What is the Key Structural Parameter for Infrared ... - ACS Publications

Dec 29, 2015 - Department of Science, Faculty of Education, Hirosaki University, ... Physics, Graduate School of Science and Technology, Hirosaki Univ...
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What is the Key Structural Parameter for Infrared Absorption Enhancement on Nanostructures? Toru Shimada,*,† Hiroshi Nakashima,‡ Yuta Kumagai,† Yuta Ishigo,‡ Masamichi Tsushima,‡ Akihiko Ikari,§ and Yushi Suzuki*,‡ †

Department of Science, Faculty of Education, Hirosaki University, 1 Bunkyo-cho, Hirosaki, Aomori 036-8560, Japan Department of Advanced Physics, Graduate School of Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki, Aomori 036-8561, Japan § Department of Advanced Physics, Faculty of Science and Technology, Hirosaki University, 3 Bunkyo-cho, Hirosaki, Aomori 036-8561, Japan ‡

ABSTRACT: The key structural parameter for greater enhancement of infrared absorption on metal nanostructures was identified by systematic and exhaustive surface-enhanced infrared absorption (SEIRA) measurements for well-defined periodic gold square column (SC) arrays on silicon wafers fabricated using electron beam lithography. The SC arrays have size parameters compatible with those of vacuumevaporated thin metal films, which are used conventionally for SEIRA. The crucially important parameter determining the enhancement factor for infrared absorption is the ratio of the gap size to the nanoparticle size. An electrostatic SC model calculation based on a nonresonant-type electromagnetic mechanism shows good quantitative agreement with experimental observations of enhanced infrared absorption of adsorbed species. Furthermore, results show that the electrostatic SC model contains the previously proposed lightning-rod effect’s case. The clarified enhancement mechanism for infrared absorption of molecules adsorbed onto metal nanostructures is useful to elucidate applications such as designing SEIRA active substrates, analyzing reactions on electrodes, and detecting minute chemicals as highly sensitive chemical sensors and biosensors.

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INTRODUCTION Metal nanostructures such as rough metal surfaces, metal island films, and metal nanoparticles have opened new doors to surface-enhanced spectroscopy (SES). One of the many phenomena in SES is surface-enhanced infrared absorption (SEIRA) spectroscopy: infrared absorption of molecules is enhanced on metal nanostructures. SEIRA forms a new branch of infrared vibrational spectroscopy. Therefore, SEIRA provides not only the fingerprint of any molecular system but also complementary information related to Raman scattering. The phenomenon was reported first by Hartstein et al.1 and Hatta et al.2−5 in the 1980s. After their work, several SEIRA experiments were conducted not only for scientific interest but also for practical interest. The applications of SEIRA are indeed expanding rapidly: for example, for analysis for minute chemical species, for thin films on a solid surface, and for reactions on electrodes and biochemical fields. Details of such applications have been well-documented in several review articles and a book about SEIRA.6−10 To design an efficient SEIRA active substrate for applicative utilizations, it is necessary to elucidate a key structural parameter of nanostructures determining the enhancement factor of infrared absorption. Furthermore, to understand SEIRA deeply, it is also necessary to elucidate the SEIRA enhancement mechanisms explaining the parameter. Although © XXXX American Chemical Society

numerous reports have clarified the infrared enhancement mechanism, some controversy persists. The SEIRA mechanism is conventionally explained mainly by two mechanisms. One is the chemical mechanism, which explains enhancement by chemical interactions between the molecule and the surface.11−13 The contribution of the chemical effects, however, changes dramatically depending on the manner of the interaction between the chemisorbed molecules and the metal nanoparticle surface. Another is the electromagnetic (EM) mechanism, which can be categorized from the perspective of whether a certain type of resonance dominantly affects the infrared enhancement or not. In this study, the former is called a resonant-type mechanism. The latter is a nonresonant-type mechanism. A resonant-type EM mechanism explains the enhancement of infrared absorption mainly by the localized electric field near the metal nanoparticles, which is induced by the excitation of collective electron resonance or a localized plasmon mode, as in surface-enhanced Raman scattering (SERS). Therefore, the plasmon-like mechanism requires strong absorption by excitation of the localized plasmon mode in the metal Received: September 24, 2015 Revised: December 10, 2015

