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

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78 CHAPTER 5. MODELLING AND ANALYSIS OF THE OPT. PROP.semi-infinite homogeneous substrate (N 2 ); for simplicity we assume the refractive indicesN i as real constants (and N 0 = 1). Referring to fig. 5.3, the constructive interferenceoccurs whenever the difference between the optical paths travelled by the reflected beamsis an integer multiple m of the wavelength, i.e. [126]N 1 (BC +CD)−N 0 AD = 2dN 1 cosθ 1 = mλ m = m hcE mwhere E(λ) = hc/λ is the photon energy. The period of the interference figure (forexample as a function of E) is then given by∆E = E m+1 −E m =hc2dN 1 cosθ 1,directly related to the thickness and refractive index of the film. In this simple example,the period ∆E is independent of the energy and inversely proportional to d; in all realcases, however, this is not true due to the dispersion of the refractive indices, so a completeanalysis of the optical constants is required to estimate the thickness.In order to characterize the nanostructured substrates, we proceed as in the previouscase, building an optical model and then performing a best-fit procedure to extract theoptical constants. We extend the model employed for the bare LiF(110), including asecondCauchylayertodescribethedepositedlayer, thatrequiresopticalconstantsslightlydifferent from the substrate. Then, in order to reproduce the anisotropy of Ψ and ∆, weaddontopofthe“film”layerabirefringentsurfacelayer, havingdifferentrefractiveindicesin the directions parallel and perpendicular the ripples, which accounts for the rippledsurface morphology. An accurate treatment would require to fully consider the sawtoothlikeshape of the ripples; here, instead, we apply a simpler approximation, treating theripples as parallel cylinders aligned in the plane of the sample. This is implemented bycombining two Bruggeman effective medium layers, with depolarization factors L || = 0along the ripples and L ⊥ = 0.5 in the perpendicular directions (see fig. 1.11(c)), in abirefringent material placed on top of the film; both the EMA layers are composed inequal proportion of air and of the underlying film material. As in the previous case, weneglect any effect of surface contamination or disorder. The overall structure of the modelis sketched in fig. 5.4(c). All the components employed (EMAs, birefringent layers, etc.)are standard elements provided by the WVASE software.The best-fit Ψ and ∆ curves corresponding to the experimental spectra of a nanopatternedLiF (fig. 4.3) are reported in fig. 5.4(a,b). The best-fit thickness of the film and ofthe roughness layer, for the particular sample under scrutiny, were 249 nm and 4.2 nm,respectively, while a ripple periodicity of about 35 nm was deduced from AFM. The agreementbetween the simulations and the experiments is again not excellent, but the mainfeatures of the ellipsometric spectra are all well reproduced. The calculated curves forthe plane of incidence parallel and perpendicular the ripples direction are indeed slightlyshifted, the differences being more pronounced in ∆ than in Ψ, and in agreement with theexperiments, indicating that the approximation to cylinder is good for a first order analysis.The thickness of the effective layer was instead quite underestimated in comparisonto the AFM data; in the ideal case of a perfect ripple structure, the depth of the valleysis equal to half of the periodicity, corresponding to ≈17 nm for the current case; if wefurther include some disorder and roughness, then we would expect a thickness greaterthan ≈20 nm, which is clearly in contrast with the value of merely 4.2 nm extracted fromthe fit.
