Infrared Near-Field Detection of a Narrow Resonance Due to

Jan 11, 2007 - Kerstin Mueller , Xiujuan Yang , Melissa Paulite , Zahra Fakhraai , Nikhil Gunari and Gilbert C. Walker. Langmuir 2008 24 (13), 6946-69...
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Infrared Near-Field Detection of a Narrow Resonance Due to Molecular Vibrations in a Nanoparticle Vyacheslav Romanov*,†,‡ and Gilbert C. Walker†,§ UniVersity of Pittsburgh, Department of Chemistry, Pittsburgh, PennsylVania 15260, U.S. Department of Energy, National Energy and Technology Laboratory, P.O. Box 10940, Pittsburgh, PennsylVania 15236, and UniVersity of Toronto, Department of Chemistry and Institute for Optical Sciences, Toronto, Ontario M5S 3H6, Canada ReceiVed August 31, 2006. In Final Form: NoVember 1, 2006 Di-iron nonacarbonyl particles on a gold surface have been imaged using an apertureless near-field scanning infrared microscopy. First and second harmonic detection, with and without an auto-homodyning option, have been used to collect the near-field spectrum of a single vibrational mode of the bridging carbonyls in di-iron nonacarbonyl nanocrystalline flakes on a gold surface. The experimental results have been compared to two theoretical models, a static image-dipole effective medium and an image dipole modified by a Fresnel coefficient for the appropriate observation angle. The calculations have taken into account the roughness of the gold film. The phase dependence of the near-field contrast has been investigated using broadband and tunable CO2 lasers. Particle size effects on contrast and spatial resolution have been studied to determine the limits of applicability of the half-space approximation.

Introduction Infrared (IR) spectroscopy is widely used to measure the concentrations of specific chemical groups by detecting the vibrational resonance absorption. The line shape of such “fingerprint” resonances can uncover conformations and intermolecular interactions. However, using conventional lenses it is not possible to focus infrared radiation into a spot much smaller than 10 or even 20 µm in diameter. Near-field microscopy provides us with superior resolving capability of optical and spectroscopic imaging by “confining” photons within a spatial region that is much smaller than their wavelength.1-4 This resolution improvement is attractive if it can be associated with spectroscopy. Recently, aperture-based infrared scanning near-field optical microscopy (SNOM) performed in spectroscopic mode, using the free electron laser, began delivering spatially resolved information on the distribution of chemical species and on other laterally fluctuating properties.5 This is one approach that reaches chemical selectivity by detecting specific vibrational modes with high lateral resolution. To understand the near-field behavior of the diffracted infrared light, Dazzi et al. have developed a model for a homogeneous layer in which a buried localized absorbing region is enclosed; the latter is characterized by two narrow absorption bands.6,7 Calculations have been made using the R-matrix propagation algorithm based on the differential theory of gratings. They showed that the shape of the diffracted electric field is similar to the shape of the absorbing region only when the size of this * To whom correspondence should be addressed. E-mail: romanov@ netl.doe.gov. Phone: (412) 386-5476. Fax: (412) 386-4806. † University of Pittsburgh. ‡ U.S. Department of Energy. § University of Toronto. (1) Dunn, R. C. Chem. ReV. 1999, 99, 2891-2927. (2) Michaels, C. A.; Stranick, S. J.; Richter, L. J.; Cavanagh, R. R. J. Appl. Phys. 2000, 88, 4832-4839. (3) Hartschuh, A.; Sanchez, E. J.; Xie, X. S.; Novotny, L. Phys. ReV. Lett. 2003, 90, 095503(1)-095503(4). (4) Hartschuh, A.; Anderson, N.; Novotny, L. J. Microsc. (Oxford) 2003, 210, 234-240. (5) Vobornik, D. et al. Infrared Phys. Technol. 2004, 45, 409. (6) Dazzi, A.; Salomon, L. International Workshop on Infrared Microscopy and Spectroscopy with Accelerator Based Sources; Lake Tahoe, CA, 2003. (7) Gross, N. et al. Eur. Phys. J.: Appl. Phys. 2001, 16, 91.