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DOI: 10.1021/acs.jpcc.5b09315 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Therefore, the primary purpose of this study is to elucidate the enhancement mechanism of infrared absorption on conventionally used vacuum-evaporated thin metal films for SEIRA, which is necessary to obtain the design guide for an efficient SEIRA substrate. For this study, we fabricated well-defined periodic metal nanostructures by the application of the EBL technique for SEIRA active substrates, which have compatible size parameters such as the nanoparticle sizes and gap sizes between nanoparticles, with vacuum-evaporated thin metal films. Such structures, fabricated using the EBL technique, enable quantitative analyses without the assumption of averaged structures. The structures on a substrate for the EBL fabrication were designed as gold SC arrays, which have different edge lengths of squares and interparticle separation distances of the squares on a silicon substrate. The SC arrays are the most feasible structure for this study, not only because the structure is directly applicable to the SC model but also because a square array is thought to be the most optimized structure for SEIRA enhancement.20 That is, the structure gives maximum enhancement. A schematic illustration of the SC array is presented in Figure 1(a). The fabricated SC arrays were used for systematic and exhaustive SEIRA measurements. By analyzing the obtained spectra, this study clarifies the dependence of enhancement factor of SEIRA for adsorbed molecules on the edge length of the metal square and the interparticle separation distance of the squares. Furthermore, the systematic and exhaustive measurements enable us to ascertain the crucial

nanoparticles. The resonant-type mechanism alone, however, cannot explain the experimental evidence indicating that the enhancement extends to several monolayers away from the surface because of its short-range effects. A kind of resonanttype mechanism that does not incorporate plasmon excitation directly has also been proposed as an EM mechanism. The system is modeled in terms of the effects of the perturbation of the optical properties of the metal island film by surfaceadsorbing molecules.14,15 On the other hand, a nonresonant-type EM mechanism explains the enhancement of infrared absorption by an intuitive electrostatic model. A square column (SC) model was proposed in 2003.16 The SC model includes the assumption of random nanoparticles of a vacuum-evaporated silver film as well-defined SCs. Although the calculated infrared absorption intensity based on the SC model shows good quantitative agreement with the experimentally obtained result, a challenge remains because the actual shapes of the evaporated nanoparticles differ greatly from those of well-defined SCs. The structure consists of nanoparticle islands of various shapes and sizes. The difficulty in modeling a system such as the SEIRA active substrates normally derives from the lower reproducibility of substrates because of the nature of vacuum-evaporated thin metal films, which are used conventionally for SEIRA. The vacuum evaporation technique is extremely convenient. It is used mostly to fabricate the SEIRA active substrates. However, the fabricated nanostructures only allow quantitative analyses based on their averaged structure because of certain dispersions of structural parameters such as the particle shape, particle size, and gap size: vacuum-evaporated thin metal films comprise assemblies of several structural islands. Moreover, although the morphology is controllable partially by the metal evaporation rate, the substrate temperature during evaporation, and the postannealing temperature when the thickness is fixed, the structural parameters differ independently of each other.17−19 Recently, another nonresonant-type EM mechanism explains the enhancement of infrared absorption for a two-dimensional hexagonal close-packed array of spherical nanoshells by the lightning-rod effect (LRE).20 Although the substrate had a welldefined structure and although the results provide fruitful insight into SEIRA mechanisms, the study was performed mainly on various computational calculations, which were then merely compared with an experimentally observed extinction spectrum. Therefore, experimental verification has been sought. As described above, the proposed nonresonant-type EM mechanisms present challenges to be verified: the well-defined structure for the SC model and the experimental evidence for the LRE. To meet these challenges, electron beam lithography (EBL) is an excellent technique for fabricating well-defined metal nanostructures for experimental SEIRA measurements. Recently, some SEIRA-active substrates fabricated using the EBL technique were indeed used for SEIRA measurements. Those studies, however, were based mainly on nanoantennas such as long nanoantennas,21−25 ring resonators,26 and nanocrescents,27 with structures tuned to the collective resonances which provide strongly enhanced near-field intensities for SEIRA. Their structures differ greatly from those of the vacuum-evaporated thin metal films in terms of their size and shape. Therefore, such studies using the SEIRA active substrates fabricated using the EBL technique do not provide fruitful insight into the enhancement mechanisms of conventional SEIRA for vacuum-evaporated thin metal films.

