1. Introduction

Bulk bismuth (Bi) presents outstanding optical properties, related with its giant interband electronic transitions, such as a giant infrared refractive index (n ∼ 10) and a negative ultraviolet – visible permittivity [1]. These properties are thought to enable a strong visible and infrared absorption [1–4] and an ultraviolet – visible plasmonic response [1–3,5,6] in deeply subwavelength Bi nanostructures. These effects are of utmost importance for a growing number of applications based on Bi nanostructures, including photocatalysis [7–10], photodetection [11,12], or optical modulation [13,14]. For exploiting the full potential of such applications by rational nanostructure design, knowing the dielectric function of Bi nanostructures in a broad spectral range, from the far infrared to the ultraviolet, is needed. However, such data are not available, despite of several claims of quantum electronic confinement effects implying a size-dependence for the electronic structure of bismuth nanostructures [15–18]. In fact, very few attempts to determine it were reported in the past years, in the case of specific nanostructures such as bismuth thin films [19] and nanowires [15], and they were limited to narrow spectral windows in the far and mid infrared, respectively.

In here, we determine the far infrared – to – ultraviolet dielectric function of Bi thin films with nominal thicknesses t_Bi varied from 11 nm to 78 nm. All the studied films display a continuous structure and a dielectric function comparable to that of bulk Bi, except the thinnest one (t_Bi = 11 nm). In this case, our analysis suggests that the deviation from bulk values originates from the discontinuous film structure, the incident light interacting with an effective medium consisting of Bi and air. This leads us to propose that the observed deviation does not primarily originate from quantum electronic confinement.

2. Optical properties of the Bi films

The studied Bi films, grown on Si substrates, present nominal thicknesses t_Bi = 11 nm, 17 nm, 21 nm, 28 nm, and 78 nm, determined by Rutherford backscattering spectroscopy (RBS). The optical properties of the films were characterized by spectroscopic ellipsometry at photon energies from the far infrared to the ultraviolet (0.05 to 4 eV, 25 to 0.3 µm). Details about the film fabrication and characterization, including ellipsometry measurements, are given in Appendix A. Figure 1(a) shows the experimental spectra of the ellipsometric angles Ψ and Δ for the studied films, measured at an angle of incidence of 70°. The full sets of spectra (measured at different angles of incidence) of these films are shown in Appendix B (Fig. 4). Clear trends can be seen on both Ψ and Δ upon increasing t_Bi. For instance, Ψ increases in the whole far infrared – to – ultraviolet region.

 

Fig. 1. Far infrared - to - ultraviolet ellipsometry characterization of the films and of their dielectric function. (a) Spectra of the ellipsometric angles Ψ and Δ at the angle of incidence of 70°: experimental spectra (dots) and the corresponding best-fit ones (lines). (b) Spectra of the real and imaginary part (ɛ₁ and ɛ₂) of the best-fit dielectric function of each film. The model used for the ellipsometry analysis is shown on the left panel.

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To determine the dielectric function ɛ = ɛ₁ + iɛ₂ of each Bi film, its experimental Ψ and Δ spectra measured at different angles of incidence were fitted simultaneously using a bilayer model. This model, which is depicted in Fig. 1(b) and further detailed in Appendix B (Fig. 5), consisted of a layer of dielectric function ɛ covered by a roughness layer of dielectric function ɛ_rough. ɛ was described by a sum of Kramers Kronig – consistent oscillators. ɛ_rough was described with a Bruggeman model mixing ɛ and the dielectric function of air with an equal weight. The thicknesses of the two layers, t and t_rough were fixed at the values found from the structural characterization, as explained in Appendix A. In short, t_rough is the average peak-to-valley roughness found by atomic force microscopy (AFM), and t is the remaining film thickness underneath this roughness as determined by combining AFM, RBS and scanning electron microscopy (SEM). The t and t_rough values are given Table 1, together with the corresponding geometrical thickness of the films: t + t_rough. With such thicknesses being fixed, the only parameters left free during the fit procedure were those of the Kramers Kronig – consistent oscillators describing the dielectric function ɛ of the film.

