Performance analysis of nitride alternative plasmonic materials for localized surface plasmon applications

Transcription

1 Purdue University Purdue e-pubs Birck and NCN Publications Birck Nanotechnology Center Performance analysis of nitride alternative plasmonic materials for localized surface plasmon applications U. Guler Birck Nanotechnology Center, Purdue University, Gururaj V. Naik Birck Nanotechnology Center, Purdue University, Alexandra Boltasseva Birck Nanotechnology Center, Purdue University; Technical University of Denmark, Vladimir M. Shalaev Birck Nanotechnology Center, Purdue University, Alexander V. Kildishev Birck Nanotechnology Center, Purdue University, Follow this and additional works at: Part of the Nanoscience and Nanotechnology Commons Guler, U.; Naik, Gururaj V.; Boltasseva, Alexandra; Shalaev, Vladimir M.; and Kildishev, Alexander V., "Performance analysis of nitride alternative plasmonic materials for localized surface plasmon applications" (2012). Birck and NCN Publications. Paper This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information.

2 Appl Phys B (2012) 107: DOI /s Performance analysis of nitride alternative plasmonic materials for localized surface plasmon applications U. Guler G.V. Naik A. Boltasseva V.M. Shalaev A.V. Kildishev Received: 20 January 2012 / Published online: 21 March 2012 Springer-Verlag 2012 Abstract We consider methods to define the performance metrics for different plasmonic materials to be used in localized surface plasmon applications. Optical efficiencies are shown to be better indicators of performance as compared to approximations in the quasistatic regime. The near-field intensity efficiency, which is a generalized form of the wellknown scattering efficiency, is a more flexible and useful metric for local-field enhancement applications. We also examine the evolution of the field enhancement from a particle surface to the far-field regime for spherical nanoparticles with varying radii. Titanium nitride and zirconium nitride, which were recently suggested as alternative plasmonic materials in the visible and near-infrared ranges, are compared to the performance of gold. In contrast to the results from quasistatic methods, both nitride materials are very good alternatives to the usual plasmonic materials. 1 Introduction Intensive studies and promising results on localized surface plasmon resonances (LSPR) have appeared in the pub- Electronic supplementary material The online version of this article (doi: /s ) contains supplementary material, which is available to authorized users. U. Guler G.V. Naik A. Boltasseva V.M. Shalaev A.V. Kildishev ( ) School of Electrical and Computer Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA kildishev@purdue.edu A. Boltasseva DTU Fotonik, Technical University of Denmark, Kgs. Lyngby 2800, Denmark lished literature over the last three decades. Following the improvements of both computing capabilities and nanomanufacturing techniques, the LSPR systems under consideration by researchers world-wide became more and more sophisticated [1]. It is well known that the resonance conditions in an LSPR system depend on the material properties of the plasmonic particle and the host medium as well as on the size and shape of the particle [2]. Efficient scatterers and absorbers with nanoscale dimensions are useful in a wide range of applications with diverse operating wavelengths. So far, the majority of the studies in LSPR systems have focused on the shape and size of plasmonic nanoparticles and shells in order to obtain resonances in different regions of the electromagnetic spectrum [3]. Gold and silver have experienced the most interest in such studies, due in part to their superior performance in the visible region. However, with increasing demands for plasmonic structures operating at longer wavelengths, especially in the technologically important spectrum of the near-infrared, alternative plasmonic materials are becoming attractive [4, 5]. Conventional metals have extremely large magnitudes of real permittivity and quite high losses in the visible and near-infrared. Moreover, their optical properties cannot be tuned or modified easily. Conventional metals are also disadvantageous in terms of nanofabrication and integration, especially because of their incompatibility with standard silicon manufacturing processes. Thus, alternative plasmonic materials are vital from a technological perspective. Recently, semiconductor-based plasmonic materials have been proposed as alternatives to metals in the near-infrared [6], while transition-metal nitrides have been proposed in the visible and near-infrared regions [7, 8]. With many different materials suggested for plasmonic applications, the need to evaluate their performance for spe-