Figure 1. (a) Schematic illustration of the gold square column (SC) arrays on a silicon wafer fabricated using the electron beam lithography (EBL). Ls and Lg, respectively, denote the edge length of the square and the interparticle separation distance of the squares on a Si substrate. (b) Schematic drawing of the three-layer system consists of air (layer 1), a composite layer with the gold SC arrays and PAA (or air for naked SC arrays) (layer 2), and a silicon substrate (layer 3) for model calculation using the Fresnel equation. The effective, i.e., spaceaveraged, dielectric function of the composite film (layer 2) was used for the calculation. B

DOI: 10.1021/acs.jpcc.5b09315 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C parameter, which decides an enhancement factor as the ratio of the separation distance to the square size. The experimentally obtained results are reproduced well by simple calculations based on an electrostatic nonresonant-type model or an SC model using the effective medium theory (EMT).16 This study also shows that the model based on the LRE20 is a special case of the SC model when the electric field in the nanoparticles is screened.

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METHODS

Fabrication of Square Column Arrays Using Electron Beam Lithography. All gold SC arrays, which had different square and gap sizes, were fabricated in the Takeda−Sentanchi Building’s super clean room at The University of Tokyo. Each array occupies 500 × 500 μm2 on a silicon substrate. After ultrasonic cleaning of silicon wafers with acetone, ethanol, and ultrapure water, the silicon wafer was spin-coated with an EBL positive resist (ZEP520A-7; Zeon Corp.) at 5000 rpm and baked on a hot plate at 180 °C for 15 min. Then EBL was performed (F5112; Advantest Corp.) operating with acceleration voltage of 50 kV and a dose of 104 μC cm−2. After exposure, the resist was developed in n-amyl acetate (ZEDN50; Zeon Corp.) for 70 s and rinsed twice in an 89:11 solution of methyl isobutyl ketone (MIBK) and isopropyl alcohol (IPA) (ZMD-B; Zeon Corp.) for 60 s. The wafer was dried using nitrogen gas flow. Finally, a 3 nm adhesive layer of chrome and a 50 nm layer of gold were deposited onto the substrate using electron beam evaporation. To remove the remaining resist, the wafer was sonicated in dimethylacetamide (ZDMAC; Zeon Corp.) at 55 °C for 1 h followed by soaking in the ZDMAC for 1 day and rinsed with acetone, ethanol, and ultrapure water. The fabricated SC array structure was confirmed using a scanning electron microscope (SEM, JSM7000F; JEOL). Fabrication of Polyacrylic Acid Thin Film on the Substrate. Polyacrylic acid (PAA; Wako Pure Chemical Industries Ltd.) was spin-coated onto the substrate with the SC arrays. A 200 μL droplet of 10 g L−1 PAA ethanol solution was dropped on the substrate mounted on the spin-coater. Then the substrate was rotated at 5400 rpm for 5 min and dried to evaporate ethanol before infrared measurements. Spectroscopic Characterization by Infrared Microscopy. Fourier transform infrared (FT-IR) spectra were obtained using a spectrometer and a universal microscope accessory (670 and 610-IR; Varian Inc.). Unpolarized light with 250 × 250 μm2 cut with a square aperture illuminated the sample. The SC arrays with PAA existed in the whole area of the focused light at the sample because each array was expanded to 500 × 500 μm2. Light passing through the sample was detected using a liquid nitrogen cooled mercury cadmium telluride (MCT) detector. All spectra were recorded with resolution of 4 cm−1 with 128 scans.

Figure 2. Typical SEM images of the SC arrays. (a) Designed squares were 350 nm long and 300 nm gap separating the squares. (b) Designed squares were 150 nm long and 100 nm gap. Each SC array occupies a space of 500 × 500 μm2 on a Si substrate.

ones, although the SC edges are not exactly at right angles but are slightly rounded. The rounded edges, however, appear to be good for this experiment because there is less concern about the enhancement effect at the acute edge. The fabricated SC arrays were identified by the square size (Ls) and the gap size between the squares (Lg). The combinations of parameters used for fabrication are presented in Table 1. Figure 3 presents transmission spectra for the SC arrays shown in Figure 2. Very flat transmission spectra were observed around 1700 cm−1, which corresponds to the region for the vibrational mode of the target species in this study (PAA). The Table 1. Combination of Structural Parameters for the Fabricated Gold Square Column (SC) Arrays on Silicon Wafer Which Were Used for SEIRA Active Substratesa