Table 1. Nominal thickness t_Bi of the films, layer thicknesses t_rough and t used for the ellipsometry analysis, and geometrical thickness of the films, t + t_rough.^a

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An excellent agreement between the best-fit spectra and the experimental ones is found for all the films (Fig. 1(a) and Appendix B, Fig. 4). The corresponding best-fit spectra obtained for the ɛ₁ and ɛ₂ of each Bi film are shown in Fig. 1(b). For the thinnest film (t_Bi = 11 nm), a broad and moderately strong absorption band peaking at 0.9 eV and extending in the near infrared and visible is seen in the ɛ₂ spectrum. In relation with such absorption, ɛ₁ takes values close to 0 in the visible and ultraviolet together with relatively high positive values in the infrared. Upon increasing t_Bi to 17 nm, the absorption band becomes markedly more intense and sharper, ɛ₁ taking large negative values in the visible and ultraviolet, and large positive values in the infrared. Upon increasing again t_Bi, the values of ɛ₁ and ɛ₂ converge asymptotically to those of bulk Bi, which are reached for the film with t_Bi = 78 nm [1] that will thus be considered hereafter as the bulk reference. For bulk Bi, ɛ₂ reaches values of up to 120 at the absorption band maximum, ɛ₁ increases up to 100 in the infrared and decreases down to - 25 in the visible.

It is worth noting that the dielectric function of the Bi film with t_Bi = 17 nm is already close to that of bulk Bi, with peak ɛ₁ and ɛ₂ values reaching 70% of the bulk ones. Therefore, the dielectric function of very thin Bi films, say with t_Bi > 15 nm, is comparable with that of bulk Bi. In contrast, for thinner films (here, for t_Bi = 11 nm) the dielectric function departs strongly from the bulk one. As we will show in the next section, this trend correlates with the film structure, which is continuous for t_Bi > 15 nm and discontinuous for t_Bi = 11 nm.

3. Structure of the Bi films

To demonstrate this correlation, we show the structure of selected films (t_Bi = 11 nm, 21 nm and 78 nm) studied by top-view SEM and AFM. Combining these two techniques is the most practical choice for determining accurately the nanostructure of the films. Especially they provide a more thorough information than cross-section SEM images (which we reported in refs. [1] and [2] for Bi films with ∼30 nm and 78 nm thicknesses). The top-view SEM images presented in Fig. 2(a) show that the film with t_Bi = 11 nm presents a discontinuous near-percolation structure, where voids with a near 10 nm width separate clusters of densely packed/coalesced nanoparticles. The in-plane size of these clusters ranges from 50 to 150 nm. For larger t_Bi values, the films present a continuous structure consisting of densely packed grains and few to no voids. The fraction of voids thus drops abruptly from the film with t_Bi = 11 nm to the film with t_Bi = 21 nm. Upon increasing t_Bi from 21 nm to 78 nm, the in-plane size of the grains increases from 50-150 nm to 100-200 nm while the few remaining voids are filled.

 

Fig. 2. Structure of selected Bi films. (a) Top-view SEM images of the films with t_Bi = 11 nm, 21 nm, and 78 nm. (b) AFM images and profiles of these films. (c) Cross-section schematic representation of the film structure. The film with t_Bi = 11 nm has a discontinuous near-percolation structure. This structure is built from nanoparticles with a 20-50 nm in-plane size. They are arranged in clusters with a 50-150 nm in-plane size. The clusters are separated by voids with a near 10 nm width. Films with larger t_Bi have a continuous structure with few/no voids. The corresponding thicknesses t and t_rough are depicted for each film.

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Complementary information is provided by the AFM images and profiles presented in Fig. 2(b). For the film with t_Bi = 11 nm, they show that the in-plane size of the nanoparticles forming the clusters ranges from 20 to 50 nm. Note that AFM measurements do not reveal the full depth of the voids observed by SEM, because their width is too small compared with the tip size. For the same reason, they might underestimate the depth of the contact region between densely packed/coalesced nanoparticles. Therefore, combining SEM and AFM measurements is necessary to provide a full picture of the film structure, especially for discontinuous near-percolation films such as that with t_Bi = 11 nm.

As summary, Fig. 2(c) shows a cross-section schematic representation of the structure of the 3 films drawn based on the SEM and AFM information. For t_Bi = 11 nm, the film has a discontinuous near-percolation structure. For t_Bi = 21 nm, the film has a continuous structure with few voids. For t_Bi = 78 nm, the film is also continuous yet without voids. These trends are a direct consequence of the growth mechanism of Bi on the surface-oxidized Si substrate, which follows a nucleation – growth – coalescence – percolation scheme as t_Bi increases, in the same way as noble metals (Appendix C, Fig. 6).

