Article pubs.acs.org/JPCC
UV Plasmonic Behavior of Various Metal Nanoparticles in the Nearand Far-Field Regimes: Geometry and Substrate Effects J. M. Sanz,†,‡ D. Ortiz,†,‡ R. Alcaraz de la Osa,‡ J. M. Saiz,‡ F. González,‡ A. S. Brown,§ M. Losurdo,∥ H. O. Everitt,⊥,# and F. Moreno*,‡ ‡
Group of Optics, Department of Applied Physics, University of Cantabria, Avda de Los Castros, s/n 39005 Santander, Spain Departments of §Electrical and Computer Engineering and #Physics, Duke University, Durham, North Carolina 27708, United States ∥ Institute of Inorganic Methodologies and of Plasmas-CNR and INSTM, Via Orabona, 4-70126 Bari, Italy ⊥ U.S. Army Aviation and Missile RD&E Center, Redstone Arsenal, Alabama 35802, United States ABSTRACT: The practical efficacy of technologically promising metals for use in ultraviolet plasmonics (3−6 eV) is assessed by an exhaustive numerical analysis. This begins with estimates of the near- and far-field electromagnetic enhancement factors of isolated hemispherical and spherical metallic nanoparticles deposited on typical dielectric substrates like sapphire, from which the potential of each metal for plasmonic applications may be ascertained. The ultraviolet plasmonic behavior of aluminum, chromium, copper, gallium, indium, magnesium, palladium, platinum, rhodium, ruthenium, titanium, and tungsten was compared with the well-known behavior of gold and silver in the visible. After exploring this behavior for each metal as a function of nanoparticle shape and size, the deleterious effect caused by the metal’s native oxide is considered, and the potential for applications such as surface-enhanced Raman spectroscopy, accelerated photodegradation and photocatalysis is addressed.
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INTRODUCTION Plasmonics, a very active branch of nanophotonics, generally considers the electrodynamics of an electronic plasma confined in and near nanometer-sized metallic structures. The interaction with electromagnetic radiation in the visible or near-infrared frequency range generates very fast plasma oscillations and can lead to localized surface plasmon resonances (LSPRs) when the frequency of the incident field is properly tuned. LSPRs localize and strongly enhance the incident field near the nanostructure at dimensions much smaller than its wavelength. Exploiting these characteristics, plasmonic-based solutions have important practical applications in areas such as chemical sensing, health monitoring, therapeutics, optical communications, information storage, surface enhanced Raman and fluorescence spectroscopy, and photocatalysis.1,2 The ability to tune the LSPR by adjusting the composition, shape, and size of nanometer scale metallic structures has been actively investigated over the past decade.3,4 Most of this research has been performed on structures whose LSPR occurs in the visible, near-infrared, and even the terahertz spectral regions (i.e., λ > 400 nm).5 Gold (Au) has been widely used because of its compelling electromagnetic properties, its resistance to oxidation, its biocompatibility, and the ease with which gold nanoparticles may be functionalized.6 Until very recently, however, there has been little work on ultraviolet (UV) plasmonics (200 < λ < 400 nm, or 3−6 eV), in part © 2013 American Chemical Society
because the popular metals gold and silver do not exhibit plasmonic behavior beyond the visible and near UV, respectively.6−8 However, in response to an increasing demand to detect, recognize, and destroy biological toxins,9,10 to enhance biological imaging, and to characterize semiconductor devices at the nanometer scale, interest in UV plasmonics is growing.11−13 It has been recognized for some time that aluminum (Al) might be a compelling metal for UV plasmonics because its bulk plasma frequency is 13 eV.8,11,12,14−16 However, aluminum oxidizes even more rapidly than silver, a problem that introduces scientific and practical difficulties for implementing effective stable nanodevices. Consequently, there is a need to explore other