Measurement of the Distribution of Site Enhancements in Surface-Enhanced Raman Scattering

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Science  18 Jul 2008:
Vol. 321, Issue 5887, pp. 388-392
DOI: 10.1126/science.1159499

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On nanotextured noble-metal surfaces, surface-enhanced Raman scattering (SERS) is observed, where Raman scattering is enhanced by a factor, , that is frequently about one million, but underlying the factor is a broad distribution of local enhancement factors, η. We have measured this distribution for benzenethiolate molecules on a 330-nanometer silver-coated nanosphere lattice using incident light of wavelength 532 nanometers. A series of laser pulses with increasing electric fields burned away molecules at sites with progressively decreasing electromagnetic enhancement factors. The enhancement distribution P(η)dη was found to be a power law proportional to (η)–1.75, with minimum and maximum values of 2.8 × 104 and 4.1 × 1010, respectively. The hottest sites (η >109) account for just 63 in 1,000,000 of the total but contribute 24% to the overall SERS intensity.

Molecules on nanotextured noble-metal surfaces (1, 2) or nanoparticle aggregates (3, 4) frequently evidence giant Raman scattering cross sections. This surface-enhanced Raman scattering (SERS) effect has enabled a variety of chemical sensing applications (5), including the detection of single molecules by Raman scattering (6, 7). The average value of the Raman enhancement, , is frequently about 106 compared with molecules without a SERS substrate. “Hot” spots where the local field enhancement η is 109 or more have been detected by searching nanoparticle aggregates with powerful microscopes (68). At a hot spot it is possible to measure the Raman spectrum of single molecules (68). The existence of hot spots suggests that the average enhancement represents a broad distribution of microscopic enhancement factors, so a SERS signal might result from a few molecules at hot sites or the preponderance of molecules at “cold” sites (9).

SERS mechanisms may involve electromagnetic enhancement, chemical enhancement, or resonance enhancement. The benzenethiolate (BT) molecule is frequently used as a probe of electromagnetic enhancement. BT forms a densely packed, well-ordered self-assembled monolayer (SAM) on Ag (10) of the type frequently used in chemical sensing measurements. Because BT has weak electronic interactions with metal surfaces and does not absorb at the laser wavelength, the chemical and resonance enhancements are unimportant. In electromagnetic enhancement, an incident laser field, Ein, excites surface plasmons to create a complex pattern of spatially varying electromagnetic fields (11, 12). At any location, the local field is gEin, where g is the local enhancement factor. For the purposes of this study, it is sufficient to use the approximation (13) that the local Raman cross-section enhancement η = σReR0 = g4, where σRe and σR0 are enhanced and unenhanced cross sections, respectively (12). The distribution of local field enhancements will be denoted P(g)dg, and the distribution of Raman cross-section enhancements is P(η)dη = P(g)dg.

Electromagnetic calculations have been used to study what sorts of metallic nanostructures create hot sites and how large η could conceivably be at the hottest sites (9, 1418). One model system for computational studies consists of two closely spaced metal nanoparticles. In the gap between two closely spaced Ag nanoparticles (9, 1820), η may be as large as 1011. The distribution P(η)dη has been computed for 25-nm-diameter Ag spheres separated by 2 nm by La Rue and co-workers (9). The computed distribution was a power law proportional to η–1.135, was 6.7 × 107, and the smallest and largest enhancements were about 1.5 × 103 and 2 × 1010, respectively.

A method to measure P(η)dη could have several applications. Ordinary Raman measurements are sensitive only to , which can lead to difficulties in quantifying SERS signals in analytical applications (21, 22). A great deal of effort has gone into developing methods to fabricate useful SERS materials (23), and a knowledge of P(η)dη would be more useful than a measurement of to optimize a fabrication technology (22). However, it is not possible to determine P(g)dg or P(η)dη distributions by using linear Raman ensemble measurements. This task requires either a nonlinear spectroscopy or a molecule-by-molecule census. But single-molecule measurements would not be sensitive enough to observe the colder sites. In studies of molecules in disordered media, photochemical hole burning (PHB), a nonlinear method that involves a burning pulse and a probing pulse (24), has been an effective method for extracting distributions of molecular energy level spacings (25), so an analogous method might be used to measure P(η)dη. Photobleaching of adsorbed dye molecules (9, 26) has been suggested as a method of determining P(η)dη because the photobleaching efficiency increases in regions of greater local field enhancement. Vibrational pumping of adsorbed dyes has also been suggested in this context (27).