This growth mechanism impacts the optical properties of the film. Upon increasing t_Bi, the dielectric function of the Bi film gets closer to that of bulk Bi as the film becomes continuous and the density of voids decreases. It is especially remarkable that the strongest variation in ɛ₁ and ɛ₂ occurs when t_Bi increases from 11 to 17 nm and the film structure turns from discontinuous to continuous with a few voids. The variation in ɛ₁ and ɛ₂ is smaller when t_Bi increases above 17 nm and the few voids in the continuous film are gradually filled.

4. Relation between the structure and optical properties of the Bi films

All the previous results point at a dominant effect of the Bi film discontinuity on the measured dielectric function when t_Bi = 11 nm. In order to investigate the origin of such effect, finite difference time domain (FDTD) simulations of the optical properties of a discontinuous Bi film were performed. To simplify the problem while including the main structural features of such film, it was considered as a square array of densely packed truncated nanospheroids. We assumed that the material constituting these nanospheroids has the same dielectric function as bulk Bi taken from ref. [1]. The nanospheroid height H was 17 nm, the nanospheroid diameter D was varied between 20 and 50 nm, and the separation gap G between nanospheroids was varied between 0 and 10 nm, in accordance with the geometrical film thickness t + t_rough (Table 1), nanoparticle in-plane size and void width found for the film with t_Bi = 11 nm. Further technical details about the FDTD simulations are given in Appendix D (Fig. 7). In Fig. 3(a) are shown the elementary cell used for the simulation with D = 50 nm and G = 10 nm and the corresponding electric field map at a photon energy of 1.5 eV. This map reveals mildly warm spots between the nanospheroids, which also present low internal and transmitted fields as a result of their strong absorption and dense packing.

 

Fig. 3. FDTD simulations of the optical properties of discontinuous Bi thin films consisting of densely packed Bi nanospheroids. (a) Example of elementary simulation cell seen in cross-section across the meridional plane of the nanospheroid, with a map of the x-polarized electric field amplitude at E = 1.5 eV (lowest value = 0, highest value = 1.5 relative to the incident field amplitude). In this example, the cell width is 60 nm, the nanospheroid diameter D = 50 nm and height H = 17 nm, the separation gaps between nanospheroids is G = 10 nm. The incident light impinges downwards along the z axis and is x-polarized. (b) Simulated effective dielectric function (real part ɛ₁ and imaginary part ɛ₂) of discontinuous Bi films with different nanospheroid diameters D and separation gaps G (red and blue lines). The dielectric function of bulk Bi (black line) is shown for comparison. This dielectric function is the same as that of the film with t_Bi = 11 nm shown in Fig. 1b. For any value of D and G, the discontinuous film presents much smaller values of ɛ₁ and ɛ₂ than bulk Bi.

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FDTD simulations also provided the reflectance of the discontinuous film for the different values of D and G (Appendix E, Fig. 8). The obtained reflectance values are much smaller than those of a continuous Bi film with the same layer thicknesses (t and t_rough) as the film with t_Bi = 11 nm. This implies that the simulated effective dielectric function of the discontinuous film also presents much smaller values than the bulk one, as shown in Fig. 3(b). This trend is very similar to the one found in the 0.05–2.5 eV region for the measured dielectric function of the discontinuous Bi film with t_Bi = 11 nm (Fig. 1(b)). In particular, the peak value of ɛ₂ for the discontinuous film is decreased with respect to the bulk one in a comparable proportion (81% and 71%) in both the measured (Fig. 1(b)) and simulated (Fig. 3(b), G = 0 nm) spectra.

Furthermore, simulations show that ɛ₂ peaks at a different photon energy (between 0.8 and 1.5 eV) depending on the values of D and G. Therefore, in a random array of nanospheroids characterized by a broad distribution of D and G, the ɛ₂ spectrum would display a broad band spreading in the near infrared, visible and ultraviolet, as the one measured for the discontinuous Bi film with t_Bi = 11 nm (Fig. 1(b)). Such broad band is indeed observed in simulated ɛ₂ spectra taking a broad polydispersity into account (Appendix F, Fig. 9). These simulated spectra show features similar with those of the measured spectrum in the whole spectral region considered. They account well for the strong decrease in the peak ɛ₂ values with respect to the bulk, and for the ɛ₂ values closer to the bulk ones at photon energies above 2.5 eV. ɛ₂ values close to or higher than the bulk ones in this spectral region can originate from localized plasmon-like resonances in Bi nanoparticles with a weakly anisotropic or weakly truncated shape (as shown in Appendix F, Fig. 9, left panel), which present a high extinction cross section [14].