region is larger than the wavelength. When it is smaller, one has to discuss the concept of lateral resolution of such a microscopy and the main parameters limiting this resolution. Dazzi6 reported that the resolving power in this case is closely related to the absorbing region’s size and shape. Their spectral analysis revealed that the absorption bands are not only localized above the absorbing region but also can be detected away from the source. The bands may also be shifted by several wavenumbers in some cases. These theoretical results demonstrate that the use of nearfield microscopy is not straightforward and has to be done in a rigorous and cautious way to get relevant data. Different nearfield configurations may lead to somewhat different conclusions. Interestingly, Dazzi suggested that the resolution could be improved by illuminating the sample with a wide-angle aperture “in order to destruct the spatial coherence giving rise to the above mentioned diffraction patterns or to generate the evanescent field inside the sample, such as in the SNOM configuration”. Aperture-based SNOM suffers from low efficiency due to attenuation and the absorption of light passing through a small metal-coated aperture.8-11 By using apertureless SNOM, where the light is scattered by a metallic needle,12-19 the resolution of the system can be substantially improved20-25 to around 20 nm (8) Hecht, B.; Sick, B.; Wild, U. P.; Deckerd, V.; Zenobi, R.; Martin, O. J. F.; Pohl, D. W. J. Chem. Phys. 2000, 112, 7761-7774. (9) Dragnea, B.; Preusser, J.; Schade, W.; Leone, S. R.; Hinsberg, W. D. J. Appl. Phys. 1999, 86, 2795-2799. (10) Unger, M. A.; Kossakovski, D. A.; Kongovi, R.; Beauchamp, J. L.; Baldeschwieler, J. D.; Palanker, D. V. ReV. Sci. Instrum. 1998, 69, 2988-2993. (11) Hecht, B.; Bielefeldt, H.; Inouye, Y.; Pohl, D.; Novotny, W. L. J. Appl. Phys. 1997, 81, 2492-2498. (12) Zenhausern, F.; Martin, Y.; Wickramasinghe, H. K. Science 1995, 269, 1083-1085. (13) Adam, P. M.; Royer, P.; Laddada, R.; Bijeon, J. L. Ultramicroscopy 1998, 71, 327-331. (14) Aubert, S.; Bruyant, A.; Blaize, S.; Bachelot, R.; Lerondel, G.; Hudlet, S.; Royer, P. J. Opt. Soc. Am. B 2003, 20, 2117-2124. (15) Masaki, T.; Goto, K.; Inouye, Y.; Kawata, S. J. Appl. Phys. 2004, 95, 334-338. (16) Hayazawa, N.; Inouye, Y.; Sekkat, Z.; Kawata, S. Chem. Phys. Lett. 2001, 335, 369-374. (17) Hayazawa, N.; Inouye, Y.; Sekkat, Z.; Kawata, S. J. Chem. Phys. 2002, 117, 1299-1301. (18) Hayazawa, N.; Tarun, A.; Inouye, Y.; Kawata, S. J. Appl. Phys. 2002, 92, 6983-6986. (19) Hayazawa, N.; Yano, T.; Watanabe, H.; Inouye, Y.; Kawata, S. Chem. Phys. Lett. 2003, 376, 174-180.

10.1021/la0625594 CCC: $37.00 © 2007 American Chemical Society Published on Web 01/11/2007

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at mid-infrared wavelengths, as reported by Keilmann.26 Previously, Knoll and Keilmann reported a resolution of better than 100 nm27-30 by using the apertureless near-field scanning infrared microscopy (ANSIM). Apertureless near-field scanning IR microscopy has been developed for nanometer-scale chemical imaging.31-33 The apertureless near-field scanning infrared microscopy can also probe surface-enhanced nonlinear optical processes.34-36 It can reveal subwavelength details because it uses a sharp probe to disturb evanescent fields near the light-scattering objects rather than beam focusing.37-39 The perturbation of the local electromagnetic fields in turn induces detectable changes in the farfield signal. To obtain the signal contrast, an IR laser is tuned to the wavelengths that are characteristic of the stretching vibrations of the investigated organic molecules.40 Traditionally, the ANSIM relative near-field contrasts are described by the static dipole approximation of the coupleddipole model.41 In a coupled-dipole method, an array of dipole moments P is found from the matrix equation

AP ) E

(1)

where E is the total field at each dipole and A is the interaction matrix. According to the static dipole approximation, the structure made of the sample (dielectric constant s) and the AFM cantilever tip with the radius of curvature a and the coating characterized by the dielectric constant t at a distance z from the sample’s surface (Appendix A) can be represented by two dipoles. Unlike the situation for the forward-scattering setup,27 where the total extinction cross section is detected, in this work the back-scattered light was detected. For |t| >> 1, assuming the effective medium approximation, the power signal should be proportional to the scattering cross section (Rayleigh limit),

Csca )

k4|Reff|2 6π

(2)

where Reff ) 4πR3(1 + β)/(1 - β/(4(1 + z/a)3)) and β ) (s 1)/(s + 1) for an incident p-polarized plane electromagnetic wave. (20) Hamann, H. F.; Gallagher, A.; Nesbitt, D. J. Appl. Phys. Lett. 1998, 73, 1469-1471. (21) Hillenbrand, R.; Keillmann, F. Appl. Phys. Lett. 2002, 80, 25-27. (22) Lahrech, A.; Bachelot, R.; Gleyzes, P.; Boccara, A. C. Opt. Lett. 1996, 21, 1315-1317. (23) Lahrech, A.; Bachelot, R.; Gleyzes, P.; Boccara, A. C. Appl. Phys. Lett. 1997, 71, 575-577. (24) Knoll, B.; Keilmann, F. J. Microsc. (Oxford) 1999, 194, 512-515. (25) Bridger, P. M.; McGill, T. C. Opt. Lett. 1999, 24, 1005-1007. (26) Keilmann, F. J. Electron Microsc. 2004, 53, 187. (27) Knoll, B.; Keilmann, F. Nature 1999, 399, 134-137. (28) Knoll, B.; Keilmann, F. Opt. Commun. 2000, 182, 321-328. (29) Taubner, T.; Hillenbrand, R.; Keilmann, F. J. Microsc. (Oxford) 2003, 210, 311-314. (30) Hillenbrand, R.; Keilmann, F. Phys. ReV. Lett. 2000, 85, 3029-3032. (31) Akhremitchev, B. B.; Pollack, S.; Walker, G. C. Langmuir 2001, 17, 2774. (32) Raschke, M. B.; Molina, L.; Elsaesser, T.; Kim, D. H.; Knoll, W.; Hinrichs, K. ChemPhysChem 2005, 6, 2197-203. (33) Brehm, M.; Taubner, T.; Hillenbrand, R.; Keilmann, F. Nano Lett. 2006, 6, 1307-1310. (34) Azoulay, J.; Debarre, A.; Richard, A.; Tchenio, P. J. Microsc. (Oxford) 1999, 194, 486-490. (35) Azoulay, J.; Debarre, A.; Richard, A.; Tchenio, P. Appl. Opt. 2000, 39, 129-134. (36) De Groot, P. J.; Postma, G. J.; Melssen, W. J.; Buydens, L. M. C.; Deckert, V.; Zenobi, R. Anal. Chim. Acta 2001, 446, 71-83. (37) Sasaki, H.; Sasaki, Y. J. Appl. Phys. 1999, 85, 2026-2030. (38) Krug, J. T., II; Sanchez, E. J.; Xie, X. S. J. Chem. Phys. 2002, 116, 10895-10901. (39) Palanker, D. V.; Simanovskii, D. M.; Huie, P.; Smith, T. I. J. Appl. Phys. 2000, 88, 6808-6814.

