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

86 CHAPTER 5. MODELLING AND ANALYSIS OF THE OPT. PROP.we set the thickness of the effective layer d eff to half the ripples periodicity Λ (d eff = Λ/2),and we assume the particles centered at half height inside the layer (d z = d eff /2 = Λ/4).The in-plane periodicities of the inclusions, d x and d y (d y = Λ), are chosen accordingto the mean values extracted from the AFM data, neglecting in first approximation thecontributions of their finite spread on the LSP response. In fact, while there are ampledemonstrations that the LSP resonances in isolated NPs pairs are a strong function oftheir mutual separation [69, 71, 73, 74] (see also §1.3.4), the 2D rectangular symmetryof our arrays has the positive effect of limiting the impact of the interparticle dipolarcoupling on the LSPs, via a partial cancellation of the dipole interactions between theNPs (fig. 5.16). This effect, discussed more in detail in §5.2.2, is qualitatively supportedby the observation of remarkably narrow LSP peaks, compared to what would be expectedconsidering the spread in the NP-NP distance [69, 71, 73, 74]. Moreover, such cancellationeffects also makes the LSP response less sensitive to the morphological disorder.Considering instead the geometry of the nanoparticles, the LSP can be critically affectedby the dispersion of sizes and shapes. In our samples, the NP dimensions are suchthat multipolar LSP are fully negligible, therefore the presence of a distribution of NPsizes affects the LSP resonances mainly via the appearance of intrinsic finite-size correctionsto the bulk Au dielectric constant [151, 154, 214] (cfr. §1.3, §1.3.2). These effectshave been included in the model, as already explained before (see fig. 5.6(b)), although,for the typical mean size and deviation under consideration here, they yield a relativelyminor impact on the LSP [65]. NP shape effects, namely the distribution of in-planeaspect ratios, provide instead a significant LSP broadening and weakening mechanisms,through the onset of a corresponding distribution of depolarization factors (eq. (5.1)).As described in §3.2, we can independently control the NPs aspect ratio and spacing byappropriately tuning, during the samples fabrication, the substrate temperature and thethickness of the deposited gold layer. We exploit this possibility by realizing two differentclasses of samples, respectively featuring in-plane isotropic Au NPs arranged on a rectangularlattice and in-plane elongated Au NPs arranged on a square grid. In both cases, anoptical anisotropy arises in the system, respectively originating from the anisotropic EMcoupling in the array and from the single-NP intrinsic anisotropic polarizability, which inturn determines anisotropic EM interactions between the NPs.In the next paragraphs we will review the morphological and optical characterizationsfor such classes of samples, and then exploit the capabilities of our model to assess thedifferent contributions of the intrinsic and collective effects on the LSP.Morphological characterizationThe quantitative morphological parameters corresponding to the first sample are summarizedin fig. 5.9 (cfr. the AFM measurement of fig. 3.8(c)). In panel (a) we report arepresentative AFM image of the LiF(110) surface following homoepitaxial growth of LiFat T = 350 ◦ C, deposition of t Au ≈ 5 nm of Au and annealing at T = 400 ◦ C. The ripplemorphology has a mean periodicity Λ ≈40 nm, and the formation of Au NPs slightlyelongated along the ridges direction after the annealing can be easily noticed.The experimental distribution of the NPs sizes were obtained by careful analysis ofthe AFM data. First, the NPs present in the images were isolated by the applicationof a threshold setting to separate them from the background. The NPs isolated by thisprocedure in a 1μm 2 AFM image, containing about one thousand of particles, had theirperimeters fitted with sets of coherently aligned ellipses. The ellipses axes are then used