This leads us to propose that the dielectric function of the thinnest film studied here (t_Bi = 11 nm) is very different from that of bulk Bi mainly because of effective medium effects. The dielectric function measured for this film is an effective quantity resulting from the polarization of a Bi:void heterogeneous medium, where the Bi nanostructures are described by a dielectric function close to the one of bulk Bi. Such effective medium effects may also affect, yet more weakly, the dielectric function of thicker films still containing a few voids. This would explain their small difference with the dielectric function of bulk Bi. Note that effective medium effects have also been reported to affect strongly in a broad spectral range the dielectric function of very thin noble metal films near percolation [20]. However, the way the dielectric function of discontinuous films deviates from the bulk one is spectrally very different for Bi and noble metals. For example, the ɛ₂ of the nearly percolated Au films in ref. [20] is much larger than the bulk one in the visible and near infrared. In contrast, the ɛ₂ of the discontinuous Bi film takes (slightly) larger values than the bulk one only in the ultraviolet and part of the visible, and it takes much smaller ɛ₂ values than the bulk one in the remaining part of the visible and the infrared. This very different behavior can be related to the very different electronic structures and dielectric functions of Bi and Au.

In contrast, it seems that quantum electronic confinement does not have a dominant effect on the far infrared – to – ultraviolet dielectric function of even the thinnest film studied here, despite of the fact that it presents a discontinuous structure built from nanoparticles. This conclusion is in line with our previous work [5] in which we modeled satisfactorily the measured ultraviolet – visible plasmon – like resonances of flattened Bi nanoparticles using classical electrodynamic calculations based on the dielectric function of bulk Bi. This also seems consistent with the results of a very recent work [21], which showed that quantum confinement – induced spin-charge interconversion occurs in Bi ultrathin films only when they present a discontinuous structure and a thickness smaller than 3 nm. Accordingly, a continuous 10 nm – thick or even thinner Bi film might present a dielectric function comparable to the bulk one. A similar trend has been observed in the case of few – nm Bi₂Se₃ films based on a careful material fabrication and spectroscopic ellipsometry characterization [22,23].

5. Conclusion and outlook

Summarizing, the Bi films with nominal thickness equal to or larger than 17 nm present a dielectric function similar to the bulk one in the whole 0.05–4 eV region and a continuous structure. In contrast, the film with a 11 nm nominal thickness presents a dielectric function very different from the bulk one and a discontinuous structure. From an analysis based on FDTD simulations, we propose that such different dielectric function is the result of the effective medium behavior of the discontinuous film. This suggests that the outstanding optical properties of bulk Bi are shared by continuous Bi films down to the ultrathin film regime (thickness < 10 nm). This opens the way, for instance, to achieving a near total absorption of visible light with ultrathin and continuous Bi films. At such aim, it will be interesting to grow such ultrathin and continuous Bi films within optical cavities. Also, our results suggest that the dielectric function of bulk Bi can be used as input value for the rational design of flattened nanostructures such as nanocylinders or nanoflakes. Besides that, we also remark that the effective medium properties we put forward for the discontinuous Bi film are appealing for the fabrication of films with light trapping properties optimized by nanoscale design. Tailoring the film nanostructure [5,24] enables tuning its effective optical dispersion in a broad range. This is useful to meet the requirements for an optimal light harvesting [25] in Bi nanostructured materials, in particular for photocatalytic systems based on near-percolation Bi nanostructures [26,27].

Appendix A. Details about the fabrication and characterization of the Bi films

Fabrication and structural characterization. The Bi films were grown by pulsed laser deposition on standard surface oxidized Si substrates. The number of laser pulses on a Bi target was controlled to tune the amount of deposited Bi and thus the nominal thickness t_Bi of the films. Here, t_Bi is an equivalent thickness defined as the geometrical thickness that a film would present if the deposited Bi atoms were perfectly arranged, i.e. if the film had a perfectly flat surface and a continuous structure with the atomic density ρ_Bi of bulk Bi. It is determined from the areal density of Bi atoms N_Bi measured by RBS, following the relation t_Bi = N_Bi/ρ_Bi.