Our method for determining P(η)dη uses the electric fields from powerful nonresonant laser pulses to photochemically damage molecules adsorbed on a SERS substrate. This type of photodamage is characterized by a sharp electric field threshold, Eth. The value of Eth depends on the type of molecule, the wavelength, and the pulse duration, but it is typically 1 to 10 GV m–1 (28). This sharp threshold behavior, which photobleaching does not exhibit, greatly simplifies the theoretical analysis needed to extract P(η)dη from experiment. For a given Ein, photodamage will occur only at sites where gEinEth, so as the PHB laser field is increased molecules with the largest g burn away first, followed by molecules at sites with progressively smaller g. Meanwhile, the sample loses Raman intensity at a rate proportional to η = g4 (26). The disappearance of the photodamaged molecules and the appearance of photoproducts can be monitored via Raman spectroscopy with a weak probe laser. In this study, the PHB method is illustrated by using a SERS substrate composed of an Ag film on nanospheres (AgFON) (35, 23, 29) having an adsorbed layer of BT.

The experimental concept is depicted in Fig. 1 (30). A BT SAM was deposited on AgFON (330-nm nanospheres coated by 150-nm Ag) fabricated with use of methods developed by the van Duyne group (23, 29). The 1-ps duration, 532-nm PHB laser pulses were focused to 140 μm (Gaussian 1/e2 diameter) spots. The pulse energies ranged from 1 to 1000 nJ, and Ein ranged from 10 to 300 MV m–1. A 0.5-mW continuous-wave 532 Raman laser probed molecules at the center of the PHB beam where Ein was spatially uniform to alleviate complications caused by averaging over the spatial beam profile (26).

Fig. 1.

(A) Raman spectroscopy with a continuous-wave (CW) laser, of a SERS sample consisting of AgFON with BT monolayer. (B) SERS spectrum of BT. (C) Scanning electron micrograph of AgFON surface. (D) The sample was exposed to an intense PHB pulse with laser field Ein. BT molecules at sites with local field enhancement g were damaged if gEinEth, where Eth is the threshold field needed to damage BT. (E and F) The Raman spectrum after PHB shows loss of BT plus new transitions from photoproduct molecules. The loss of BT is quantified by using the integrated area of the phenyl CH-stretch transition at 3050 cm–1.

Representative Raman spectra of BT on AgFON after exposure to PHB pulses are shown in Fig. 2. Before PHB the observed spectra agree well with the literature, and the largest peaks give the expected Raman intensity of ∼5000 counts mW–1 s–1 (3). The bulk Raman enhancement factor was determined by using the established method (31) of comparing the BT SERS intensity to a thin layer of liquid benzenethiol. We used a geometric model for the Ag surface, where the area is a factor Embedded Image greater than a flat surface (R is nanosphere radius and h the Ag coating thickness) and the measured value of 3.3 × 1014 cm–2 for the molecular packing density on flat Ag(111) (10), to obtain = 8.5 × 105. Given the possibility of error in our geometric model and the packing density, we assigned a wide error bound of ∼50% so that = 9 × 105 ± 4 × 105.

Fig. 2.

Raman spectra of BT on an AgFON substrate after the indicated number of PHB pulses, at a lower and higher value of the incident field, Ein.

As shown in Fig. 2, in the range of 10 to 100 PHB pulses the BT Raman transitions lose intensity, and new photoproduct transitions grow in, most prominently on the red edge of the 1550 cm–1 CH bend and in the 2000 to 2200 cm–1 range of carbonyl stretching. On the basis of studies in an O2-depleted atmosphere, we believe that the observed photoproduct results from field ionization of BT to produce a transient species that later reacts with ambient O2. Raman signals from the photoproduct have about the same SERS enhancements as BT. The dramatic spectrum observed after a single PHB pulse at Ein = 9 × 107 V m–1 indicates large SERS enhancement of the photoproduct. This result is compelling evidence that PHB pulses damage BT but not the SERS substrate. As support for this conclusion, we observed that after 103 intense PHB pulses with Ein = 200 MV m–1 there was no evident effect on the AgFON surface plasmon resonance.