3 286 U. Guler et al. cific applications has become increasingly important. Here, we consider LSPR applications and provide a consistent performance comparison metric. One of the methods to compare material performance is to examine the case of particles with sizes much smaller than the wavelength of excitation [9]. However, for some of the local-field enhancement applications, particles with relatively large dimensions are favorable since scattering efficiency is known to be proportional to a 6, where a is the radius of a spherical particle [10]. For larger scatterers, higher-order resonance modes are also excited and the system of collective oscillations becomes more complicated than the quasistatic case. Therefore, more detailed examination of material performance is needed. In this study, we use the concept of near-field intensity efficiency along with Mie calculations in order to provide a more comprehensive and convenient comparison metric for material performance without imposing any restriction on the size of the particle. We then use this metric to evaluate the performance of spherical nanoparticles made of a conventional metal (gold) and two nitride plasmonic materials, titanium nitride (TiN) and zirconium nitride (ZrN). TiN and ZrN are good alternative plasmonic materials for applications in the visible and infrared spectral regions, and they offer many advantages over gold and silver, including compatibility with industry-standard silicon nanofabrication techniques [7]. 2 Theory In 1908, Gustav Mie made an attempt to solve Maxwell s equations for single, spherical particles in order to obtain a deeper understanding of interaction of light with such particles [11]. The general idea behind what is now known as Mie theory is to expand the incident field into spherical harmonics and obtain the scattered field and the field inside the spherical particle by using coefficients extracted from the boundary conditions. The details of the procedure are clearly explained by Bohren and Huffman [12]. For a particle under illumination, the optical crosssections describe how the particle interacts with the incident light. The scattering cross-section, C sca, is the ratio of the scattered power to the incident power at large distances from the particle. In a similar manner, the absorption cross-section, C abs, is the ratio of the absorbed power within the particle to the incident power. Both the scattering and absorption efficiencies, denoted as Q sca and Q abs, respectively, are cross-sections normalized to the size of the particle. Another efficiency which helps to define total interaction of light with particle is the extinction efficiency and can be found as Q ext = Q sca + Q abs. Explicit expressions for the efficiencies are Q sca = C sca πa 2 = Q ext = C ext πa 2 = 1 2πa 2 I i Re 2π π 0 0 r 2 sin θdθdφ, 1 2πa 2 I i Re 2π π 0 0 ( Esθ H sφ E sφh sθ) ( Eiφ H sθ E iθh sφ E sθ H iφ + E sφh iθ) r 2 sin θdθdφ, where a is the radius of particle, I i is the incident irradiance, and the integration is performed over an imaginary sphere with radius r a. Rather than calculating the field distribution and performing the integration, it is easier to express the efficiencies in terms of Mie scattering coefficients as Q sca = 2 (ka) 2 (2n + 1) ( a n 2 + b n 2), Q ext = 2 (ka) 2 n=1 (2n + 1) [ Re(a n + b n ) ]. n=1 Researchers regularly use the above-mentioned efficiencies for a preliminary examination of plasmonic particles which are to be used for near-field enhancement applications [13]. However, as mentioned previously, these efficiencies are defined for observation distances far away from the particle. Thus they only account for far-zone fields. On the other hand, for most of the local-field enhancement applications, we are interested in field intensities in the close proximity of the resonant particle, which includes contributions from evanescent fields. Messinger et al. addressed this issue in an earlier study and suggested a more generalized expression for the scattered-field enhancement [14]. Later, Quinten extended the discussion to aggregates of spherical metal particles [15]. Including the scattered radial field components, which have evanescent behavior, and removing the restriction on the observation distance, the generalized scattering efficiency can be defined as Q sca = r2 2π π πa 2 E s Es sin θdθdφ, (3) 0 0 where the observation point can be chosen arbitrarily. In the limit of r a, Eq.(3) converges to the far-field scattering efficiency since all evanescent components disappear. Messinger et al. also defined a near-field intensity efficiency from the generalized expression by choosing the observation point at the surface of the particle, r = a, which can be written in terms of scattering coefficients as { Q NF = 2 an 2[ (n + 1) (2) h n 1 (ka) 2 +n (2) h n+1 (ka) 2 ] n=1 (1) (2) + (2n + 1) b n 2 h (2) n (ka) 2 }. (4)