The focus of this study is the bridging carbonyl vibrational resonance of a di-iron nonacarbonyl. Tri-µ-carbonyl(hexacarbonyl)di-iron(0), Fe2(CO)9, has been previously investigated for its interesting photochemistry.42,43 This molecule can be used as a model for spectral properties of much larger organometallic systems. We also test the validity of the above model by collecting experimental near-field images and argue for the value of improvements using another model. Experimental Methods Far-Field Spectroscopy. Despite several attempts to complete the assignment of the vibrational frequencies for Fe2(CO)9,44 no quantitative frequency dispersion of its dielectric function has been reported so far. The most complete analysis was done by Jang et al;45 they summarized the earlier experimental data and proposed tentative band assignments to close the gap between theoretical and experimental results. In this article, we improved upon the work of Adams and Taylor46 by eliminating artifacts from the transmission spectrum and by studying samples at widely ranging iron carbonyl concentrations. This research allows us to build a parametric model for the dispersion of the dielectric function in the ν(CO) region (Appendix B and Supporting Information). In addition, we apply Bruggeman’s analysis47 to recent experimental data48 of nondestructive testing of iron carbonyl composites to evaluate the low-frequency contributions. Solid flakes of Fe2(CO)9 (Aldrich, 99.5% pure) were ground with an agate mortar and pestle into a powder with particle sizes of 50 to 200 nm, which was then mixed with CsCl fine powder (submicrometer particle sizes) at ratios ranging from 0.5 to 30 wt %. The mixture was pressed in a pellet press die for more than 25 min at 40 N‚m torque into less than 0.5-mm-thick pellets. IR transmission spectra were collected by a Fourier transform infrared spectrometer (Nicolet AVATAR model 360, Madison, WI) at 0.5 cm-1 resolution (two data points per division) within a spectral range of 400 to 4000 cm-1. Absorption and reflection have been separated by collecting transmission spectra of the powders with varying low volume fractions of Fe2(CO)9. By running tests at various concentrations of the analyte and by using different matrix materials (KBr, CsCl, CsI), it was possible to identify the peaks belonging to iron carbonyl. Thus, the imaginary part of the refractive index, k, can be determined as a function of wavenumber R)

4π kν c

(3)

where R is an absorption coefficient, ν is the wavenumber, and c is the speed of light. We used the best-fit combinations of Lorentzian oscillators to describe the experimental data:

(ν) ) ∞ +

∑ν

Sjνj2

j

2 j

- ν2 - iνΓj

(4)

(40) Akhremitchev, B. B.; Sun, Y.; Stebounova, L.; Walker, G. C. Langmuir 2002, 18, 5325. (41) Burke, G. J.; Pogio, A. G. Report UCID 18834; Lawrence Livermore Laboratory: Livermore, CA, 1981. (42) Poliakoff, M.; Turner, J. J. J. Chem. Soc. A 1971, 2403. (43) Romanov, V.; Stebounova, L.; Akhremitchev, B.; Walker, G. Proc. ANTEC. 2004, 2364. (44) Park, E. S.; Andrews, S. S.; Hu, R. B. J. Phys. Chem. B 1999, 103, 9813. (45) Jang, J. H.; Lee, J. G.; Lee, H.; Xie, Y.; Schaefer, H. F., III. J. Phys. Chem. A 1998, 102, 5298. (46) Adams, D. M.; Taylor, I. D. J. Chem. Soc., Faraday Trans. 2 1982, 78, 1551. (47) Angelescu, C.; Negosanu, M.; Ioachim, A.; Itoacsen, M.; Sandu, D. D. 16eme Colloque International Optique Hertzienne et Dielectriques Groupement AMPERE; Universite du Maine, Le Mans, France, 2001; p 369. (48) Ghodgaonkar, D. K.; Ali, N. A.; Giubbolini, L. 15th World Conference on Non-Destructive Testing; Rome, Italy, 2000.