metals that might be nanostructured for use in UV plasmonics. Here we present a theoretical analysis of several candidate metals and compare their performance in the UV to the performance of gold and silver in the visible spectral region. All candidate metals have a bulk plasma frequency higher than 3 eV, high enough that their LSPRs may occur in the UV region. Of the many metals in the periodic table that meet this criterion,17 the 12 metals selected for this investigation are aluminum (Al), gallium (Ga), indium (In), rhodium (Rh), ruthenium (Ru), tungsten (W), titanium (Ti), chromium (Cr), Received: June 11, 2013 Revised: August 16, 2013 Published: August 19, 2013 19606
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palladium (Pd), copper (Cu), platinum (Pt), and magnesium (Mg). Several of them, Pd, Pt, Ru, Rh, Ga, and especially Al, have already been investigated for surface-enhanced fluorescence (SEF), Raman spectroscopy (SERS), or label-free detection of biomolecules in the UV.18−20 The metals Al, Ga, In, and Mg are of particular interest because they may be deposited in the ultrapure environment of molecular beam epitaxy and integrated with active optoelectronic devices, while the rest were chosen because of their potential as electrodes for enhanced photocatalysis or photodegradation. Although early measurements have found enhancement factors for the transition metals to be considerably weaker than for Au and Ag in the visible,21−26 a systematic, practical comparison of the UV performance of these metals is needed, much as it was in the early days of plasmonics with metals whose LSPRs were primarily in the visible spectral region.3 In this investigation we specifically consider isolated metallic nanoparticles located on a dielectric substrate, like sapphire (n = 1.78) to mimic typical experimental conditions.27 This analysis of the anisotropic environment of a single nanoparticle resting on and interacting with the substrate provides a more practical initial assessment of the potential these metals possess for UV plasmonics than can be ascertained from simple isotropic analyses of isolated spherical nanoparticles. It also prepares the way for considering the additional complexity that arises when the interaction with other nanoparticles is introduced. The isolated nanoparticle on the substrate system will be excited by a monochromatic, linearly polarized plane wave, and the electromagnetic scattering problem will be numerically analyzed by using the discrete dipole approximation (DDA) method.28 The objective is to consider and compare the plasmonic absorption efficiency, the near field distribution, and related near field electromagnetic parameters for each metal. We conclude by exploring the effects of oxidation on UV plasmonic performance for selected metals.
Figure 1. The two scattering configurations analyzed: hemispherical (top) and spherical (bottom) nanoparticles on a sapphire substrate. Calculations were done for normal incidence and linearly polarized light as indicated in both figures.
ε(ν) = ε∞ −
νp2 ν(v + iγ )
+ εinter(ν)
(1)
where γ is a damping constant and νp is the plasma frequency. The Fröhlich frequency at which εr = −2 is approximately vf ≅(νp/(3)1/2) and corresponds to the frequency at which LSPRs may be excited in isolated metallic particles whose radius is much smaller than the wavelength. Figure 3a shows the value of the Fröhlich energy Ef = hνf for the different metals analyzed, ordered by the corresponding group of the periodic table. Vertical continuous lines denote the energy interval to be analyzed for each metal. The Fröhlich energy for most of the selected metals is larger than 4 eV, significantly higher than that for Au and even Ag. As with Au and Ag, Group VI elements tungsten and chromium have intraand interband transitions that extend into the UV, and the correspondingly large εi limits the potential of these elements for UV plasmonics. Conversely, the Fröhlich energy for Rh and Ga is Ef > 6 eV, above the range for which the dielectric function is available (Figure 3a), but the effects of nanoparticle shape and size, the substrate, the possibility of multiple scattering, and other factors lower the plasmonic resonance into the UV region. To estimate the efficiency of generating LSPRs, consider the figure of merit17,41