4 Performance analysis of nitride alternative plasmonic materials for localized surface plasmon applications 287 Fig. 1 (a) Quality factor obtained for nanoparticles in the quasistatic limit. (b) Real and (c) imaginary part of dielectric constants for Au, TiN and ZrN The generalized form of the scattering efficiency can be a rather useful tool for figure-of-merit (FOM) considerations when particles with dimensions exceeding the quasistatic limit are examined for local-field enhancement applications. 3 Results and discussion Since plasmonic resonances are strongly material-dependent, a definition for the figure-of-merit or quality factor is required in order to classify materials for different applications. For LSPR applications, the most convenient way to define a quality factor is to consider a sphere in the quasistatic limit, which leads to Q = ε /ε, where ε and ε are the real and imaginary parts of the dielectric constant, respectively [16]. Although this approach can be useful in some cases, its reliability is limited by the validity of the quasistatic approximation, that is, a λ. Figure 1(a) presents the quality factors for Au, TiN and ZrN nanospheres calculated with this conventional formula for small particles. The optical constants for the materials used in the analysis and throughout this paper are plotted in Figs. 1(b, c). The dielectric functions of TiN and ZrN films deposited by a procedure described elsewhere [7] are retrieved from measurements made by spectroscopic ellipsometry (V-VASE, J.A. Woollam Co.). The optical constants of Au are obtained from Johnson and Christy [17]. Gold nanoparticles clearly provide much better performance when compared to the metal nitrides. However, for localfield enhancement applications, nanoparticles are usually employed at their corresponding resonance wavelengths. Thus, the maximum enhancement obtained with a gold particle does not necessarily occur at the same wavelength as the best performance for TiN. Accordingly, the size that provides the corresponding enhancement is not the same for both particles. Therefore, there are other parameters not included in our consideration with quasistatic approximation. Scattering efficiency is a useful tool for determining the optimum conditions for a resonant particle. However, as described earlier in this work, it is valid for observation distances far away from the particle. In consequence, detailed information on how the scattering efficiency varies with changing distance cannot be obtained from far-field definitions. Figure 2(a) gives Q sca obtained from Eq. (2) for spherical Au nanoparticles with varying radii in the visible and near-infrared regions. The well-known dipolar resonance for Au can be observed around 520 nm for small particles, and the amplitude increases with radius up to 92 nm where the quadrupole mode becomes observable. For larger sizes, the dipolar resonance red-shifts clearly and diminishes slightly while the quadrupolar peak gets stronger. Within the calculation range, changes in the amplitude of both peaks with increasing size are relatively small when compared to the nearfield intensity enhancement. Since the observation point is on the surface of the particle for the case of near-field intensity efficiency, the observation distance increases with increasing particle size. Thus, the amplitude of the resonance peak starts to decrease after some maximum value, as can be seen in Fig. 2(b). Due to this fact, the particle size that gives the maximum enhancement on the surface is smaller than that required for the maximum far-field enhancement. One important detail to mention is that the parameter distinguishing the near field from the far field is the distance normalized to the wavelength of interest. Thus, a very similar behavior of peak narrowing can be observed also for the wavelength axis of the corresponding plots. Another difference is the spectral position of dipolar peak which is red-shifted more strongly with increasing particle size in near-field efficiency plots. Since determining the maximum efficiency point is vital for many LSPR applications, the spectral peak positions should be carefully examined for each observation point of interest. As mentioned previously, the near-field efficiency converges to the far-field scattering efficiency for large observation distances. As shown in the supplementary material, S1, the generalized efficiency evolves as the observation