As the PHB pulse irradiation continued, after 103 to 104 pulses the photoproduct transitions disappeared. This continued photodamage of the photoproduct further emphasizes that photoproduct molecules reside in local environments that continue to possess large local field enhancements. In the 103 to 105 pulse regime, BT molecules that were not photodamaged continued to evidence the same Raman spectrum as unirradiated molecules. With subsequent irradiation, after 105 to 106 high-field pulses, the BT Raman spectral lineshapes evolved and broadened. We believe that this spectral evolution is associated with gradual laser substrate damage.

To quantify the extent of photodamage, we focused on BT transitions well separated from the photoproduct, specifically the integrated area of the 3050 cm–1 peak arising from aromatic CH-stretch transitions. The aromatic phenyl moiety of BT is most susceptible to high-field damage, and nonaromatic photoproducts will have their CH-stretch transitions shifted to the 2850 to 2950 cm–1 range. Figure 3A shows a series of burning curves based on monitoring the 3050 cm–1 CH stretch. The burning curves were not appreciably different when other BT Raman transitions were monitored. The experimental observable in Fig. 3A is the fractional change I(n)/I0 in Raman intensity after n PHB shots at field Ein. Although I(n) is quite dependent on n during the first 100 pulses, the intensity drop caused by photodamage is complete at 1000 pulses. To model this behavior, we assumed that each PHB pulse had a constant probability for inducing photodamage. Then, at a site with enhancement factor g irradiated by n pulses at field Ein, this probability PPHB(g;Ein,n) is Embedded Image(1) Embedded Image where n0 is the number of pulses needed to damage 1/e of the BT molecules. Then I(n)/I0 can be written in terms of the microscopic distribution function P(g)dg Embedded Image(2) Embedded Image Although it is possible to determine P(g)dg from the data in Fig. 3A, a more accurate determination was made by averaging the results from five fresh regions of the SERS sample, each exposed to 1000 PHB pulses. We can define a critical value of the local field enhancement gcr = Eth/Ein such that the probability of photodamage is unity at sites with ggcr and zero at sites with g < gcr Then Eq. 2 becomes Embedded Image(3) Equation 3 shows that I/I0 is a function of gcr ∝ 1/Ein, so in Fig. 3B we plotted I/I0 versus 1/Ein. To determine P(g)dg from Fig. 3B, we could take the numerical derivative of the data and divide by g4. However the data in Fig. 3B were unexpectedly well fit by an exponential function, leading to an empirical analytical form for P(g)dg and P(η)dη, Embedded Image(4) The value of the constant A in Eq. 4 is determined by the constraint ∫P(g)g4dg = = 9 × 105 ± 4 × 105. The value of the constant A′ in Eq. 4 is determined by varying the value of Eth subject to the normalization condition ∫P(η)dη = 1; the best fit was obtained with Eth = 6.7 ± 0.6 GV m–1. Knowing Eth for BT, with the relation Eingcr = Eth, we obtain the useful upper abscissa in Fig. 3B. Lastly, we can fit the burning curves in Fig. 3A by using Eqs. 1 and 2 with one additional parameter n0 = 10, which characterizes the number of PHB pulses needed to complete the photodamage process.

Fig. 3.

(A) PHB curves for CH-stretch transition of BT molecules on AgFON SERS substrates. From top to bottom, Ein = 15, 30, 43, 88, 140, and 200 MV m–1. The smooth curves are calculated from the local field enhancement distribution P(g)dg using the statistical model for PHB of Eq. 1. rel. indicates relative. (B) Fraction of BT CH-stretch SERS intensity after 1000 PHB pulses. The different symbols represent measurements on different samples. The PHB curve fits an exponential function (solid line). At given Ein, only molecules where the local field enhancement exceeds a critical value gcr (upper abscissa) are damaged by PHB pulses. One-half of the overall SERS signal comes from sites with g > 100.

