Exploring the Optical Potential of Nano-Bismuth ... - ACS Publications

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Exploring the Optical Potential of Nano-Bismuth: Tunable Surface Plasmon Resonances in the Near Ultraviolet-to-Near Infrared Range Johann Toudert,* Rosalia Serna, and Miguel Jiménez de Castro Laser Processing Group, Instituto de Ó ptica, CSIC, Serrano 121, 28006 Madrid, Spain

ABSTRACT: Although the optical and plasmonic properties of noble metal (Ag and Au) nanoparticles (NPs) have been thoroughly studied and reported, less information is available concerning NPs made of non-noble metals or semimetals that present a more complex electronic structure. In this work, we combine experiments and modeling to explore the optical response of bismuth NPs in the near-ultraviolet, visible, and near-infrared, which has not been studied so far, despite the unusual and interesting electronic properties of bulk Bi. Two dimensional distributions of Bi NPs with different topologies have been prepared and embedded in a protecting and transparent dielectric matrix, thus providing robust materials suitable for structural and optical characterizations. The Bi NP distributions display optical resonances whose spectral position and width are topologysensitive. The observed macroscopic optical response has been modeled by quasistatic effective medium models, and the analysis shows that the optical resonances present features similar to those of surface plasmon resonances, such as environmental sensitivity. In contrast to noble metals resonances, important nonradiative damping is evidenced in the whole near-ultraviolet-tonear-infrared range, likely due to interband desexcitation paths available in Bi in relation to its electronic structure. Finally, dynamic calculations of the optical extinction performed as a function of the NP’s size and shape show a roadmap for tuning the spectral position of the optical resonances in Bi NPs in the whole near-ultraviolet, visible, and near-infrared range.

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INTRODUCTION Due to classical or quantum electron confinement, nanoparticles (NPs) present peculiar optical properties that differ from the corresponding bulk material. Collective excitation of free electrons in metal NPs gives rise to the (localized) surface plasmon resonance (SPR) phenomenon, which may result in a strong resonant optical absorption as well as near-field and scattering enhancements. The absorption/scattering cross sections, together with the magnitude and topology of the near-field, are strongly sensitive to several structural parameters, such as the NP's size, shape, and environment,1−4 in addition to the nature of the metal, which paves the way in which the NP's optical response can be tuned.1,5 All these parameters determine the peak wavelength (usually in the near-ultraviolet, visible, or near-infrared) and spectral width of the SPRs. Usually, the SPR spectral width in a single isolated metal NP reflects the plasmon desexcitation, which can occur through radiative or nonradiative processes. Nonradiative damping of a SPR may result from interaction of the conduction electrons with defects, grain boundaries, the NP’s interface, and so on1 or from decay through interband transitions.6 The latter process © 2012 American Chemical Society

requires the SPR to spectrally overlap with the metal interband transitions. Since the interband transitions in Ag are excited only in the ultraviolet spectrum, interband damping is absent in the visible and near-infrared so that narrow and intense SPRs can be observed for nonradiating Ag NPs in this range.1,5 In contrast, because of the interband transitions in Au in the visible, weakly damped SPRs of Au NPs can be excited only below the interband threshold, that is, from the red to the infrared.6 Up to now, most of the optical studies about metal NPs have been devoted to Ag and Au because of their strong SPR signals in the visible or near-infrared. Nevertheless, there are some early studies1,5 and very recent works7−10 on the optical response of NPs of different metals, such as Pt, Pd, or Al. In these works, the properties of SPRs in non-noble metal NPs are analyzed, and the different radiative and nonradiative contributions to the SPR desexcitations are identified and correlated to the electronic band structure of the bulk metal.10 Received: July 3, 2012 Published: August 10, 2012 20530

dx.doi.org/10.1021/jp3065882 | J. Phys. Chem. C 2012, 116, 20530−20539

The Journal of Physical Chemistry C

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Figure 1. TEM plan-view micrographs and NP size histograms (number of NPs as a function of the effective in-plane diameter, D, calculated using the Feret method) of a-Al2O3/Bi NPs/a-Al2O3 thin films with Bi effective thickness tBi of (a) 2, (b) 3, and (c) 4 nm. In addition, a schematic cross section view of an a-Al2O3/Bi NPs/a-Al2O3 thin film presenting well separated Bi NPs is shown in part d.