5 288 U. Guler et al. Fig. 2 Scattering efficiency (first column) and near-field intensity enhancement at the particle surface (second column) forau(a, b), TiN (c, d) and ZrN (e, f) distance changes. Note that convergence to the far-field efficiency for smaller wavelengths occurs at shorter distances, due to the fact that the ratio of wavelength to distance is the actual parameter that determines the near-field to far-field transition. This argument also explains the red-shift of the dipolar peak for the near-field plots: for a fixed point of observation, the distance can be within the near-field region for a longer wavelength while it is in the far-field zone for a shorter wavelength. We also examined TiN in this study since it has been shown to exhibit plasmonic properties [8]. According to the conventional quality factor calculations presented in Fig. 1(a), TiN seems to be a poor resonator. However, when we check the scattering efficiency plot of Fig. 2(c), we conclude that TiN can be a good scatterer for applications in the near-infrared region. Figure 2(d) shows that a maximum enhancement of at the surface of the TiN sphere occurs at a wavelength of 777 nm with a sphere radius of 75 nm. This value is larger than the enhancement obtained with an Au sphere of the same size and at the same wavelength. We can obtain a similar but smaller enhancement with Au at the same wavelength only if the particle radius is around 115 nm. The resonance wavelength for the dipolar mode of TiN particles is particularly important for bio-imaging and biosensing applications since the spectral window between nm is accepted as the wavelength region of choice in these applications [18]. Another important region in the electromagnetic spectrum is the neighborhood of 1550 nm due to its pervasive use in telecommunications. In contrast to the quality factor provided in Fig. 1(a), TiN shows better

6 Performance analysis of nitride alternative plasmonic materials for localized surface plasmon applications 289 performance in terms of the field enhancement for both the near field and the far field in this spectral region. An intensity enhancement value of is achieved at the surface of a particle with a 190 nm radius, while a particle with a 260 nm radius provides an enhancement of 2.92 in the far field. The evolution of the field enhancement from the near field to the far field for TiN particles is presented in the supplementary material S2. It should be noted that, as the observation distance increases, the dipolar resonance peak first shifts out of the calculation range and then moves back to far-field scattering efficiency value. Zirconium nitride particles were also examined in this study. The behavior of ZrN is similar to that of Au in the visible region, as is expected from its dielectric function. Far-field and near-field intensity efficiencies of ZrN particles are given in Figs. 2(e, f), where different ranges are used for the particle radii. The maximum scattering efficiency at large distances is 3.6 at a wavelength of 596 nm. When compared to Au, the maximum value of Q sca obtained from a ZrN particle is lower. However, when we examine the nearfield intensity enhancement maxima for both materials, it appears that ZrN provides slightly better value, Q NF = 40, at a wavelength of 508 nm. It should be noted that the dipolar resonance for ZrN particles occurs at shorter wavelengths compared to Au. More importantly, small ZrN particles provide higher intensity enhancement at the surface. This can be explained by the smaller loss expected from ZrN at shorter wavelengths (see Fig. 1(c)). Obviously, smaller particles that provide equivalent field enhancement efficiencies are favorable for nanometer-scale applications. Supplementary material S3 illustrates how the field enhancement evolves from the particle surface to the far field for spherical ZrN particles with varying particle sizes. With spherical metal particles, the observation of dipolar resonances at infrared wavelengths is not feasible. For nitrides, however, the near-infrared range is accessible. Our calculations show that TiN has a maximum scattering efficiency at 1477 nm with dipolar resonance behavior. As a result of the dipolar peak at large wavelengths, one can expect higher-order resonances in the visible and infrared regions of the spectrum. In Fig. 3(a) we show the scattering efficiency of a TiN nanosphere with a radius of 248 nm. In addition to the scattering efficiency of the particle, efficiencies obtained from the first three individual oscillation modes are also presented. The quadrupolar mode has its own maximum value at a wavelength of 803 nm, while the overall peak maximum of scattering efficiency is obtained at 866 nm. The overlap of the first three modes results in a scattering efficiency peak that is larger than the actual multi-polar modes. The superposition of modes and the resulting interference effect in the far-field regime was studied previously by Burrows et al. where the authors blue-shifted the dipolar resonance via inter-particle coupling and obtained an enhanced extinction value by overlapping different resonance modes at the quadrupolar peak position [19]. The near-field efficiency presented in Fig. 3(b), on the other hand, possesses modes with better distinguished spectral positions but larger peak tails. In order to show how these modes affect the overall response of the particle in the near field, we present the radial component of the electric field, E r, for the first three individual modes of the scattered field at a wavelength of 1477 nm in Figs. 3(c, d, e) and the total radial component of the scattered field in Fig. 3(f). Clearly, the overall response of the particle at the dipolar resonance is affected by the higher-order modes, and the symmetry observed in the case of the individual l = 1 mode cannot be preserved. This is in agreement with Q NF values since both the dipolar and quadrupolar modes provide significant contributions to the particle response. The octupolar mode is very weak as can be seen in Fig. 3(e). As a result of this superposition of modes, the overall field intensity in the near field of the particle, as given in Fig. 3(g), deviates from a pure dipolar response, in contrast to the far-field efficiency values. This contradiction comes from the fact that higher-order modes are more localized when compared to the dipolar mode [20]. The other peak observed in the scattering efficiency of TiN particle with a 248 nm radius occurs at 866 nm. With an increased size factor (radius/wavelength ratio) in this case, we can easily predict a resonance peak with higher-order modes. Figures 3(h, i, j) show the first three individual oscillation modes, while Fig. 3(k) shows the radial component of the total scattered field. Not surprisingly, all three modes have significant contributions with the quadrupole mode dominating. For the case of Q NF, although the spectral distances between the peak centers are larger, the peak tails of each mode extend to longer wavelengths when compared to Q sca and perturb the near-field distribution at lower-order resonance wavelengths. As a result, the field intensity distribution near the particle has quadrupolar behavior with an intensity concentration in the forward direction, as shown in Fig. 3(l). From our discussion here it is clear that a simple system consisting of a single spherical particle can have complicated plasmonic behavior in the near field and, as a consequence, approximations may lead to serious errors. Since the field localization is dependent on the oscillation modes, and since the field enhancement in the near field is affected by the interference of modes, these issues should be addressed in the analysis of performance for specific applications. The overlap of resonance modes is expected to be different for each material, and the overall performance of the material will be affected accordingly. The near-field intensity efficiency metric includes this information by nature, since it is the integration of the field over the desired fictitious spherical surface at the observation distance without any far-field approximation.