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SYSTEM GEOMETRY AND MATERIALS UNDER STUDY Two basic geometries, single nanometer-sized spheres and hemispheres on flat dielectric substrates, are analyzed (Figure 1). Spherical nanoparticles provide useful physical insight and represent many experimental situations, while hemispherical nanoparticles illustrate simple geometrical dependencies for nonspherical structures on substrates and capture the essential plasmonic spectral behavior.29,30 Indeed, Ga nanoparticles naturally form hemisphere-like geometries when deposited on substrates.19,20,27 For both basic geometries, the nanoparticle radius is 20 nm and the substrate is sapphire.27 The ensemble is illuminated by a normal incident monochromatic plane wave linearly polarized as indicated in the figure. The dielectric functions of most metals have been obtained from various sources in the literature: group II (Mg),31 group IV (Ti),32 group VI (Cr, W),33 group VIII (Ru),33 group IX (Rh),33 group X (Pd and Pt),34,35 and group XI noble metals (Au and Ag,32 Cu31). Figure 2a plots the real and imaginary parts of the dielectric function, ε = εr + iεi, for Mg, Ag, and Rh. The dielectric functions for group XIII metals (Al, Ga, and In, see Figure 2b) were measured in situ by spectroscopic ellipsometry applied to thick films (see Methods) and confirmed by values reported in the literature.36−39 The dielectric function of bulk metals is given by a Drude model40 with a high-frequency limit dielectric constant ε∞ and of the interband transitions, εinter(ν),
Q LSP =
v Re{ε} ≈− Δv Im{ε}
(2)
Qmax LSP
The maximum value of eq 2 is plotted in Figure 3b at the energy E = hν where that maximum occurs. The correlation between Ef and the spectral position of Qmax LSP is best when the approximation outlined in eq 2 is most valid: low absorption metals that produce narrow plasmonic spectra. By comparing these figures, it becomes evident that the most promising metals for UV plasmonics are Mg, Rh, Al, Ga, and In. By contrast, Ti, Cr, and W will have weaker UV LSPRs, and it is 19607
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Figure 2. (a) Real and imaginary part of the dielectric function for Mg, Ag, and Rh based on values in the literature. (b) Real and imaginary part of the dielectric function for Al, Ga, and In measured using spectroscopic ellipsometry. The horizontal red line represents εr = −2, which defines the Fröhlich energy Ef. The shadowed region corresponds to the UV range 3−6 eV.
Figure 3. (a) Fröhlich energy Ef of the bulk dielectric functions and (b) the maximum plasmonic performance value, Qmax LSP, plotted at the spectral position where it is achieved. Vertical lines represent the energy range to be analyzed for each metal. The shadowed region corresponds to the UV range 3−6 eV.
the incident field strength, and Qabs is normalized as described in the Methods section. (a). Near Field. In near field, |E|2max(ν) and ⟨|E|2⟩(ν) were calculated for 100 incident photon energies spanning 1.5−6.5 eV. To estimate these enhancements, the nanoparticle surface boundary was discretized into a mesh; the electric field intensity (Ij) was obtained for each intersection point (j) in the mesh. Because all data points should be equal in calculated surface average, the average intensity over the surface was evaluated by assigning the appropriate weight to each point (given by sin θ, see Figure 4). At the incident energy for which maximum enhancement is obtained, the near field distribution on the nanoparticle surface could always be described by a dipolar field distribution. For example, Figure 4 shows the near field intensity for a Ga hemispherical nanoparticle of radius R = 20
not clear whether the LSPRs for Ru, Pd, Pt, or Cu will fall in the UV region.