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gap size, Lg/nm

square size

RESULTS AND DISCUSSION Square Column Arrays. Two typical SEM images of the gold SC arrays are presented in Figure 2. They were taken with acceleration voltage of 10.0 kV. Each scale bar in the SEM images corresponds to 3 μm. The designed squares in Figure 2(a) were 350 nm long with a 300 nm gap separating the squares. Those in Figure 2(b) were 150 nm long with a 100 nm gap. Structural parameters of the fabricated SC arrays observed using SEM show good agreement with the designed

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A schematic image of the SC array is presented in Figure 1(a). DOI: 10.1021/acs.jpcc.5b09315 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 3. Transmission spectra for the SC arrays around 1700 cm−1 which correspond to the region for the vibrational mode of the target species in this study (PAA). Black (gray) line is for the square with 150 (350) nm long and 100 (300) nm gap. The inset shows the same transmission spectra for a wider range of wavenumber.

Figure 4. Typical infrared absorption spectra in the carbonyl stretching region for PAA on the Si substrate with and without the SC arrays. (a) For the fixed square size at 350 nm and the varieties of the gap sizes of 150−300 nm. The bottom spectrum corresponds to a PAA layer formed directly on the bare silicon substrate without metal SC arrays. (b) For the fixed gap size at 100 nm and the varieties of the square sizes of 100−250 nm.

flat and almost perfect transmission spectra indicate that the fabricated SC arrays have a perfect periodic structure: if it is composed of clusters of nanoparticles, broad plasmon modes formed through interactions and hybridization of the individual nanoshell plasmons are observed.20 The inset in Figure 3 shows the same transmission spectra for a wider range of wavenumbers. Stronger absorption in a higher wavenumber region was observed for the SC arrays with square size of 350 nm and gap size of 300 nm (gray line in Figure 3). Extinction at a higher wavenumber for a larger square size might be attributable to a surface scattering effect because the nanoparticle size corresponds approximately to one-tenth of the wavelength in this infrared region. Both transmission spectra shown in Figure 3 show transmittance that is greater than one at a lower wavenumber, probably because of the antireflection effect. Transmittance around 1700 cm−1 was almost always greater than 90% for the studied SC structures. Therefore, the effect of the plasmon-like resonant-type EM enhancement is less dominant in this study if it contributes. Infrared Absorption. Figure 4 presents typical infrared absorption spectra in the carbonyl stretching region for PAA on the silicon substrate with and without the SC arrays. Whereas Figure 4(a) presents results measured for the fixed square size at 350 nm and the varieties of the gap sizes of 150−300 nm, Figure 4(b) presents results measured for the fixed gap size at 100 nm and various square sizes of 100−250 nm. The bottom spectrum in Figure 4(a) corresponds to a PAA layer formed directly on the bare silicon substrate without metal SC arrays, which was also obtained on the same substrate. Such bare places exist around the area of each SC array (500 × 500 μm2), which are boundary places. The spectra show characteristic stretching absorption bands of the carbonyl group ν(CO) around 1700 cm−1. Although extinction relating to the SC plasmon is not observed around this region (Figure 3), the infrared absorption spectra clearly show the enhancement effect depending on the nanoparticle structures. When the square size is fixed, a smaller gap size gives a stronger absorption peak. When the gap size is fixed, a larger square size gives a stronger absorption peak. Independence of the enhancement on plasmon extinctions is not surprising because, for the case of spherical gold nanoparticles dispersed in a comb copolymer,

infrared absorption of the adsorbed molecule on gold nanoparticles is even more enhanced when the tail of a plasmon resonance of gold nanoparticles in the visible region is shorter.28 No requirement of plasmon resonance alleviates concern about tuning plasmon resonances across the broad infrared region. To clarify the square size and the gap size effects, enhancement factors of the infrared spectra are shown, respectively, as a function of a square size and gap size in Figures 5(a) and 5(b). The enhancement factors were calculated by dividing the absorbance of infrared spectra for the PAA CO stretching mode on the SC arrays by that directly on the bare silicon substrate (without the SC arrays). To eliminate differences of the volume of PAA in the gap of each SC array, the enhancement factors were divided by the area sizes without gold SCs, where PAA molecules can exist. It is defined as an enhancement factor in this study. Figure 5(a) clearly exhibits the dependence of infrared absorption enhancement factor on the gap size. Enhancement factors increase nonlinearly when the gaps become small on any square size (100−350 nm). The degree of variation is greater for larger square sizes of the SC arrays. The gap size effect is weakest for the 100 nm square size. These facts indicate that the smaller gap size is effective to enhance the infrared absorption for the SC arrays with a fixed square size. The square size effect is also shown clearly in Figure 5(b). When the enhancement factors are shown as a function of the square size with fixed gap sizes, the enhancement factors increase when the square size becomes large. When the gap size is 100 nm, the largest enhancement factor of the five gap sizes is obtained, but for the 300 and 350 nm in the square size, no data are available for the 100 nm gap, which exhibits the greatest degree of variation of the five gap sizes. These indicate that the larger square size is effective to enhance infrared absorption for the SC array with a fixed gap size. Data presented in Figure 5 suggest two criteria of enhancement for the SC structure on the substrate to obtain higher enhancement for infrared absorption: (1) a smaller gap D