The structure of the films was characterized by AFM and SEM. More details about the experimental procedures and the setups used are given in Ref. [1]. The AFM characterization reveals surface roughness for all the films. Therefore, they can be considered as a bilayer stack, with a roughness layer of thickness t_rough on a layer of thickness t. Here, t_rough is taken equal to the average peak-to-valley roughness determined by AFM. Note that, for the film with t_Bi = 11 nm, the presence of voids weakly affects the t_rough value because of their small size and limited coverage. To determine t, one writes the relation: t_Bi = cov x (t + 0.5t_rough), where cov is the coverage of the substrate surface by the film. This relation expresses that the amount of deposited Bi determined by RBS is shared between the two layers in a proportion that depends on their thicknesses and on the substrate coverage. The SEM characterization provides the substrate coverage values: 80% for the thinnest film (discontinuous structure) and 100% for the others (continuous structure). One then obtains t from the relation: t = t_Bi/coverage – 0.5t_rough. Finally, from the obtained thicknesses, one determines the geometrical film thickness, which represents the distance between the substrate surface and the top of the film roughness: t + t_rough.

Ellipsometry characterization. The ellipsometry spectra (ellipsometric angles Ψ and Δ) of the Bi films on the Si substrates were determined by spectroscopic ellipsometry at 2 angles of incidence (50°, 70°) in a range from 0.05 eV (far infrared) to 4 eV (near ultraviolet). Measuring ellipsometry spectra at these two angles of incidence is sufficient to accurately determine the dielectric function of the films. Two ellipsometers (Woollam IR-VASE and Woollam VASE) were used to cover this spectral range. The back side of the Si substrates was roughened mechanically to avoid back reflected light to reach the detector. The ellipsometric characterization of the film with t_Bi = 78 nm is detailed in ref. [1].

Appendix B. Ellipsometry characterization of the Bi films

 

Fig. 4. Spectra of the ellipsometric angles Ψ and Δ at the angles of incidence of 50° and 70°: experimental spectra (red dots) and the corresponding best-fit ones (black lines), for all the films. The spectra of the film with t_Bi = 78 nm are shown in ref. [1]. MSE values of 5.6, 3.3, 1.8, and 2.2 have been obtained for the 11 nm, 17 nm, 21 nm and 28 nm, respectively.

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Fig. 5. Bilayer structure used to model the Bi films for ellipsometry fitting.

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Appendix C. Growth mechanism of the Bi films

In our deposition conditions, nucleation and growth (steps 1 and 2) occur for t_Bi up to 1-2 nm with the formation of truncated spheroidal nanoparticles [5]. For larger t_Bi up a few nm, coalescence events (step 3) make the nanoparticles grow laterally [5]. Percolation is reached for t_Bi above 10 nm for which the deposit consists of a discontinuous layer (step 4). In line with that, the film with t_Bi = 11 nm studied in this work displays a near-percolation structure. Upon further increasing t_Bi the voids within the discontinuous layer get filled by Bi to promote the formation of a continuous layer. For t_Bi > 15 nm, a continuous layer with few voids is already formed. Further Bi deposition leads to a filling of the remaining voids (step 5) and to a vertical growth that leads to an increase in the continuous layer thickness (step 6). Even when consisting of a continuous layer with t_Bi > 30 nm, the Bi deposit presents a small roughness reminiscent from the initial stages of growth.

 

Fig. 6. Schematics of the Bi film growth mechanisms with characteristic values of the nominal Bi thickness t_Bi. The thickness thresholds are estimated from our experiments. These are indicative (not exact) values.

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Appendix D. Details about the FDTD simulations of discontinuous Bi films

3D-FDTD simulations were performed with the OptiFDTD32 software. A parallelepipedal elementary cell, with the geometry shown in Fig. 7(a) and Fig. 7(b), was used.

 

Fig. 7. (a) Top view of the elementary cell used for the simulation, with the corresponding x-polarized electric field amplitude map in the equatorial plane of the Bi nanospheroid, for D = 50 nm, H = 17 nm and G = 10 nm. E is the incident electric field. (b) Cross-section of the elementary cell, showing the location of the input plane (incident field) and of the viewer plane (where the reflectance spectrum is measured). (c) Bilayer structure used to determine the effective dielectric function of the Bi discontinuous film from the FDTD – calculated reflectance spectra.