IR Detection of Nanoparticle Molecular Vibrations

Figure 1. Experimental setup of the apertureless near-field scanning infrared microscope with a beam stop that serves to minimize the interference signal. The homodyned signal is demodulated by the lock-in amplifier (not shown). Near-Field Spectroscopy. The ANSIM apparatus built at the University of Pittsburgh is based on a commercial atomic force microscope (MultiMode AFM, Digital Instruments, Inc., Santa Barbara, CA), a CO/CO2 laser source, an optical bench for alignment and focusing of the laser beams at the cantilever tip and collecting the scattered light, an IR detector, and a lock-in amplifier for detection of the nonlinear effects of the tip interaction with evanescent IR fields (Figure 1). To obtain signal contrast, a CO2 laser is tuned to the wavelengths that are characteristic of the stretching vibrations in organic molecules. The cantilever tip oscillates in tapping mode (normal to the surface of the sample), and the back-scattered light is collected at harmonics of the frequency of the cantilever oscillation. The intensity of such a signal normalized to the reference intensity, usually generated by the substrate, as a function of the wavenumber is called a near-field reflectance spectrum. Detection of the weak scattered field can be enhanced by optional homodyning.49-52 We used commercial silicon nitride cantilevers with a sharp tip and 10 nm radius of curvature that were coated with 25 nm of platinum (MikroMash, Tallinn, Estonia). The beam stop (small disk blocking the propagation of light) in the center of the laser beam and the collimating lens are designed to illuminate the sample with a wide-angle aperture in order to destruct the spatial coherence and to minimize the interference from the background scattering. The calibration of the grating drive of the laser is done by recording the peak power values over the entire range and comparing them to the literature data. CO2 laser lines are typically separated by approximately 4 cm-1, which limits to some extent the spectral resolution of the technique. The beam is expanding within 0.01° both horizontally and vertically and can be considered to be a parallel beam in simulations. The MCT detector-preamplifier adjustable bandwidth (dc to 5 MHz) was typically adjusted to between 500 kHz and 1 MHz for better sensitivity and lower background noise. A phase-sensitive detector of the wide bandwidth lock-in amplifier demodulated (in a fundamental responding mode) the homodyned IR signal at the first harmonic of the tapping frequency of the AFM cantilever, 166167 kHz. Both homodyning and the lock-in detection used the phase auto-tune option for signal maximization. The same platinum-coated (25 nm) cantilever tip with a radius of curvature of ∼35 nm was used for the entire set of fitted data. We collected the iron carbonyl versus gold relative near-field contrast spectra at the second harmonic without homodyning and (49) Stebounova, L.; Akhremitchev, B. B.; Walker, G. C. ReV. Sci. Instrum. 2003, 74, 3670. (50) Maghelli, N.; Labardi, M.; Patane, S.; Irrera, F.; Allegrini, M. J. Microsc. (Oxford) 2001, 202, 84-93. (51) Sasaki, Y.; Sasaki, H. Jpn. J. Appl. Phys. 2000, 39, L321-L323. (52) Labardi, M.; Patane, S.; Allegrini, M. Appl. Phys. Lett. 2000, 77, 621623.

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Figure 2. Second harmonic near-field image of closely spaced small Fe2(CO)9 particles. The heights are 10 nm (left) and 30 nm (right). A bright spot (higher than the background voltage, in the top image) between the particles was observed over a wide range of excitation wavelengths. The bottom image shows the signal voltage (mapped according to the grayscale bar) across the entire scanned area, 1 µm × 2 µm. The top image corresponds to a single line scan through the bright cross marks. separately at the first harmonic with homodyning. A broadband IR source (a CO laser converted to a CO2 laser without a grating) was also used for comparison. The results have been compared to simple theoretical models including the tip oscillation with an amplitude of 35 nm. The height of the particles selected for the near-field spectral analysis was 50 to 100 nm. It was observed that the near-field reflectance signal from thinner flakes strongly depends on their height. It was also observed that gold reflectance can be anomalously high (Figure 2) between the adjacent particles (within 100 nm), even using second harmonic detection without homodyning. The detection limit for the thickness of the iron carbonyl flakes was between 1 and 3 nm. Whereas the lateral spatial resolution for particles thicker than 4 nm was approaching 10 nm, thinner particles could not be imaged with such good lateral resolution.

Results and Discussion Detection at the second harmonic of the cantilever oscillation, without homodyning, resulted in the near-field spectrum of iron carbonyl that has multiple peaks near the frequency of vibrational resonance of bridging carbonyls, 1826 cm-1 (Figure 3). This is not what was expected on the basis of a simplified coupled-dipole model where surface effects are approximated by an image dipole (Figure 4). The calculations took into account the roughness of the gold film. The reflectivity of gold films has been studied for centuries. In recent years, several publications have discussed the correlation between reflectivity and various surface roughness characteristics.53,54 In situ AFM roughness analysis on a typical 20 nm × 20 nm section of the gold substrate surface gave an rms roughness of 0.7 nm and Ra ) 0.12 nm. A higher-resolution AFM showed that the typical rms roughness of our films is 0.3 to 0.5 nm for gold evaporated directly on a glass substrate and 0.2 nm for films produced by evaporation onto mica and removal of the mica to present an ultraflat gold surface. The reflectivity of the gold substrate has been simulated for gold films with conductivity dominated by spherically shaped features with a radius of curvature between 0.2 and 0.3 nm. The resulting reflectivity is significantly lower than that of a perfectly flat surface of bulk gold, but the general shape of the spectrum remains the same. (53) Munoz, R. C.; Arenas, C.; Kremer, G.; Moraga, L. J. Phys.: Condens. Matter 2000, 12, L379. (54) Munoz, R. C.; Vidal, G.; Kremer, G.; Moraga, L.; Arenas, C. J. Phys.: Condens. Matter 1999, 11, L299.

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Figure 3. (Left) Second harmonic self-homodyned relative near-field scattering signal of di-iron nonacarbonyl on a gold surface, interpolated by PCHIP, the piecewise cubic Hermite polynomial (step 3 nm) and the cubic spline (Matlab 7.0). (Right) First harmonic auto-homodyned relative near-field scattering signal of di-iron nonacarbonyl on a gold surface. The contrast variations in resonance regions are more dramatic than without homodyning.