which allows tuning their topology, i.e. the Bi NPs size, shape, and in-plane distribution.28,29 Optical transmittance measurements performed in the near-ultraviolet, visible, and nearinfrared, at several incidence angles and polarizations, have been correlated with the nanostructure as characterized by transmission electron microscopy (TEM). It is found that the optical response of a single layer of Bi NPs is strongly sensitive to its topology. By using quasistatic effective medium models, we are able to successfully simulate the transmittance spectra of these Bi NPs embedded in a-Al2O3, and we show the existence of optical resonances in the Bi NPs. Finally, we investigate theoretically the influence of the size, shape, and environment of a single Bi NP on its optical resonances in the near-ultraviolet, visible, and near-infrared. For this purpose, we have first calculated in the quasistatic approximation the field enhancement spectrum of a spherical Bi NP and its extinction spectra as a function of the dielectric function of the surrounding medium. Then we have modeled the extinction and scattering spectra of an oblate spheroidal Bi NP as a function of its long axis length from a few nanometers (quasistatic approximation) to hundreds of nanometers (modified long wavelength approximation: MLWA8−10). From these results, it is possible to assess the potential of Bi NPs as environmental sensors and investigate the size- and shape-mediated tunability of their optical response from the near-ultraviolet to the near-infrared, together with the mechanisms driving their resonant optical behavior.

In this context of exploring the optical properties of NPs of different natures, little has been done about bismuth, despite the fact that it is an interesting element because of its rich electronic band structure. Indeed, in the past, most of the studies about Bi have been focused on its peculiar electrical properties.11−13 Bulk monocrystalline Bi is a semimetal that presents a particularly high mean free path (in the micrometer range at room temperature14), a long de Broglie wavelength (about 50 nm11,12) and a low effective mass11,12 for the conduction electrons and giant magnetoresistance effects.11,12 Electronic confinement effects have been observed in monocrystalline Bi thin films11,18 and Bi nanowires,12 resulting in a thickness- or diameter-controlled conductivity and allowing a semimetal-to-semiconductor transition at thicknesses or diameters of a few tens of nanometers.15 In addition, although the optical response of bulk Bi14,16,17 and Bi thin films18−21 has been at the focus of several studies, very few results have been reported concerning the optical response of Bi nanostructures, such as NPs.22−27 Moreover, these studies are restricted to Bi NPs of uncontrolled or very specific size, shape, and organization.22−27 Therefore, at this moment, it is necessary to analyze and discuss in detail the optical response of Bi NPs as a function of their size, shape, and environment. In addition to the inherent fundamental interest, addressing the role of these parameters will have impact for optimizing devices based on the optical response of Bi NPs, such as environmental or thermo-optical sensors.28 In this paper, we first investigate by experimental means the optical response of tailor-made two-dimensional (2D) distributions of Bi NPs. To avoid aging or diffusion of the Bi NPs, they have been embedded in a dielectric matrix. Amorphous aluminum oxide (a-Al2O3) has been chosen, since it shows excellent chemical stability and transparency in the wavelength range of study28 and is thus a suitable host matrix for performing a reliable optical and structural characterization of the 2D distributions of Bi NPs. The distributions of Bi NPs were prepared by the pulsed laser deposition (PLD) technique,

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EXPERIMENTAL METHODS The PLD technique has been used to grow nanostructured thin films consisting of a 2D distribution of Bi NPs sandwiched between two thin a-Al2O3 layers (a-Al2O3/Bi NPs/a-Al2O3). For this purpose, sequential ablation of an Al2O3 target and a high purity Bi target was achieved using a 193 nm pulsed ArF laser in a vacuum chamber with a base pressure of 10−6 Torr.30 Substrates of fused silica, silicon, and carbon-coated mica held 20531



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work that PLD enables the formation of high quality stable continuous polycrystalline Bi thin films with a smooth surface, in contrast with other physical vapor deposition techniques that tend to form easily oxidized porous films with a high surface roughness.20 Optical Characterization of the 2D Distributions of Embedded Bi NPs. Figure 2a shows the optical transmittance

at room temperature were used simultaneously for each deposition to have the same films available for different characterization techniques. First, a 20-nm-thick a-Al2O3 buffer layer was deposited on the substrates. Bi was then deposited on this buffer layer to form Bi NPs (following a Volmer−Weber-like mechanism). Finally, a second 20-nm-thick a-Al2O3 layer was deposited to cap the Bi NPs and protect them from the ambient. Films containing different amounts of Bi were grown by adequately choosing the number of pulses on the Bi target, leading to Bi effective thickness (tBi) values ranging from 2 to 6 nm, as determined from a calibration performed by Rutherford backscattering on thick films. As the Bi content was increased, the topology of the 2D Bi NPs distribution varied from well separated Bi NPs (nucleation regime) to structures with Bi NPs in contact (percolation regime). In addition, a continuous 120nm-thick Bi film was grown as reference, under conditions similar to those of the a-Al2O3/Bi NPs/a-Al2O3 thin films. Structural characterization of the a-Al2O3/Bi NPs/a-Al2O3 thin films grown on carbon-coated mica substrates was performed by conventional TEM. Optical characterization of these trilayered films prepared on fused silica was performed by transmittance measurements at normal incidence in the 300− 1700 nm range using a Varian Cary 5000 dual-beam spectrophotometer. The optical characterization of these films was completed by transmittance measurements at oblique incidence (70°) with linearly P- or S-polarized light using a VASE spectroscopic ellipsometer from J. A. Woollam Co., Inc. Spectroscopic ellipsometry measurements on the continuous 120-nm-thick Bi film was performed using the VASE ellipsometer, to determine its complex dielectric function that was extracted using the WVASE32 software provided by Woollam Co., Inc.