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Figure 6. Enhancement factors for IR absorption as a function of the ratio of the gap size to the square size of the SC arrays (R = Lg/Ls). The broken line represents the calculated enhancement factor based on a nonresonant-type EM mechanism.

with different heights and/or different periodicities give the same distinguishable tendency (details are not shown in this study, and the results are in preparation for publication). These results also support the reasonability of the small difference of the enhancement factors estimated from the experiments. Model Calculation. The theoretical enhancement factors of SEIRA were estimated from the simulated absorbance spectra of PAA on the SC arrays, which were obtained from transmission spectra obtained using the Fresnel equation.29 For simplicity in using the Fresnel equation, the system was modeled as a three-layer system based on EMT. The three-layer system consists of air (layer 1), an effective composite layer with the gold SC arrays and PAA (or air for naked SC arrays) (layer 2), and a silicon substrate (layer 3). A schematic drawing is presented in Figure 1(b). The contribution of the overlayered PAA on the SCs is probably negligible because the species outside the composite film do not contribute to the enhancement absorption.30 Therefore, the PAA thickness was regarded as having the same height as the SCs (50 nm): the PAA completely fills the gap separating the SCs. The dielectric functions of gold εs and silicon εSi were taken from the Handbook of Optical Constants of Solids.31 To use the Fresnel equation to calculate the system based on EMT, the effective, i.e., space-averaged, dielectric function εeff of the composite film (layer 2) was required. The effective dielectric function εeff of the composite film (layer 2) was simply estimated as a series capacitor. Ls + Lg εeff (ω) = L Lg s + ε ε

Figure 5. (a) Dependence of IR absorption enhancement factor on the gap size of the squares. (b) Dependence of IR absorption enhancement factor on the square size.

size is better and (2) a larger square size is better. These criteria, however, might not be mutually independent because, when the center position of the SC is fixed, enlargement of the square results in shrinkage of the gap size. It is therefore desirable to evaluate these effects for enhancement factors simultaneously. Suzuki et al. reported that the intensity of the electric field in gap Eg, where the target species exist in this study, is altered dramatically by the ratio of the gap size to the square size (R = Lg/Ls) based on the SC model.16 Ratio R is apparently a good parameter to evaluate both effects (sizes of square and gap effects) simultaneously. Therefore, the enhancement factors are shown as a function of R in Figure 6. Each marker denotes the square size of the SCs. Almost all markers are distributed on the same smooth curve, irrespective of the sizes of squares and gaps. The reasonability of small differences of the enhancement factors estimated from the experiments, especially less than a factor of 4, can be confirmed through the enhancement factors for the ratio of one (R = 1). Those were estimated from five different measurements: Lg = Ls = 100, 150, 200, 250, and 300 nm. The averaged enhancement factor and the standard deviation of them were 3.0 and 0.20, respectively. The standard deviation is small enough to distinguish the small difference of the enhancement factors. Furthermore, the enhancement factors estimated from the other experiments for the SC arrays

s

g

(1)

In that equation, εs and εg, respectively, denote the dielectric functions of the metal SC and the gap. For PAA adsorption systems, the dielectric function of the gap εg corresponds to the dielectric function of PAA εPAA. For naked SC systems, the dielectric function of gap εg corresponds to the dielectric function of air εair. The dielectric function of PAA εPAA was approximated by the Lorentz oscillator model. E

DOI: 10.1021/acs.jpcc.5b09315 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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f ω02