5.1. LITHIUM FLUORIDE NANOSTRUCTURES 798.07.6||184180 [deg]7.2 [deg]1766.86.4172||1.0 2.0 3.0 4.0a. E [eV]b.1.02.0E [eV]3.04.01.44substratefilmBirefringent layerCauchy layerN1.421.401.38Cauchy layerc. d.0.51.52.5E [eV]3.54.5Figure 5.4: Panels a, b: experimental (continuous lines) and calculated (dashed lines)Ψ and ∆ curves for LiF substrates after homoepitaxial deposition of 250 nm of LiF, atincidence θ = 50 ◦ and plane of incidence either parallel (red lines) and perpendicular(black lines) the ripples ridges. Panel c: sketch of the optical model employed for thecalculations. Panel d: real parts of the calculated refractive indices for the substrate (redline) and the deposited layer of LiF (black line).The calculated real parts of the refractive indices for the substrate and the film areshown in fig. 5.4(d) (the imaginary parts are zero at all wavelengths). The two curvesare slightly different, with variations within the 1% of the absolute values, leading tothe observed interference effects; in particular, moving towards higher energies, the realrefractive index of the film increases more rapidly than the substrate, indicating thepossible presence of absorptions at energies lower than the band gap, consistent with theformation of crystal defects or color centers [200, 201] during the deposition of LiF.Summarizing the results of this section, we characterized the optical properties of theLiF substrates before and after the deposition of LiF films, performed for inducing theformation of the ripples nanostructures. The refractive index of bulk LiF was calculatedfor the bare LiF(110) samples, and found to be isotropic within the experimental accuracy.The deposited layer of LiF, instead, exhibited a slightly different behaviour with respectto the bulk, and showed a weak optical anisotropy referable to the ripple morphology. Thevariations of the refractive indices were found to lie within the 1% of the bulk value, andthe birefringence was much weaker than the optical anisotropy observed on the gold NPsarrays. Therefore, in the framework of the model presented in the next section, we willneglect these effects, and treat the substrates as homogeneous and isotropic materials.
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Università degli studi di GenovaFa
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4 CONTENTS5.2.2 Optical anisotropy
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6 Introductionconfining the EM ener
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8 Introduction
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10 CHAPTER 1. THEORYEλBkFigure 1.1
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12 CHAPTER 1. THEORYfrom which, sep
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14 CHAPTER 1. THEORY≈ ω 0 like
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16 CHAPTER 1. THEORYε 1 (λ) = N 2
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18 CHAPTER 1. THEORYThe correspondi
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20 CHAPTER 1. THEORYso the induced
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22 CHAPTER 1. THEORYε MG −ε aε
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24 CHAPTER 1. THEORYUV range, this
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26 CHAPTER 1. THEORYwhich is called
Page 28 and 29: 28 CHAPTER 1. THEORYwhere Γ 0 = v
Page 30 and 31: 30 CHAPTER 1. THEORYpoints of the c
Page 32 and 33: 32 CHAPTER 1. THEORYand then monoto
Page 34 and 35: 34 CHAPTER 1. THEORYposition, has t
Page 36 and 37: 36 CHAPTER 1. THEORYfieldorequivale
Page 38 and 39: 38 CHAPTER 1. THEORY
Page 40 and 41: 40 CHAPTER 2. EXPERIMENTAL METHODSt
Page 44 and 45: 44 CHAPTER 2. EXPERIMENTAL METHODS2
Page 46 and 47: 46 CHAPTER 2. EXPERIMENTAL METHODSs
Page 50 and 51: [001][100]50 CHAPTER 3. SELF-ORGANI
Page 52 and 53: 52 CHAPTER 3. SELF-ORGANIZED NPS AR
Page 76 and 77: 76 CHAPTER 5. MODELLING AND ANALYSI
Page 98 and 99: 98 CHAPTER 6. COMPOSITE MEDIA BASED
Page 100 and 101: 100 CHAPTER 6. COMPOSITE MEDIA BASE
Page 102 and 103: 102 CHAPTER 6. COMPOSITE MEDIA BASE
Page 104 and 105: 104 Conclusionsparticular cases of
Page 106 and 107: 106 Acknowledgements
Page 108 and 109: 108 BIBLIOGRAPHY[14] Shouheng Sun,
Page 110 and 111: 110 BIBLIOGRAPHY[44] Q A Pankhurst,
Page 112 and 113: 112 BIBLIOGRAPHY[74] Prashant K. Ja
Page 114 and 115: 114 BIBLIOGRAPHY[103] Tobias Kraus,
Page 116 and 117: 116 BIBLIOGRAPHY[137] F. Brouers, J
Page 118 and 119: 118 BIBLIOGRAPHY[169] Christy L. Ha
Page 120 and 121: 120 BIBLIOGRAPHY[201] G. Baldacchin
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