Figure 4. Computer simulations of Fe2(CO)9 vs gold near-field contrast based on the static-dipole/image-dipole model and the effective medium approximation. The rough gold surface enhances the relative contrast of the iron carbonyl particles.

Then the relative near-field reflectance of the sample (Figure 4) can be estimated as being proportional to

|Reff(Ptxsample)| |Reff(PtxAu)| because of self-homodyning of the signal by the background scattering. The use of homodyning did not have any major impact on the spectral profile, except for a significant rise in the magnitude of the scattering signal at the peaks (Figure 3). Because the homodyning option is designed to auto-tune the reference beam’s phase shift for maximum amplitude of the interference demodulation signal at the lock-in detector reference frequency,49 it can hop between phases for maximum scattering by gold and iron carbonyl. However, without this option, the self-homodyned signal is optimized for the maximum phase of gold as the main scattering source. Then the difference between auto-homodyned and self-homodyned spectra should correlate with the phase relation between scattering from the sample and the substrate. In fact, the simulated phase difference (coupled-dipole model, Figure 5) follows the same pattern as the apparent depression in the self-homodyned spectrum (∼1836 cm-1 in Figure 3). A clear manifestation of such phase-related effects has been observed at the wavelengths where the brightness of the particles is about the same as the brightness of the substrate. Slow (40-45

Figure 5. Computer simulations of Fe2(CO)9 vs the gold near-field phase shift based on the static-dipole/image-dipole model and the effective medium approximation.

min) scans at 1856 cm-1 demonstrated that the phase jumps (∼π rad) at the lock-in amplifier cause immediate contrast reversals in the near-field image. The correlation is very strong within one scan line (i.e., 11.7 nm on a 3 µm × 3 µm (256 pixel × 256 pixel) image, Figure 6). Particle sizes (height, 30-150 nm; horizontal extension, 0.21.0 µm) had no effect on the sign of the contrast. Because the optical alignment and focusing had been performed above the gold surface, the starting phase (scanning from top to bottom) has been identified as optimal for gold. We observed that the iron carbonyl particles were darker than the substrate in this phase and brighter during the phase reversals. Similar effects have been observed with a broadband CO2 laser (Supporting Information) whenever second harmonic detection was used along with the auto-homodyning option. Numerical Simulations to Assess Reflected Dipole Waves. Because the image dipole approximation has obviously failed to accurately describe the near-field interaction of the iron carbonyl particles with the gold substrate near the narrow vibrational resonance, we consider alternative computational schemes. Taubenblatt and Tran55 compared coupled dipole results obtained by the finite-element solution to Maxwell’s equations56 using a full Sommerfeld calculation with those that they obtained using (55) Taubenblatt, M. A.; Tran, T. K. J. Opt. Soc. Am. A 1993, 10, 912.

IR Detection of Nanoparticle Molecular Vibrations

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Figure 7. Comparison of the static image dipole (left) and Fresnel reflection coefficient (right) approximations of the coupled dipoles model.

Figure 8. Geometrical model of a cantilever tip (80 patches) and a surface (half-space) for NEC simulations.

Figure 6. (Top) AFM height image 3 µm × 3 µm (256 pixels × 256 pixels). (Middle) First harmonic auto-homodyned near-field image. (Bottom) ∼1.5 µm × 0.5 µm segment of the top part of the near-field image; the dotted line represents a single scan line. The vertical dimensions of the particles range between 50 and 150 nm. The contrast reversal is accompanied by a reference signal phase shift and has no correlation to particle size.

the image dipole method modified by the appropriate Fresnel reflection coefficient. For a spherical polystyrene particle of 300 nm diameter on Si (the refractive index used was 3.85 + 0.018i), they found that the approximate image dipole is in good agreement with exact (Sommerfeld) calculations for forward scattering (angle of incidence, 65°) but its estimates for back-scattered p-polarized light are slightly off, by a factor of approximately 1.5. For the particles that were very close to the surface, the reflection terms resembled those that are due to a static dipole above a dielectric half-plane. Overall, they found that the Fresnel reflection method works well for an observation point far from the surface; a perfectly conducting substrate is well approximated by an image dipole. In this work, therefore, we adopt their approach and have computed the narrow band spectrum by using a numerical electromagnetic code (NEC)57-59 with Sommerfeld terms to account for the reflected dipole waves. For an observation point far from the surface, the reflection term is approximated by the field from an image dipole that is modified by Fresnel (planewave reflection) coefficients55 (Figure 7) Compared to the previously described static dipole approximation, this introduces the phase lag between the interfering incident and reflected electromagnetic waves. An additional advantage over the (56) Wojcik, G. L.; Vaughn, D. K.; Galbraith, L. K. Calculation of Light Scatter from Structures on Silicon Surfaces. In Lasers in Microlithography; Ehrlich, J. S., Tsao, J. Y., Eds.; SPIEsThe International Society for Optical Engineering: Bellingham, WA, 1987; Vol. 774, pp 21-31. (57) Lager, D. L.; Lytle, R. J. Report UCRL-51688; Lawrence Livermore Laboratory: Livermore, CA, 1974. (58) Lager, D. L. & Lytle, R. J. Report UCRL-51821; Lawrence Livermore Laboratory: Livermore, CA, 1975. (59) Burke, G. J. & Pogio, A. J. Report UCID-18834; Lawrence Livermore Laboratory: Livermore, CA, 1981.