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Cell elements. In this cell, a Bi nanospheroid was standing on a substrate with a dielectric constant of 16 (comparable with that of Si) and was surrounded by a medium with a dielectric constant of 1 (air). Its dielectric function was described as the sum of Kramers Kronig consistent oscillators with the parameters given for bulk Bi in ref. [1]. The truncated nanospheroid height H was set to 17 nm, to match with the geometrical thickness (t + t_rough = 11 + 6 nm) of the film with t_Bi = 11 nm. Its diameter D was varied between 20 and 50 nm.

Cell dimensions and boundary conditions. The height of the elementary cell was 150 nm, and its width W was adjusted to fulfil W = G + D, G being the separation gap between nanospheroids in the square array, varied between 0 and 10 nm. To generate such array, periodic boundary conditions were applied on the ± x and ± y boundaries. To account for a semi-infinite incident medium and substrate, perfect matching layers were applied to the ± z boundaries.

Wave parameters and reflectance simulations. The incident electric field was x - polarized and incident from the air medium, downwards along the z axis, i.e. at normal incidence. Reflectance spectra were calculated by inverse Fourier transform of a light pulse, analyzed in the viewer plane located ∼ 60 nm above the nanospheroid. This distance is sufficiently large so that the viewer plane lies in the far-field region. A mesh size of 0.5 nm was used for all the calculations and enabled obtaining converged reflectance spectra.

Effective dielectric function. To determine the effective dielectric function ɛ = ɛ₁ + iɛ₂ of the discontinuous Bi film formed by the square array of nanospheroids, its FDTD – calculated reflectance spectrum was fitted assuming a bilayer structure. This structure is shown in Fig. 7(c). ɛ consisted of a sum of Kramers Kronig - consistent oscillators whose parameters were left free during the fit. ɛ_rough was described by a Bruggeman model mixing ɛ and the dielectric function of air with equal weight. The thicknesses of the bottom and top layer were set to 11 and 6 nm, respectively, to match with the layer thicknesses t and t_rough used to model the film with t_Bi = 11 nm and so that the corresponding geometrical film thickness equals the nanospheroid height H. Note that the simplified assumption we made for the dielectric function of the substrate (take it equal to 16 at all wavelengths instead of using the exact wavelength-dependent dielectric function of Si) affects only weakly the value of the effective dielectric function of the Bi discontinuous film, provided the same dielectric function is used for the substrate in both the FDTD simulations (Fig. 7(b)) and bilayer structure (Fig. 7(c)).

Appendix E. FDTD reflectance spectra of discontinuous Bi films

 

Fig. 8. FDTD reflectance spectra for discontinuous Bi films consisting of a square array of Bi truncated nanospheroids, with different diameter D and separation gap G, and a height H = 17 nm. These spectra are compared with that of a continuous Bi film with the same layer thicknesses (t = 11 nm, t_rough = 6 nm) as the film with t_Bi = 11 nm.

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Appendix F. Comparison between simulation and measurement

 

Fig. 9. Left panel: ɛ₂ spectra simulated by FDTD for 6 different monodisperse arrays of Bi nanospheroids. Blue and red curves are the same as in Fig. 3(b) (truncated spheroids with different diameters D, 20 and 50 nm, and different separation gaps G, 0 and 10 nm). Green curves stand for untruncated spheroids (D = 20 and 50 nm, G = 1 nm). The spectrum of bulk Bi (black line) is shown for comparison. Right panel: Polydisperse ɛ₂ spectra calculated by a linear superposition of the monodisperse ɛ₂ shown in the left panel. “Polydisperse 1” was obtained with only the D = 50 nm monodisperse arrays (truncated spheroids: 40% G = 0, 10% G = 10 nm; untruncated spheroids: 50%). “Polydisperse 2” was obtained with the same weight for the 6 monodisperse arrays. The measured ɛ₂ of the film with t_Bi = 11 nm (orange line) and the bulk reference (black line) are shown for comparison.

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Funding

Ministerio de Ciencia, Innovación y Universidades (MICINN) (MICINN RTI2018-096498-B-I00, MINECO/FEDER TEC2015-69916-C2-1-R).

Acknowledgments

The authors thank Drs. J. Wojcik and P. Mascher from McMaster University (Canada) for performing the far infrared ellipsometry measurements. They also thank Dr. T.A. Ezquerra from the Instituto de Estructura de la Materia, IEM, CSIC (Spain) for providing access to the AFM facility.

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