In order to properly normalize P(η)dη, we need to know the minimum and maximum enhancement values, ηmax and ηmin. To determine ηmax, we need to determine the weakest pulse that causes the first detectable photodamage. From Fig. 3B, this Ein value corresponds to gcr = 450 or ηmax = 4.1 × 1010. To determine ηmin, we need to determine the weakest Ein that photodamages every molecule on the surface. Unfortunately, we could not do this without damaging the SERS substrate, so we could not extend Fig. 3A below gcr = 20 and ηmin = 1.6 × 105. It seems reasonable to extrapolate the exponential in Fig. 3B to where it intersects the abscissa at gcr = 13 and ηmin = 2.8 × 104. The resulting P(η)dη at 532 nm is shown in Fig. 4. The distribution of site enhancements is a power law with η–1.75 dependence, but at the largest enhancements, η > 109, the distribution drops off even more steeply. Thus, our measured distribution for a periodic lattice of 330-nm adjacent nanospheres falls off faster than the η–1.135 dependence obtained theoretically by La Rue and co-workers (9). The La Rue calculation (9) refers to a pair of 25-nm spheres separated by 2 nm rather than a lattice of spheres, but interestingly the authors speculated that for a collection of spheres the main difference would be a faster drop off at large η such as we see in Fig. 4. The fraction of molecules at each enhancement and the contributions of the different site enhancement factors η to the overall SERS signal are given in Table 1, derived by using Fig. 3B and numerical integration of Fig. 4. The distribution we present applies to AgFON substrates with the specific geometry used here and might be quite different for other SERS materials.

Fig. 4.

Measured distribution of SERS enhancement factors P(η)dη at 532 nm for BT monolayer on AgFON substrate with 330-nm-diameter spheres. The error bars represent estimated errors due to uncertainty in the determination of the ensemble-averaged SERS enhancement . Shaded regions denote ηmin = 2.8 × 104 and ηmax = 4.1 × 1010.

Table 1.

Contribution of the various site enhancements at 532 nm to the overall SERS signal.

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This study used 1-ps, 532-nm PHB pulses, but we know no reason why other PHB pulse durations and wavelengths could not be used. Ultrashort pulses may not be required but are desirable because at a given Ein ultrashort pulses pose less risk of substrate damage. We believe that the largest source of experimental error is our error in determining . The resulting uncertainty in P(η)dη is illustrated by the error bars in Fig. 4. Our measured distribution terminates at ηmax = 4.1 × 1010. There maybe a small number of hotter sites, but they represent such a tiny fraction of the overall SERS intensity that if they existed we could not detect them. The value ηmin = 2.8 × 104 is based on extrapolation, and if there were more or fewer cold sites than the extrapolation indicates, the fraction of hot sites in Table 1 would become proportionately smaller or larger.

Table 1 answers many questions about the inhomogeneous nature of the AgFON SERS substrate. The coldest sites (η <105) contain 61% of the molecules but contribute just 4% of the overall SERS intensity. The hottest sites (η >109) comprise just 63 molecules per million but contribute 24% of the overall SERS intensity.

Our PHB technique should be capable of measuring distributions on other SERS materials provided these substrates can withstand PHB pulses. A particularly interesting system involves stripping away the Ag-coated nanospheres (23, 31), leaving behind a periodic array of nanotriangles. The reduced area of the nanotriangle substrate, about 3% of the AgFON surface area for BT binding, reduces the overall SERS intensity but increases the average enhancement of the remaining surface. If we assume the stripping process removes the coldest 97% of the BT molecules, then from the P(η)dη distribution found here we would predict the average enhancement for BT on nanotriangles to be = 2 × 107, about 20 times greater than for AgFON. Although we cannot directly compare the nanotriangle experiments to the present work because the Ag thickness, sphere diameters, and wavelengths were slightly different, with a substrate that performed optimally at 625-nm laser wavelength McFarland et al. (31) obtained = 1.2 × 107 and with a 670-nm substrate = 1.4 × 107.

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