespondingfitresultsforΨand∆arereportedin fig. 5.1, where the optical constants of the substrate and the thickness of the roughnesslayer were employed as free fit parameters. The red curves in figure correspond to thespectra measured at θ = 50 ◦ of incidence, while the fits are plotted as black lines. The realpart N of the best-fit refractive index is shown in fig. 5.2, the imaginary part is insteadnull at all the wavelengths; the values of N are in good agreement with the reference datain the literature [202].Looking at the calculated curves in fig. 5.1, we can see that Ψ is very well reproduced,while the predicted trend for ∆ does not agree with the experiments; moreover,the roughness layer is completely rejected by the best-fit procedure. Such a behaviourindicates that our representation of the substrate is slightly over-simplified, and suggests1.441.42N1.401.380.51.52.5 3.5E [eV]4.55.5Figure 5.2: Real part of the refractive index for a Cauchy layer representative of bulkLiF, as obtained from the fits in fig. 5.1; the corresponding imaginary part is null at allwavelengths.