analytical model is the capability of the numerical code to account for the shape of the scattering tip more accurately by superposing direct and surface-reflected waves from multiple dipoles. In the presence of the surface, the interaction matrix must be modified to account for the reflection of the dipole waves from the surface, and the electric field E becomes a standing wave. Thus,

Aii )

1 - Rii R

(5)

Ai*j‚Pj ) -(Eij + Rij)

(6)

where R represents the reflected dipole wave

Eij(r) ) k2(nij × Pj) × nij

exp(ikr) + r

(

[3nij(nij‚Pj) - Pj]

)

1 ik exp(ikr) (7) r3 r2

nij is the unit-direction vector and k is the wave number of the incident radiation. Because the Sommerfeld/Norton method in NEC is limited to wires, the reflection coefficient approximation was used for all interactions. In practice, the Fresnel approximation may be adequate for use in the dipole interaction matrix55 either as a result of sufficiently good representation of the Sommerfeld terms (as for the high-refractive-index substrate) or because the direct interactions of the dipoles dominate the surface-derived interactions. We used the variable segmentation of a sphere (80 patches) to represent a perfectly conducting cantilever tip (Figure 8). The segment lengths were about 0.0025 times the wavelength. We simulated a focused beam as a sum of nine plane waves, incident at ∼80°. The observation point was specified to be 1 m away from the scatterer. The scattered signal was calculated as a function of the observation angle in the horizontal (φ) and vertical (θ) planes. The back-scattered waves were recombined alternatively as a sum of electric fields or intensities, with similar results. The double-precision NEC2D codes, originally developed by Lawrence Livermore Laboratories, and the windows utility for source deck generation and output viewing (4NEC2, version 5.3.9 by Arie Voors, [email protected]) were downloaded from the NEC archives

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Figure 9. Comparison of the theoretical models and the experimental results for the first harmonic auto-homodyned near-field spectra.

Figure 10. NEC simulations of the angular distribution in the nearfield scattering signal (plane of incidence); θ < 0 for forward scattering. The line of incidence and back scattering is at θ ) 80°.

maintained by Raymond Anderson (WB6TPU, raymonda@ ieee.org). A major addition to the NEC2 is a treatment for lossy grounds that is accurate for antennas very close to the ground surface. We tested this method by computing the z dependence of scattering signal at various wavelengths and by comparing the relative signal (iron carbonyl vs gold) away from vibrational resonance to analytical estimates within the coupled dipoles approximation. Figure 9 compares the two theoretical models and the experimental data. Unlike the static image-dipole model with an effective medium approximation, the NEC Fresnel model does generate multiple peaks in the simulated near-field spectrum. The origin of the sharp peaks is in strong directionality of the scattered waves (Figure 10). Thus, our experimental results provide evidence that the simplified effective medium approximation, which works well for materials with broad spectra, is not reliable when it comes to modeling strong narrow resonances. At the same time, when the Sommerfeld reflection term is approximated by an image dipole that is modified by Fresnel reflection for the appropriate observation angle, this model yields useful results. The NEC2 simulations showed that the low-frequency edge of the major near-field absorption band for the iron carbonyl ν(CO)b vibrational mode matches the experimental data very well, and the shape of the secondary features strongly depends on the high-frequency dielectric function, ∞. This model virtually allows us to eliminate the possibility of Fe2(CO)9 decomposition into Fe2(CO)8 isomers because the corresponding (displaced, see Supporting Information) absorption band was not experi(60) Swanson, B. I.; Rafalko, J.; Shriver, D. F.; San, Filippo, J., Jr.; Spiro, T. G. Inorg. Chem. 1975, 14, 1737.

RomanoV and Walker

Figure 11. NEC2 simulated response for ∞ ) 2.1, ∆f ) 700 kHz, and sp ) 3 nm, the best fit. The anomalous response variability between the zero detection phase (-) and the lift-off phase (--) around 1855 cm-1 is similar to the experimental observations.

mentally observed between 1805 and 1815 cm-1. On the contrary, a group of experimental data points at around 1810 cm-1 sits just above a minor local peak predicted by the model at 1815 cm-1, although one might speculate that the experimental data in the 1810-1825 cm-1 range suggest some presence of excited states of Fe2(CO)9, with the absorption bands shifted by 15-20 cm-1 rather than 25 cm-1 (complete decomposition).42 This result is significant by itself because the complex is known to undergo thermal decomposition at room temperature under a focused laser beam.60 (In our experiment, an IR laser beam with a power of 50-100 mW was focused into a small spot of ∼50 µm diameter.) From a parametric fit of the far-field IR transmittance spectra (Appendix D), we estimated that the iron carbonyl ∞ was within the range of 1.5-2.5 (90% confidence interval). After analysis of the high-concentration measurements, we hypothesized that the observation of the 1826 cm-1 peak “bleaching” anomaly at the percolation limit is due to in-matrix multiple scattering. The extinction profile-matching values of ∞ were estimated to be 1.7-2.1, with 1.8-1.9 being the best fit (far field). Interestingly, the best-fit (near-field) value, ∞ ) 2.1 (∆f ) 700 kHz) shows a strong phase dependence around 1855 cm-1 (Figure 11). This is exactly what we observed experimentally.