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RESULTS For each of the metals studied, the energy dependence of three parameters have been calculated and analyzed using DDA (see Methods): (1) the absorption efficiency Qabs(ν) of the particle system, (2) the maximum enhancement factor |E|2max(ν) of the electric field surrounding the particle, and (3) the electric field enhancement averaged over the surface ⟨|E|2⟩(ν). Although Qabs(ν) is usually associated with far-field extinction, |E|2max(ν) and ⟨|E|2⟩(ν) estimate the near-field behavior, which better predicts localized plasmonic performance for applications such as SEF or SERS. Both |E|2max(ν) and ⟨|E|2⟩(ν) are normalized to 19608
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(b). Comparative Study: 20 nm Hemispheres. In Figure 5, the spectral evolution of Qabs(ν), |E|2max(ν) and ⟨|E|2⟩(ν) are plotted for R = 20 nm metallic hemispheres on a sapphire substrate. Cu was not plotted because it behaves similarly to Au. Each of the metals except tungsten (not shown) exhibits a plasmonic resonance between 1.5 and 6.5 eV for the analyzed geometry and scattering configuration. The nature of this resonance is purely dipolar because the particle size is much smaller than the incident wavelength. Those metals for which the imaginary part of the dielectric constant is small present the strongest, narrowest resonances. For the visible and near-IR region, those metals include widely used Au and Ag of course, but also Cu and In. For the UV, both metallic Al and Mg have excellent electromagnetic properties, but both oxidize strongly and require careful processing and passivation to be practical (see section (e)). The resonances for Ga and Rh are slightly broader and weaker, and Ga is relatively unaffected by its minimal native oxide.20,27 Most of the metals possess inter- and intraband transitions that increase the imaginary part of their dielectric constants. This explains why Cr, Ru, Pd, Pt, and W have weaker, broader plasmonic resonances. Although Al also has an interband transition, it is near 1.4 eV and does not affect its UV performance. By contrast, Ag has an interband absorption near 4 eV that prevents it from extending its excellent plasmonic behavior into the UV. Notice the rather large redshift in the location of the peaks from Ef, an effect caused in most cases by the interaction with the substrate and by the size of the nanoparticles relative to the decreasing UV wavelength at increasingly high energies. For Cr and Ru an apparent blueshift is observed because of a low energy interband absorption feature. To demonstrate the potential of each metal for UV plasmonics, Figure 6 plots the maximum values of Qabs(ν) and |E|2max(ν) at the energy where the respective maxima are located. As expected, there is a good correlation between these far- and near-field parameters. However, Figure 5 reveals that the near-field peaks for |E|2max(ν) (and also for ⟨|E|2⟩(ν)) are
Figure 4. Near-field map for a hemispherical Ga nanoparticle (R = 20 nm) located on a sapphire substrate. The normal incident (xdirection) electromagnetic wave of wavelength λ = 286 nm is spolarized (z-direction). Inset: The top figure is a plot of the mesh showing the high field intensity regions, and the bottom figure is the near-field map for a spherical Ga nanoparticle (R = 20 nm, λ = 225 nm) located on a sapphire substrate.
nm illuminated by a normal incidence, s-polarized plane wave at the wavelength at which |E|2max(ν) occurs (λ = 286 nm). High intensity lobes (hot-spots) appear aligned with the polarization, slightly shifted above the equatorial plane of the nanoparticle by its geometry and substrate. Indeed, the highest intensity hot-spots are typically located near the intersection of the polarization plane, the substrate, and the nanoparticle surface for all the analyzed metals. For a spherical nanoparticle, the hot-spots are located near the intersection with the substrate, opposite the incident beam and therefore silhouetted by the sphere (Figure 4, bottom right inset).42,43 Likewise, the hot spots for hemispherical nanoparticles are also near the interface with the substrate, but the high field intensity values extend above the interface and are not silhouetted (Figure 4, top right inset). Hemispherical geometries are therefore more practical for experimental demonstrations.