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RESULTS AND DISCUSSION Topology of the 2D Distributions of Embedded Bi NPs. Figure 1 shows TEM plan-view micrographs of three aAl2O3/Bi NPs/a-Al2O3 thin films with Bi effective thickness of (a) 2, (b) 3, and (c) 4 nm. In addition, a schematic cross section view of one film with well separated NPs is shown in Figure 1d. Bi NPs are observed in the three films; however, with different sizes, in-plane projected shapes and surface densities. The structure of the film with the lowest Bi effective thickness (tBi ∼ 2 nm, Figure 1a), which consists of well separated NPs with a quasi-circular in-plane projected shape, is typical of the nucleation regime of a Volmer−Weber-like growth.31 The average characteristic in-plane diameter of the NPs according to the size histogram is in the 10 nm range. Upon increasing the Bi effective thickness (up to tBi ∼ 3 nm, Figure 1b), coalescence events lead to the formation of bigger NPs whose in-plane projected shape is mainly elliptic (and dendritic for some NPs) likely as a result of kinetic limitations.31 The average characteristic in-plane diameter of the NPs according to the size histogram is in the 20 nm range, and the size distribution is quite broad. At higher Bi effective thickness (tBi ∼ 4 nm, Figure 1c), larger and almost connected dendritic Bi NPs are observed, suggesting that the percolation threshold of the Bi deposit is reached for an effective thickness just above 4 nm. The first stages of the PLD growth of Bi on the a-Al2O3 buffer layer are thus similar to those described for other metals when deposited on a dielectric substrate.29,31 For thick Bi films, effective thicknesses higher than 20 nm, it has been shown in an early

Figure 2. (a) Transmittance spectra measured at normal incidence of four a-Al2O3/Bi NPs/a-Al2O3 thin films with Bi effective thickness tBi varied between 2 and 6 nm. (b) Normalized absorbance spectra of two nanostructured thin films, measured at oblique incidence (70°) with Sand P-polarized light. One of the films (left) presents almost spherical Bi NPs, and the other (right), in-plane elongated Bi NPs.

spectra measured at normal incidence in the 300−1700 nm range for a-Al2O3/Bi NPs/a-Al2O3 thin films with Bi effective thicknesses of about 2, 3, 4, and 6 nm. The transmittance of the film with the lowest Bi content (tBi ∼ 2 nm) is low in the nearultraviolet and increases as a function of the wavelength, reaching a high transparency. This behavior is probably due to the presence of an absorption band in the ultraviolet at a wavelength lying below the measurement range. For tBi ∼ 3 nm, the spectrum is dominated by an absorption band peaking below 400 nm (named hereafter “near ultraviolet band”), and a second band can be seen as a faint shoulder around 600 nm (“red band”). Upon further increase in the Bi content, both the near-ultraviolet and the red bands shift toward longer wavelengths, the contribution of the red band gradually increasing. As a consequence, a camel-like structure located in the near-ultraviolet to visible range is seen in the transmittance spectrum for tBi ∼ 4 nm. The transmittance spectrum of the 20532