Conclusions We conducted an experimental and theoretical study of the laterally resolved, near-field infrared spectra of the narrow vibrational resonance of the bridging carbonyl group in di-iron nonacarbonyl nanoparticles on a gold substrate. The resulting near-field spectra showed the importance of taking into account the angular distribution of the scattering signal and the phase shift of the beam reflected from the sample surface versus the substrate. A detailed theoretical model of the ANSIM experimental setup, which accounts for the lossy sample surface, detection bandwidth, lock-in amplifier phase shift, and AFM cantilever deflection, has been developed. In agreement with experimental observations, the calculated near-field backscattering spectrum shows an apparent shift of the absorption band by several wavenumbers compared to the far field observations. Because the exact magnitude of the calculated shift perfectly matches the experimental data, we conclude that the iron carbonyl sample did not undergo any laser-induced chemical transformations that could change the vibrational resonance frequencies of the bridging carbonyl groups. Thus, the application of the developed model allowed us to achieve chemical selectivity with very high lateral resolution.

IR Detection of Nanoparticle Molecular Vibrations

Langmuir, Vol. 23, No. 5, 2007 2835 Table B1. Summary of Vibrational Oscillator Strengthsa wavenumber, cm-1

Figure A1. Illuminated (with an angle of incidence of θ ) 80°) cantilever tip and a sample surface (half-space).

Appendix A: Geometrical Model for Near-Field Imaging Because of the short-range nature of the near-field interactions, the AFM cantilever tip can be represented in simulations by a sphere of radius R (Figure A1). Sufficiently large and thick samples can be modeled by a half-space characterized by the complex dielectric constant s. Using the static dipole approximation, the structure made of the sample and the tip with radius of curvature a and the coating characterized by the dielectric constant t at a distance z from the sample’s surface can be represented by a dipole (tip) and an image dipole (sample)

p ) RE

and

p′ ) (βp

(A1)

where

R)

4πa3(t - 1) (t + 2)

and

β)

(s - 1)

The detected differential signal (for vertical polarization, p′ ) βp) is proportional to the change in effective polarizability of the coupled system between the far field 3 |RFF eff| = 4πa |β + 1|

(A2)

|RFF eff| | ≈ 4 |RNF eff |β - 4|

(A3)

and the near field

Di-iron nonacarbonyl presents certain problems for direct Kramers-Kronig analysis of its spectra, which requires integration over the entire frequency range and measurement of the real part of the refractive index away from the resonances. Instead, the best-fit combinations of Lorentzian oscillators can be used to describe the experimental data on the assumption that the mid-infrared spectrum is governed by vibrational resonances. This approach enables the assignment of resonance frequencies (all within 2 cm-1 of the Adams and Taylor46 C26h assignments) and oscillator strengths of vibrational transitions. Table B1compares the fit of the experimental data with the theoretical predictions by Jang et al.:45 the E2g and E1u lines around 2015 cm-1 are compared to the E′(C3h) line. The infrared intensities in km/mol have been converted to oscillator strengths

π2Sjνj2 100nrK

this work

A&T46

this work

ν(Fe-C)t ν(Fe-C)t δ(FeCO)t δ(FeCO)b δ(FeCO)t δ(FeCO)t ν(CO)b ν(CO)t ν(CO)t ν(CO)t ν(CO)t

422 453 525 561 598 675 1826 1986 2012 2018 2086

422 454 525 560 600 672 1826 1988 2014 2018 2085

weak 0.026 weak weak 0.117 0.025 0.046 weak 0.026 0.066 0.005

Jang et al.45

A&T fit

0.005

NA

0.141 0.396 0.065

0.023 0.040

E′ (C3h): 0.103 0.143

0.003 0.051 0.044

t ) terminal, b ) bridging. Fits at alternative values of the infinite frequency dielectric constant are given in Table B2. a

Table B2. Vibrational Oscillator Strengthsa vibrational ν, Γ, mode cm-1 cm-1 ν (Fe-C)t δ(FeCO)t δ(FeCO)t ν(CO)b ν(CO)t ν(CO)t ν(CO)t

454 599 675 1826 2012 2018 2086

16 15 38 17.5 11 14 12.5

1.5 0.0245 0.116 0.026 0.042 0.0248 0.0071 0.008

oscillator strength, S vs • 1.8 2.0 2.1 0.026 0.117 0.025 0.046 0.0255 0.0115 0.0051

0.037 0.185 0.045 0.049 0.0255 0.015 0.0054

0.039 0.196 0.048 0.0506 0.0255 0.0159 0.0057

2.2 0.041 0.207 0.051 0.0523 0.0256 0.0167 0.0059

t ) terminal, b ) bridging.

oscillator strengths are quite similar to the ones obtained from the theoretical infrared intensities except for those of the terminal mode A2′′ at ν24. The observed central frequencies are in much better agreement with experimental data reported by Adams and Taylor than with the results of theoretical computations, which can be partially attributed to the differences between molecular modes and the coupled modes in polycrystalline flakes.