7 290 U. Guler et al. Fig. 3 (a) Scattering efficiency, Q sca,and(b) near-field intensity efficiency, Q NF, for a TiN sphere with a 248 nm radius. Radial field plots are given for each mode for two different scattering peak wavelengths. For the 1477 nm wavelength, (c, d, e) illustrate the scattering modes l = 1, 2 and 3, respectively. The total radial component is shown in (f), and (g) shows the corresponding intensity plot. For the 866 nm wavelength, (h, i, j) give the scattering modes l = 1, 2 and 3, respectively. The total radial component is shown in (k), and (l) shows the corresponding intensity plot 4 Conclusions We have discussed the particle efficiencies for local-field enhancement applications. The near-field efficiency approach is compared to the far-field scattering efficiencies for Au as well as for TiN and ZrN as alternative materials for plasmonic applications. In contrast to the conventional quality factor calculations in the quasistatic limit, near-field enhancement data show that TiN can be used as an efficient field enhancer for some spectral regions in the nearinfrared. Furthermore, the spectral position of the dipolar resonance makes TiN an important alternative for bioimaging and biosensing applications. On the other hand, ZrN provides resonances very similar to Au with slightly higher near-field intensities and better small-particle performance, which makes ZrN a good alternative for nanometerscale applications. The evolution of the field enhancement from the near field to the far field is also provided as supplementary data. Our results show that simplified methods such as the quasistatic approximation can be misleading in many cases. We demonstrate that a generalized enhancement efficiency, which can be obtained from Mie scattering coefficients, can be a convenient and efficient tool prior to the point where complicated simulations become necessary. Acknowledgements This work was supported in part by ARO Award W911NF , ONR MURI Grant N , AFOSR MURI Grant FA and NSF-DMR AVK wants to cite fruitful discussions with B. Lukiyanchuk (DSI, Singapore). References 1. S.J. Tan, M.J. Campolongo, D. Luo, W. Cheng, Nat. Nanotechnol. 6, 268 (2011) 2. S.A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007)

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