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percolated film (tBi ∼ 6 nm) is dominated by the red band and presents a broad absorption extending from the near-ultraviolet to the near-infrared. In other words, the minimum of transmittance gradually shifts toward the infrared and the range of absorption broadens upon increasing tBi. Such a trend is very similar to that observed in 2D distributions of noble metal NPs (Au and Ag) sandwiched between dielectric layers, which displays a red shift and a broadening of their SPR-related absorption band upon increasing the metal coverage, as a result of a flattening of the NPs, an increase in the width of their shape and size distributions and of the electromagnetic coupling between them.31 2D distributions of noble metal NPs sandwiched between dielectric layers also frequently present a uniaxial anisotropic optical response,32 the optical axis being perpendicular to the plane of the distribution. This anisotropy, which may result from either the 2D distribution of the NPs or their nonspherical shape together with a specific ensemble orientation, is driven by the existence of distinct SPR modes that can be selectively excited if the excitation field is oriented in the plane of the 2D distribution (in-plane modes) or perpendicularly to it (perpendicular modes). For instance, when noninteracting small noble metal NPs present an oblate spheroidal shape with their long axis in the plane of the 2D distribution, one in-plane and one perpendicular SPR mode can be excited, the former peaking at a longer wavelength than the latter. In-plane SPR modes are usually probed by optical transmittance measurements at normal incidence or at oblique incidence with S-polarized light, whereas perpendicular modes can be observed at oblique incidence with P-polarized light.32 Figure 2b presents the spectra obtained by optical transmittance measurements at oblique incidence (70°) and for both polarizations, for two a-Al2O3/Bi NPs/a-Al2O3 thin films, one containing nearly spherical NPs (left panel) and the other one containing coalesced NPs (right panel). Because of the large contrast between transmittance values measured under different polarizations, we have represented the absorbance A = −log(T) normalized to its highest value in the wavelength range of interest so that the shape of the spectra measured under S- and P-polarized light can be easily compared. For the case of nearly spherical NPs (left panel) a slight difference can be already observed between the two spectra at different polarizations, and it becomes clearly marked for the case of coalesced NPs (right panel). Indeed, for the second case, the S-polarized absorbance peaks at 400 nm, and a shoulder is present around 600 nm, whereas the P-polarized absorbance decreases almost linearly upon increasing the wavelength. This behavior is similar to that observed for metal NPs sandwiched between dielectric layers32 and is consistent with the existence of polarization-sensitive inplane and vertical absorption modes. Optical Characterization of the Continuous 120-nmthick Bi Film. To understand the optical response of NPs of a given nature, it is usually necessary to know the optical response of the corresponding bulk material. For this purpose, a continuous 120-nm-thick Bi film grown under conditions similar to that of the a-Al2O3/Bi NPs/a-Al2O3 thin films was studied by optical transmittance and spectroscopic ellipsometry in the 300−1700 nm wavelength range, that is, in a wider range than in previous works, which were restricted to the visible.20 The Bi film deposited on a transparent fused-silica substrate presents a null transmittance in the whole 300−1700 nm range, thus allowing extracting the dielectric function of the film from the ellipsometry data using a semi-infinite medium model. This

medium was considered as optically isotropic, and its dielectric function was modeled using a generalized oscillator model consisting of the sum of a Drude function, Kramers−Krönigconsistent Tauc−Lorentz oscillators, and a constant offset. Simultaneous fitting was performed on the tan(Ψ) and cos(Δ) spectra measured at three incidence angles (60°, 65°, 70°). The excellent agreement between the best fit and experimental ellipsometry spectra can be seen in Figure 3 (upper parts),

Figure 3. Real and imaginary part (ε1 and ε2) of the dielectric function of the continuous 120-nm-thick Bi film, as determined by spectroscopic ellipsometry, and of Ag and Au (taken from reference 33). The experimental ellipsometric Ψ and Δ spectra are also shown, together with the best fit curves.

together with the obtained spectra of the real (ε1) and imaginary (ε2) parts of the dielectric function of the Bi film, which overlap perfectly with those obtained in previous works restricted to the visible range.20 For comparison, the real and imaginary part of the dielectric function of Ag and Au taken from the literature33 are also shown. In contrast with Ag an Au, the ε1 spectrum of the Bi film does not show a monotonic decrease upon increasing the wavelength, but a slow decrease with a minimum around 900 nm, followed by a nonlinear increase at longer wavelength, which is typical of a marked nonDrude behavior in the near-infrared and consistent with previous reports about bulk Bi crystals.21 This non-Drude behavior occurs together with high ε2 values, especially in the near-infrared, likely because of the excitation of interband transitions in the visible and near-infrared ranges.21 Modeling of the Optical Response of the 2D Distributions of Embedded Bi NPs. Simulations of the optical response of a-Al2O3/Bi NPs/a-Al2O3 films corresponding to the different stages of growth of the Bi NPs have been performed considering the 2D distribution of embedded Bi NPs as an effective medium sandwiched between two a-Al2O3 thin layers, the trilayered stack being supported on a substrate, as shown in Figure 4. In the nucleation and coalescence regimes (typically for tBi ∼ 2 and ∼ 3 nm in Figure 1), the NPs present an isotropic inplane organization, and their shape can generally be reasonably considered as spherical, spheroidal, or ellipsoidal, two of the principal axes of the ellipsoids being randomly oriented in the plane of the 2D distribution. Assuming that the NPs are small compared with the wavelength of light (quasistatic size regime) and that they are separated enough, they can be considered as quasistatic dipoles (quasistatic dipolar approximation) that 20533