2

− ω − iωγ

obtained results because another 3-fold enhancement allows one to achieve about 1000 times enhancement for infrared absorption when the gap−size ratio is smaller than 0.05. One candidate is orientation effect, for which the contribution to the enhancement is three in the chemisorbed case. As described above, an extremely simple model explains the infrared absorption enhancement. Nevertheless it is not perfect: about 20% of difference exists at a maximum between the experimentally obtained results and the simulated one. Two candidates exist to explain the difference: the chemical enhancement effect and the resonant-type EM enhancement effect. The chemical enhancement effect of SEIRA, however, is negligible in this study because the target species (PAA) used for this study physisorbs onto the gold surface. Therefore, the difference of the enhancement factor between the experimentally obtained results and the calculated one might be ascribed to the resonant-type EM enhancement effect. Although the PAA thickness is assumed in this model calculation, the order of the resonant-type enhancement effect agrees rather well with that already reported, for which the estimated enhancement factor of the EM field is a tenth or less of that in the infrared region.11,33 Next, the gap−size ratio, the crucial parameter for the nonresonant-type enhancement mechanism, is discussed through the intensity of the electric field in gap Eg based on the classical electromagnetic theory. An electric field with an electric vector parallel to the substrate is expected to fulfill the following relation because of the continuity of electric fields.

(2)

In that equation, ε∞ denotes the dielectric constant above the range of vibrational frequencies; ω0 represents the resonant vibrational frequencies of the infrared active oscillator; f stands for the oscillator strength with constant values; and γ is the corresponding damping factor. Parameters were decided by fitting the simulated absorbance spectra to experimentally obtained results of 1600−1785 cm−1. The PAA film thickness was assumed to be 50 nm. Good fit to the experimental absorbance spectra was obtained with ε∞ = 2.08, f = 4.4 × 1027 s−2, γ = 1.1 × 1013 s−1, and ω0 = 3.2 × 1014 s−1. The broken line in Figure 6 shows the simulated curve for the enhancement factor. The figure shows that the crucially important parameter determining the enhancement factor is neither the square size nor the gap size alone but the ratio of the gap size to the square size (R = Lg/Ls). Considering only the gap size or the square size is one aspect of this relation. When the ratio becomes increasingly smaller, the enhancement factor quickly becomes increasingly larger. How large can this square size be while remaining on this curve? We have begun to investigate that question. Our tentative results indicate that the boundary square size (Ls) for absorption bands of the carbonyl group ν(CO) might be 500−1000 nm, which corresponds to about one-tenth of the infrared wavelength around 1700 cm−1 (about 5900 nm) used in the measurements. Extremely simple model calculations for the SC arrays show good agreement with the experimental plots. Several recent experimentally obtained results have demonstrated that the SEIRA is observed not only for coinage metals; many other transition metals are explainable by this simple model because it uses only the dielectric constant and the gap−size ratio of metal nanoparticles. The dielectric constant in the infrared region does not differ greatly among them. Moreover, the model includes a constant electric field in the gap. Therefore, the model can explain the experimental evidence indicating that the enhancement extends to several monolayers away from the surface, which cannot be explained using previous resonanttype models. Hereinafter, the enhancement factor of SEIRA is discussed quantitatively. The maximum enhancement factor in this experiment is about 8.2 for 350 nm square size and 150 nm gap size. This is, however, smaller than the reported enhancement factor for SEIRA, which is 10−1000.8 This apparent contradiction derives from the gap−size ratio of the SC arrays used for this study: the gap−size ratio, which gives the maximum enhancement factor, is only 0.43 for this study. The reported best enhancement factors are normally given by the metal nanostructures with gap sizes less than 10 nm,32 which are applicable in the enhancement model proposed in this study: a smaller R gives a larger enhancement factor. Though observed R’s in this study are somewhat larger than those of actual vacuum-evaporated thin metal films, the best enhancement factor is predictable by the nonresonant-type EM mechanism proposed in this study, for example, assuming for the SC arrays with square size of 100 nm and gap size of 5 nm (R = 0.05) the enhancement factor reaches 230. According to Figure 6, calculated enhancement factors in this study explain about 80% of actual enhancement factors except for the 100 nm square size case. Therefore, the enhancement factor of 230 corresponds to the actual enhancement factor of about 300, which is sufficient to explain the previous experimentally

εsEs = εgEg = εeff Eeff

(3)

Therein, Es and Eeff represent the electric field intensity on the inside of the metal SC and on the inside of the composite layer; εs and εg are the dielectric constants of the metal SC and the gap; and εeff stands for the effective dielectric constants of the composite layer. Equation 3 shows that the electric field component, which is parallel to the substrate, is concentrated on the part that has a smaller dielectric constant. On the basis of the SC model,16 the effective dielectric function εeff of the composite layer (eq 1) is rewritten as the following equation.