Figure 5. Absorption efficiency, Qabs(ν) (black circles), maximum electric field enhancement, |E|2max(ν) (red squares), and surface-averaged enhancement, ⟨|E|2⟩(ν) (blue triangles), for hemispherical nanoparticles of 20 nm radius located on a sapphire substrate for all metals considered except Cu and W. A dashed vertical line is placed at Ef. The shadowed region corresponds to the UV range 3−6 eV. 19609
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be explored further below.44−46 For now, it suffices to point out that the optimal wavelength for near-field enhancements (e.g., SEF or SERS) may be different than what is measured using far field techniques like absorption spectroscopy or ellipsometry. This plasmonic resonance red-shift is largest for Ru, Pd, and Pt, and only Ru remains in the UV in the near-field. (c). Influence of Shape and Size of the Nanoparticle. It is well-known that a nanostructure’s size and shape critically affect its plasmonic performance,19 and these sensitivities are even stronger in the UV.15 Using the simple geometry of a metallic sphere or hemisphere on a sapphire substrate (Figure 1), insight about the effect of nanoparticle shape and size may be obtained. Figure 7 compares numerical simulations for both shapes of Mg, Rh, Al, Ga, and In nanoparticles on sapphire supports. The top two rows compare spheres and hemispheres with 20 nm radii, revealing that the LSPR peaks for hemispheres of each metal are red-shifted more than 1.5 eV relative to the spheres. This occurs because, as compared to spherical nanoparticles, the effective dipole moment in a hemispherical nanoparticle is closer to the substrate and interacts more strongly with it.19 This can also be explained with a quasi-static image dipole approach using a dipole interaction model.47 This effect is seen even more clearly in the bottom three rows of Figure 7, which compare the spectral evolution of Qabs(ν), |E|2max(ν), and ⟨|E|2⟩(ν) for three hemispherical radii (20, 40, and 60 nm). Besides the well-understood sizedependent red shift of the peaks with increasing radius, note that the absorption peak also decreases as the particle size increases. Again, these features are strongly affected by interaction between the particle’s “effective dipole” and the substrate: both the red shift and the reduction in absorption strength are partially a result of the weakening interaction as the particles grow and the “effective dipoles” separate from the substrate.19,47 Other absorption peaks, due to other dipolar plasmonic modes, multipolar effects at higher energies, and
Figure 6. Maximum far-field absorption efficiency, Qmax abs (top), and near-field electric field enhancement peak, |E|2max (bottom), for R = 20 nm hemispherical particles of each metal on sapphire, plotted at the respective energies where the peaks occur. The shadowed region corresponds to the UV range 3−6 eV.
red-shifted with respect to the far-field peak Qabs(ν), especially when the resonances are broad. This effect has been shown to depend on the imaginary part of the dielectric constant and will
Figure 7. Absorption efficiency, Qabs(ν) (black circles), surface-averaged enhancement, ⟨|E|2⟩(ν) (blue triangles), and maximum electric field enhancement, |E|2max(ν) (red squares) for sapphire-supported nanoparticles of Mg, Rh, Al, Ga, and In. (top row) Spherical nanoparticles with 20 nm radius, then (second row) hemispherical nanoparticles with radii of 20 nm, (third row) 40 nm, and (bottom row) 60 nm. A dashed vertical line is placed at Ef. The shadowed region corresponds to the UV range 3−6 eV. 19610
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Figure 8. Spectral evolution of the surface-averaged intensity peak, ⟨|E|2⟩, for hemispherical (R = 20, 40, and 60 nm) and spherical (R = 20 nm) metal nanoparticles on sapphire (a) without and (b) with good UV coverage and performance. The shadowed region corresponds to the UV range 3−6 eV.
Figure 9. Plot of the near-field line width of |E|2max(ν) and the red-shift from the near field enhancement peak |E|2max to the far-field peak Qmax abs for hemispherical (R = 20 nm) nanoparticles on sapphire, as a function of (a) the εi value at Ef and (b) the εi value at the maximum absorption efficiency value, Qmax abs . Please note that blue right vertical axis is in reverse order from the red left one.