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models based on the quasistatic dipolar approximation. An alternative for a fast first estimation of the optical response of the almost percolated systems of NPs consists in using the Bruggeman’s model,36 which has proved to be useful in such cases. This model considers the NPs to be embedded in the effective medium, whose optical response is a function of εm, εi and the NPs volume fraction, f. Two simulations (numbered 3 and 4) have been performed using this model for two different volume fractions to treat the case of systems of NPs close to the percolation regime. In the four simulations, the dielectric function of the embedding medium, εm, was taken as equal to 2.72; that is, the value determined for PLD-grown a-Al2O3 thin films by spectroscopic ellipsometry, and the dielectric function of the Bi film as shown in Figure 3 was taken for εi. After determining the dielectric tensor or function of the effective medium, the corresponding transmittance of the trilayered stack supported on a fused-silica substrate was calculated in the framework of the Abelès matrix formalism. The layer thicknesses, effective medium model used, and input parameters for the four simulations are gathered in Table 1. Figure 5a shows the transmittance spectra obtained at normal incidence for the four simulations. Figure 5b shows the normalized absorbance spectra obtained at oblique incidence (70°) with S- and P-polarized light for simulations 1 and 2. The trends observed in Figure 5a are in excellent qualitative agreement with the experimental results shown in Figure 2 and discussed above. Indeed, in the nucleation regime (spherical and well separated NPs, simulation 1), an absorption band peaking below 400 nm is obtained. This “near ultraviolet band” is also present in the coalescence regime (ellipsoidal and well separated NPs, simulation 2), although slightly shifted toward longer wavelengths, together with a “red band” appearing as a shoulder around 600 nm. Broader absorption bands extending in the whole spectral range of the figure and presenting a camellike spectral shape resulting from the contribution of both nearultraviolet and red bands are obtained from simulations 3 and 4, as observed experimentally for almost percolated Bi NPs in Figure 2. These two simulations also reproduce well the changes in the spectral shape of the camel-like absorption band when the amount of Bi is increased, that is, the spectral broadening toward the near-infrared, the increase in the contribution of the red band, and the shift of the minimum of transmittance toward the near-infrared. The trends observed in Figure 5b are also in good qualitative agreement with the experimental results. Especially, simulation accounts well for the difference between S-polarized absorbance (peak at 400 nm and shoulder around 600 nm) and P-polarized absorbance

Figure 4. Schematic representation of the layered structure equivalent to an a-Al2O3/Bi NPs/a-Al2O3 film as used for calculating its transmittance spectra using an effective medium-based approach.

interact through their quasi-static electric dipolar fields. Under such conditions, the optical response of the effective medium is described by a dielectric tensor whose in-plane and vertical components, εeff,xy and εeff,z, read as, for a 2D distribution of monodisperse ellipsoidal NPs:34 ⎧ ⎡ ⎤ ⎪ NS(αa + αb) ⎢ ⎥ ⎪ εeff, xy = εm⎢1 + ⎡ ⎥ NS ⎤ 2t ⎣1 − 8Λ (αa + αb)⎦ ⎥⎦ ⎪ ⎢⎣ ⎪ ⎨ ⎪ ⎡ ⎤−1 NSαH ⎪ ⎢ ⎥ ⎪ εeff, z = εm⎢1 − ⎡ ⎥ NS ⎤ t⎣1 + 2Λ αH ⎦ ⎥⎦ ⎪ ⎢ ⎣ ⎩

(1)

where εm is the dielectric function of the homogeneous embedding medium, NS is the NP in-plane density, Λ is the center-to-center interparticle distance, t is the thickness of the effective layer, αa and αb are the quasistatic polarizabilities of the NPs along their two in-plane axes of lengths a and b, and αH is that along their vertical axis of height H. These polarizabilities are given by35 εi − εm V αu = εm + Lu(εi − εm) (2) where εi is the dielectric function of the material constituting the NPs and V is the NP’s volume. Lu is the depolarization factor of the NP along the axis u, and is a function of a, b, and H.35 Two simulations have been done using eq 1, assuming on one hand spherical NPs (simulation 1) and, on the other hand, ellipsoidal NPs (simulation 2) to describe the case of NPs in the nucleation regime and in the coalescence regime, respectively. Close to and at the percolation threshold (tBi ∼ 4 nm and above), the effective medium model described above is useless because of the complex morphology of the NPs, their dense packing, and large size that prohibit the use of simple

Table 1. Sets of Parameters Used for Calculating the Transmittance Spectra of a-Al2O3/Bi NPs/a-Al2O3 Thin Films from Effective Medium-Based Simulationsa label

thicknesses (nm) buffer/effective medium/cap

1 2 3 4

20/10/12 20/12/11 20/15/9 20/16/10

effective medium model used for the central layer

D (nm)

H (nm)

a/b

Λ (nm)

f (%)

2D distribution of ellipsoids embedded in a homogeneous matrix; dipole−dipole coupling; monodisperse34

10 20

10 12

1 0.6

20 35

13 17 25 35

Bruggeman’s model36

a The central layer of embedded NPs is considered as an effective medium layer, sandwiched between a dielectric a-Al2O3 buffer and a dielectric aAl2O3 cap. For simulations 1 and 2, the effective optical response of the central layer is derived using an anisotropic 2D model suitable to the case of ellipsoidal and well separated NPs,34 the input parameters being the diameter, D; height, H; in-plane axis ratio, a/b; and interparticle distance, Λ. For simulations 3 and 4, the effective optical response of the central layer is calculated using the Bruggeman’s model,36 with the Bi volume fraction, f, as input parameter. For comparison, the calculated value of f is given for simulations 1 and 2.