⎛1 + R ⎞ εeff = εg ⎜ ⎟ ⎝η + R⎠

(4)

Therein, R is the ratio of the gap size to the square size (Lg/Ls). η denotes the ratio of the dielectric constants of the gap to that of the metal SC (εg/εs). The electric field on the inside of the gap separating the SC columns is expressed as the following equation.

⎛1 + R ⎞ Eg = ⎜ ⎟Eeff ⎝η + R⎠

(5)

Equation 5 shows that the intensity of the electric field in the gap Eg can be expressed as a function of the ratio of the gap size to the square size R. Infrared absorption is proportional to the intensity of irradiated light to the target species, which is the square of the intensity of the electric field. Therefore, the enhancement factor for SEIRA behaves as a function of the gap−size ratio in the nonresonant-type mechanism. Finally, the relation between the SC model and the LRE is discussed. The physical origin of the LRE which explains the large field enhancement for SEIRA is metallic screening.20,34,35 That is, only a negligible electric field exists in the metal nanostructures. To implement this condition in the SC model, F

DOI: 10.1021/acs.jpcc.5b09315 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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the dielectric constant of the metal SC εs becomes a huge value from eq 3. Then η becomes infinitesimally small and negligible in the mid-infrared region. Consequently, eq 5 can be condensed as the following equation. Eg Eeff

=

ACKNOWLEDGMENTS T.S. thanks Dr. T. Hasegawa (ICR) for many stimulating discussions of these subjects and for continuous encouragement. T.S. also thanks Dr. T. Nagao (NIMS) for stimulating discussions related to enhancement mechanisms. This work was supported financially by a Grant-in-Aid for Young Scientists (b), JSPS KAKENHI Grant Number 26810001, and by Nanotechnology Network of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. A part of this work was conducted at the Center for Nano Lithography & Analysis at The University of Tokyo supported by MEXT, Japan, and at the Instrumental Analysis Center at Hirosaki University.

Ls + Lg Lg

(6)

That relation is exactly the same as the derived equation based on the LRE in an earlier report of the literature.20 Therefore, the LRE is a limiting case of the SC model when the electric field in the nanoparticles is negligible. As these points demonstrate, the SC model is probably a more generalized electrostatic model for explaining SEIRA. As a benefit of this, the SC model can also explain the infrared enhancement for dielectric materials that have large dielectric constants. A further benefit of the SC model is its applicability to spectral simulations because the model deals directly with the dielectric constant.

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REFERENCES

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CONCLUSIONS The enhancement mechanism of SEIRA was examined using well-defined SC arrays on a silicon wafer fabricated using EBL technique as a SEIRA active substrate. Systematic and exhaustive SEIRA measurements for the substrates revealed that the crucial parameter which decides the enhancement factor for infrared absorption is the ratio of the gap size to the square size. Model calculations based on the electrostatic SC model show good quantitative agreement with experimental observations of enhanced infrared absorption of adsorbed species. Results show that the SC model contains the previously proposed LRE case as a special case for screening the electric field in metal nanostructures. Therefore, the SC model is a more generalized electrostatic model for explaining SEIRA. The SC model has wide applicability not only to metals, but also to dielectric materials. The SC model is also applicable to simulate spectra because the model deals with the dielectric constant directly. The SC model, or a nonresonant-type EM mechanism, explains the enhancement of SEIRA by the electric field concentration because of the difference in the dielectric constants in the metal (gold) and the gap (PAA) between the metal nanoparticles. Although the dominant enhancement effect of infrared absorption is explainable by the nonresonanttype EM model, the model does not negate the presence of other enhancement mechanisms such as resonant-type enhancement and chemical enhancement. These other effects of the system remain as challenges to be addressed through future research. To elucidate these effects, we have planned or started additional experiments using self-assembled monolayers (SAMs) to study surface effects, changing metal to study the dielectric constant effect, changing the metal thickness and target species, and measuring a wide infrared range to assess the model applicability.

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AUTHOR INFORMATION

Corresponding Authors

*(T.S.) E-mail: [email protected]. *(Y.S.) E-mail: [email protected]. Notes

The authors declare no competing financial interest. G

DOI: 10.1021/acs.jpcc.5b09315 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.jpcc.5b09315 J. Phys. Chem. C XXXX, XXX, XXX−XXX