transverse (p-polarized) plasmon resonances may be excited, the latter arising from the electric field component of the incident field perpendicular to the substrate. For the hemispherical geometry, the dimension of the transverse dimension is half the longitudinal one, from which the resonance is split into a lower frequency longitudinal and higher frequency transverse mode. Of course the longitudinal mode is always present and dominates at and near normal incidence, so it is this mode that is of primary importance for applications like SERS or SEF. However, many of the metals that do not possess UV LSPRs for the longitudinal modes analyzed here will possess transverse LSPRs in the UV (but red-shifted from Ef) for non-normal incidence. A recently investigated example is Ga, which naturally forms hemispherical nanoparticles when deposited on sapphire and has been shown to possess transverse LSPRs in the deep UV when investigated by grazing incidence ellipsometry.8,20,27 Similar observations of transverse LSPRs in the UV are expected for elements whose longitudinal LSPRs are in the visible, including Rh, Ru, Cr, Ti, Pd, and Pt. (d). Shift of the LSP from Far to Near Field. It was noted above that the wavelengths at which near field peak enhancements |E|2max(ν) and ⟨|E|2⟩(ν) occur is red-shifted from the wavelength at which the far field peak absorption Qabs(ν) occurs (Figures 5 or 6).44−46 To understand the reason for this, consider Figure 9, whose red curve plots this red-shift versus the value of εi at Ef for all metals studied (note that Ga
interband transitions, are also observed when the size of the particle increases. Consider next the size of the enhancement. Figure 8 summarizes the dependence of ⟨|E|2⟩(ν) on shape and size for all the metals analyzed. Although most metals exhibit some plasmonic behavior in the UV region, the behavior is quite dependent upon the metal, its shape, and its size. The most promising of these UV plasmonic metals are Mg, Al, Ga, In, Rh, and Ag, all of which have peaks that red-shift and weaken as size increases. By contrast, Ru, Cr, and Ti, all of which may prove useful for specific applications, have relatively weaker UV plasmonic behavior. The peak ⟨|E|2⟩(ν) values always increase when replacing a sphere with a hemisphere of radius 20 nm, but for weaker metals like Rh, Ru, and Cr the peak value occurs not for the smallest hemispheres but near R = 40 nm. Note that W will only work in the UV over a limited size range, because its red shift is extremely dependent on the particle size (the resonance peak moves from above 6 eV to below 3 eV simply by tripling the radius). In addition, Ag, In, Ti, Ru, and Cr quickly red-shift out of the UV as size increases, a shift exacerbated by the substrate. It is important to remember that all the analysis has been done for normal incidence (Figure 1) so that the excited plasmonic resonances represent longitudinal oscillations of electrons parallel to the surface of the substrate. For incidence angles other than normal, both longitudinal (s-polarized) and 19611
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and Rh are not plotted because their Ef is unknown). A remarkably good correlation is found: metals with low dielectric losses (εi < 3: Mg, Al, Cu, Ag, Au, In) exhibit very small redshifts ( 5: Cr, Pt, Pd, Ru) exhibit a large red-shift (0.3−1 eV), because of strong damping, often the result of inter- and intraband absorption. This damping causes the near-field line width of these resonances to increase with increasing εi, as can be seen in the blue curve of Figure 9a. In fact, it was found that a power law relationship (y = a·xb) connects this inherent property of the material x with both its red-shift from far to near field (redsolid line: a = 1.23 × 10−3, b = 3.35) and its line width at the LSPR frequency (blue-dashed line: a = 7.56 × 10−2, b = 1.53). This analysis confirms that the physical mechanism responsible for the near-to-far-field shift and line broadening is metallic damping, characterized by εi at Ef. However, a more practical analysis considers the relationship between these parameters at the measurable maximum far-field absorption efficiency Qmax abs . As shown in Figure 9b, strong absorption efficiency is correlated with narrow linewidths and small nearto-far-field shifts, while metals with weak absorption efficiencies will also exhibit large linewidths and large near-to-far-field shifts (red-solid line: a = 2.09 × 10−2, b = 2.09; blue-dashed line: a = 8.92 × 10−2, b = 1.56). Note that Figure 9b also includes Ga and Rh, confirming the universal nature of this relationship.46 Indeed, this result can serve as a guideline for experimentalists interested in considering these or other metals for applications where spectroscopic techniques enhanced by surface electromagnetic effects are used and accurate spectral parameters have to be measured. (e). Considerations about Oxidation. Considering the relevance of these metals for plasmonic applications, understanding the oxidation of metal nanoparticles is crucial for predicting and characterizing the UV plasmonic response. Experimental reports on the effect of nanoparticle oxidation on plasmonic performance are limited to a nearly exclusive focus on the noble metals Au and Ag.48 The room temperature oxidation of nanoparticles generally occurs upon atmospheric exposure after nanoparticle synthesis. The rate of oxidation can vary from very fast (90%) and resist oxidation (reflectivity