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extensively studied for the case of noble metal NPs,1 for the case of Bi NPs, there is no available optical information so far. Except for the fact that size and shape distributions are assumed to be monodisperse in simulations 1 and 2, the input structural parameters account reasonably for the nanostructure of the aAl2O3/Bi NPs/a-Al2O3 thin films with tBi ∼ 2 and ∼ 3 nm, respectively. Under such conditions, the excellent qualitative agreement between simulated and experimental transmittance spectra suggests that taking the dielectric function of the Bi thick film for εi is a reasonable choice. Therefore, the intrinsic electronic properties of the PLD-grown Bi NPs such as those shown in Figure 1 should not depart drastically from those of thin films grown by the same technique. This conclusion is in line with earlier works, which showed that the dielectric function of PLD-grown continuous thin films is independent of their thickness in the 20−200 nm thickness range20 and may suggest that there is not an important dependence of the electronic properties of PLD-grown Bi nanostructures or polycrystalline thin films on their dimensions. Optical Resonance of a Spherical Bi NP and Influence of the Environment. Since the dielectric function given in Figure 3 is an adequate input for a qualitative description of the optical response of 2D distributions of Bi NPs, it is useful for realizing a theoretical study aiming at the exploration of the optical response of a single Bi NP. For discussion purposes, simulations for Au and Ag NPs are also included. In the simplest case of a single spherical NP in a homogeneous dielectric medium and in the quasistatic size regime, valuable information about its optical response can be obtained after calculation of its field enhancement factor, η, and extinction efficiency, Qext,quasistatic. In the quasistatic dipolar approximation, the classical field enhancement factor, η = |E|2/|E0|2, at the surface of a sphere (along the diameter parallel to the incident field E0) and the extinction efficiency, Qext,quasistatic, are given, respectively, by38,8

Figure 5. (a) Transmittance spectra at normal incidence of four aAl2O3/Bi NPs/a-Al2O3 thin films calculated using the structure, models, and parameters presented in Figure 4 and Table 1. (b) Normalized absorbance spectra of the trilayered thin films labeled 1 (spherical NPs) and 2 (ellipsoidal NPs), calculated at oblique incidence (70°) with S- and P-polarized light.

3εi η= εi + 2εm

2

Q ext,quasistatic

⎡ ⎛ D ⎞2 ⎤−1 = ⎢π ⎜ ⎟ ⎥ k Im[α] ⎣ ⎝2⎠ ⎦ (3)

(almost linear decrease upon increasing the wavelength) in the case of coalesced NPs. At this point, it has to be highlighted that obtaining a quantitative agreement between simulation and experiment is out of the scope of this work. It would require the implementation of models able to take into account more accurately the nanostructure of the films and their interaction with light. In particular, close to the percolation threshold, where the densely packed Bi NPs present complex shapes and are so large that retardation effects are expected to play a significant role, numerical methods 37 would be more appropriate than the crude quasistatic Bruggeman’s model which, in addition, overestimates the interaction between NPs if their field enhancement factor is low. In contrast, in the nucleation and coalescence regimes, the optical response of 2D distributions of NPs embedded in a dielectric matrix can be quite accurately described by 2D effective medium models in the quasistatic dipolar approximation, provided they take into account the real size and shape distribution of the NPs.34 When using such effective medium models, a critical issue for simulating the optical response of the NPs is usually the choice of the dielectric function, εi, of the NPs, which may depart strongly from that of the corresponding bulk material due to finite size effects. Although finite size effects have been

where α is the polarizability of the sphere, obtained from eq 2 with Lu = 1/3 whatever u. Figure 6a presents the Qext,quasistatic and η spectra calculated using these relations, for 5-nm-sized Bi, Ag, and Au NPs in a-Al2O3 (εm = 2.72). This size was chosen to ensure that the quasistatic dipolar approximation is valid and that the extinction is due to pure absorption (no scattering). The dielectric functions shown in Figure 3 were taken for εi in the case of Bi and also for Ag and Au, for which confinement/ interface effects on the electronic properties of the material were not taken into account. Under such conditions, the optical response of plasmonic NPs can be compared in the absence of radiative losses and nonradiative surface-mediated losses, thus allowing a direct observation of the influence of nonradiative volume losses. The Ag NP presents a peak in its extinction spectrum at about 450 nm, due to the well-known SPR in a Drude-like metal. Resonant behavior is also evidenced for the Au NP with a maximum around 550 nm; however, it presents a lower peak value and a larger bandwidth as a result of the nonperfect Drude behavior of the Au dielectric function below 600 nm or, in other words, the interband damping of the SPR.1 The extinction spectrum of the Bi NP presents features comparable to those of the Au NP, with a maximum value around 300 nm 20535



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Figure 6. (a) Calculated spectra of the extinction efficiency, Qext,quasistatic, and field enhancement factor, η (inset), at the surface of a spherical Ag NP, Au NP, and Bi NP embedded in an a-Al2O3 matrix (εm = 2.72), in the quasistatic dipolar approximation. (b) Calculated spectra of the extinction efficiency Qext,quasistatic, of a spherical Bi NP as a function of the dielectric constant, εm, of the surrounding dielectric medium. A wide range of εm values is explored with the aim of a fundamental understanding of the effect of εm on Qext,quasistatic, but one has to keep in mind that transparent media with values of εm higher than 6.25 cannot usually be synthesized. The evolution of the wavelength of maximum extinction, εMAX, is plotted in part c as a function of εm.

when εm increases from 1 to 6.25 (i.e., the usual values for transparent dielectric for embedding NPs), underlining the potential of Bi NPs for refractive index sensing. Upon a further increase in εm, λMAX red-shifts asymptotically toward 900 nm, as could be expected in view of the minimum in the ε1(λ) spectrum of Bi (Figure 3) around this wavelength. As observed for transmittance spectra of 2D distributions of Bi NPs, a camel-like structure (induced by the bump in the ε1(λ) spectrum) is evidenced when the absorption maximum shifts toward 600 nm. A strong broadening occurs upon further red shift of the absorption band in correlation with the interbandmediated increase in ε2 with λ. Tuning the Resonances of Bi NPs through Their Size and Shape. The SPRs of noble metal NPs are known to be sensitive to the dielectric constant, εm, of the environment and also to the NPs' size and shape. We will therefore explore the tunability of the transverse resonance of an oblate spheroidal Bi NP through the control of its size and shape. The term “transverse” refers to an excitation electric field, E 0 , perpendicular to the revolution axis of the spheroid; in other words, in the same plane as its long axis. For this purpose, we have performed two sets of simulations of the extinction spectra of a Bi NP embedded in a-Al2O3, one in the quasistatic dipolar approximation and the other one in the modified long wavelength approximation (MLWA). The former approximation (used in the previous section) is suitable for the case of small NPs excited homogeneously by the incoming light (typically smaller than 20 nm, that is, in the quasistatic size regime), and the latter, to larger NPs (up to hundreds of nanometers8−10), in which the excitation field is not homogeneous over the whole NP and effects such as dynamic

and a broader absorption band. This similar behavior could be understood as the result of the excitation of a SPR in the Bi NP; however, with an important interband damping consistent with the high ε2 values observed in Figure 3. Similar features are observed in the η spectra, the Bi NP presenting a lower peak field enhancement factor than the Au and Ag NP. If ε2 is small and depends weakly on λ, it is seen from eqs 2 and 3 that a resonance in the extinction spectrum is excited when |ε1 + 2εm|2 is minimized, that is, if the wavelength λ verifies ε1(λ) = −2εm, and the ε2 value influences the width of the resonance. These conditions on ε1 and ε2 are well verified for a good Drude-like metal, such as Ag in the visible and nearinfrared or Au in the near-infrared. When interband transitions play a significant role, such as for Au in the visible, or, as we have seen for Bi, in the whole visible to near-infrared range (Figure 3), damping is observed, and variations of ε2 affect the resonance condition, but as a first approximation, the criterion ε1(λ) = −2εm can be used. Indeed, it accounts well for the presence of a resonance below 400 nm for a Bi NP in an aAl2O3 matrix. It would also predict a second resonance around 1200 nm, which is nevertheless not observed, probably because of the high ε2 value inducing a strong damping, inhibiting the resonance. Following the previous criterion, a sensitivity of the resonance wavelength of a Bi NP to the dielectric function of the surrounding medium is expected and should be comparable to that of Ag NPs in the visible range. Calculations of the extinction spectra of a Bi NP as a function of the dielectric constant, εm, of the surrounding dielectric medium confirm this prediction, as shown in Figure 6b. A red shift of the resonance wavelength λMAX from 300 to 400 nm is observed in Figure 6c 20536



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Figure 7. Transverse extinction spectra of an oblate spheroidal Bi NP in an a-Al2O3 matrix as a function of its projected diameter, D, and height, H, calculated in (a) the quasistatic dipolar approximation and (b) in the MLWA. The excitation electric field, E0, is in the plane as the long axis of the spheroid (E0//D), D and H are given under the form D:H (thus, H is fixed at 1 nm in part a and at 20 nm in part b). (c) Evolution of the resonance wavelength, λMAX, taken from parts a and b as a function of the D/H axis ratio.

resonance wavelength, λMAX, increases with D/H; however, with an asymptotic behavior toward 900 nm due to the intrinsic electronic response of Bi, as explained in the previous section. Therefore, shape-mediated tuning of the resonance wavelength of Bi NPs in quasistatic conditions should be limited to the near-ultraviolet and visible range, in contrast with Au or Ag NPs, whose SPRs can easily be tuned in the visible and nearinfrared.6 As shown in Figure 7b, bigger NPs, for which quasistatic conditions are not verified, also present a transverse resonant behavior that results in an extinction band. The contribution of scattering to this extinction band is significant and increases with D, whereas the resonance red-shifts. It can be seen in Figure 7c that λMAX increases linearly with D/H; thus, without asymptotic limit. This trend, different from that observed in the quasistatic size regime, can be explained by the fact that the resonance condition for “large” Bi NPs (≥100 nm) is influenced not only by the intrinsic electronic properties of the material but also by dynamic depolarization effects.2 This result is particularly interesting since it suggests that the inplane optical resonance of oblate spheroidal Bi NPs can be tuned from the near-ultraviolet to the near-infrared if the Bi NPs are large enough.

depolarization and radiative damping play a significant role.8,39 The transverse extinction cross sections calculated using both methods, Qxyext,quasistatic and Qxyext,MLWA, are given by xy Q ext,quasistatic

xy Q ext,MLWA

⎡ ⎛ D ⎞2 ⎤−1 = ⎢π ⎜ ⎟ ⎥ k Im[αxy] ⎣ ⎝2⎠ ⎦

(4)

⎡ ⎛ D ⎞2 ⎤−1 ′] = ⎢π ⎜ ⎟ ⎥ k Im[αxy ⎣ ⎝2⎠ ⎦

⎤−1 ⎡ k2 k3 ⎥ ′ = αxy⎢1 − αxy αxy − j αxy 2πD 6π ⎥⎦ ⎣

(5)

αxy is the polarizability of the oblate NP in the xy plane (given by eq 2). α′xy is the dynamic in-plane polarizability of the NP, which corrects the static polarizability, αxy, for dynamic depolarization (second-order term) and for radiative damping (third-order term). The extinction cross sections were calculated for a Bi NP as a function of its long axis length (or projected diameter), D, with its height, H, being fixed at 1 nm for the quasistatic simulations (taking this value for H is necessary so that the quasistatic dipolar approximation remains valid for all D values considered in the simulations) and at 20 nm for MLWA calculations. The obtained spectra are gathered in Figure 7a (quasistatic approximation) and b (MLWA). Simulations in the quasistatic size regime confirm that the extinction is due to pure absorption and that the absorption band red-shifts upon increasing the D/H ratio. It can be seen in Figure 7c that the

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CONCLUSIONS In this paper, we have reported that tailor-made Bi NPs display optical resonances whose features are typical of SPRs; however, with important interband damping. These resonances have been observed experimentally for 2D Bi NPs distributions, whose optical response is found to be sensitive to the size, shape, and organization of the NPs. We have then shown that 20537



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using the optical constants of a Bi thick film, it is possible to model qualitatively the response of the Bi nanostructures. This result has allowed us to establish a convincing knowledge of the Bi NPs optical response and to extend our analysis to the theoretical study of Bi NPs as a function of their size, shape, and environment. From the calculations, it is predicted that “large” Bi NPs, elaborated, for instance, by patterning, could be good candidates for obtaining well-defined resonances, which could be tuned from the near-ultraviolet to the near-infrared. Bi NPs could also be of potential interest for refractive index sensors based on the sensitivity of their resonances to the nature of the dielectric environment. This work highlights the potential of Bi nanostructures for optical applications and could be the starting point of studies of increasing complexity, aiming at the elaboration of Bi-based nanoengineered functional materials; for instance, for thermo-optical sensing. Indeed, sharp optical resonances in predesigned embedded Bi NPs may be very sensitive to structural transformations occurring during heating−cooling cycles.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research received funding from the European Community Seven Framework Programme (FP7-NMP-2010-EU-MEXICO) under Grant Agreement no. 263878. We also acknowledge financial support from the former Spanish Ministry of Science and Innovation (Grant No. JCI2009-05098 for J.T. and project MAT2009-14369-C02-02).

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