Appendix C: Near-Field Imaging

Appendix B: Dielectric Properties of the Iron Carbonyl

Ij )

vibrational modes

a

(s + 1)

oscillator strength, S

(B1)

where nr is the real part of refractive index and K is the molar concentration. The resulting frequency dependence of the dielectric function satisfies the Kramers-Kronig condition. The experimental

To minimize the interference of the scattered IR beams, the signal is often detected or demodulated at twice the frequency of the cantilever oscillation. Probe oscillation upon approach to the surface remains harmonic. Thus, the presence of the second harmonic in the scattered signal indicates strong nonlinearity in the near-field signal upon approach to the surface. A strongly decaying z dependence of the second harmonic near-field signal typically is interpreted as an indication that the optics were aligned and focused correctly. However, the signal-to-noise ratio for first harmonic detection is much greater than for the second harmonic. The homodyned first harmonic setup allows us to collect a high-quality near-field signal by scanning very close to the sample surface at low tapping amplitudes. Typical first harmonic z plots above an ultraflat gold surface can look similar to the second harmonic z plots (Figure C1). The z dependence of the signal above the surface of a sample particle can be significantly different for both first and second harmonic detection, even for relatively flat particles (Figure C2). Because the intensity of the background electromagnetic waves cannot change dramatically within much less than the wavelength, this should be attributed to the particle properties. Simulations of the z dependence for the scattered signal at 1870 and 1880 cm-1 (Figure C3) show that such behavior should be expected for (250 nm oscillations around the z coordinate, without any background scattering. To avoid interference from far-field scattering, first harmonic detection may be preferred because it

2836 Langmuir, Vol. 23, No. 5, 2007

RomanoV and Walker

Figure C1. Typical second harmonic z plots and signal (V, all panels) as a function of tip-sample separation (nm) above the gold surface for different wavelengths. The peak signal is proportional to the laser output power, but the baseline does not change.

Figure C3. Simulated z dependence of the near-field scattered signal above the Fe2(CO)9 surface.

Figure C2. First (1f) and second (2f) harmonic z plots of the IR near-field signal (V, all panels) at 1876 cm-1 and the amplitude of cantilever oscillation of 250 nm above (top and middle panels) and next to (bottom panel) an Fe2(CO)9 particle. Lateral dimensions of the particle: ∼0.5 µm × 1.0 µm, height 50 nm. Whereas both first (middle) and second harmonic (top) plots show interferometric features above the Fe2(CO)9 flake, the first harmonic z plot above the gold surface near the particle (bottom) is very similar to z plots away from any particles.

yields a relatively higher signal-to-noise ratio at very low amplitudes of cantilever oscillation.

Appendix D: NEC2 Simulations and the Lock-In Detection Mode For the near-field spectrum, the best-fit range of ∞ appears to be between 2.0 and 2.2, whereas the theoretical plots for 1.5

Figure D1. Typical NEC2 simulated response for ∞ ) 1.5, 1.8, 2.0, and 2.2, which accounts only for the difference between the scattered signal from the tip touching the surface and the tip’s farfield position.

to 1.8 have very high peaks at 1865-1875 cm-1 (Figure D1) and the predicted response for 2.4 is too flat. These spectra are lacking some features that would be present for the simulations of a focused beam but demonstrate similar trends. Alternatively, the same results as for ∞ ) 2.1 should be observed for the ∞ ≈1.8

IR Detection of Nanoparticle Molecular Vibrations

Figure D2. Transient modes’ contribution to the near-field response for ∞ ) 2.1. The signal as a function of the wavenumber changes very little for some ranges of the tip-sample separation: between 0 and 0.1 nm, from 0.2 to 0.4 nm, and above 2 nm. The large peak at 1855 cm-1 is due to only the transient modes.

Langmuir, Vol. 23, No. 5, 2007 2837

Figure D5. NEC2 simulated response for ∞ ) 2.2, ∆f ) 700 kHz/sp ) 3 nm ()), and ∆f ) 500 kHz/sp ) 9 nm (-); the same phases are represented as in Figure D4. Technically, the correlation with experimental data is still good, but the plot starts to become too flat, especially within the absorption band.

The lock-in amplifier output signal is calculated as

SL ) Figure D3. Cantilever deflection model. The cantilever body’s additional (after the tip touched the surface) deflection, down to the sp value, is assumed to be quasi-harmonic.

t I∫-∞ cos(2πft + φ) SD(z(t′)) FD(t - t′) dt′ dt

(D1)

where f is the reference frequency (frequency of the cantilever oscillation), φ is the phase shift introduced within the lock-in amplifier (which is assumed to be in phase with the maximum near-field signal), and SD is the signal proportional to the power collected by the infrared detector, which depends on the tipsample separation z

z(t) ) z0 cos(2πft) - sp

(D2)

where z0 is the amplitude of the cantilever oscillation. The instrument convolution function can be approximated by the exponential decay function

FD(t - t′) ) exp(-2π∆f(t - t′)) Figure D4. NEC2 simulated response for ∞ ) 2.0 within the phase variation from 0 (upper trace line) to the tip’s lift-off from the surface (lower trace line); a good fit is shown for ∆f ) 700 kHz/sp ) 3 nm ()). The data variability near the absorption band is better accounted for by ∆f ) 500 kHz/sp ) 8 nm (-).

to 1.9 if the oscillator strength of the 2018 cm-1 line is taken to be 0.05, which is still within the margin of error. The error is large because of the the doublet splitting of a single molecular line in the polycrystalline iron carbonyl. In fact, the solid angle Ω averaging of the power absorbed by the (0001) face of the polycrystalline flake46 can increase the line intensity by a factor of 3 (up to 0.035-0.045):

Figure D2 shows that transient electromagnetic modes (during the tip approach or lift-off phase) may give significant contributions at certain wavelengths, depending on the speed of the cantilever approach to the surface and the time that it stays in direct contact with the sample. Our model treats these factors by introducing the effective set point sp, which accounts for the maximum change in the cantilever’s deflection after it comes into contact with the surface (Figure D3). Here we call the “contact” a condition when the scattering field can be estimated in the zero (practically less than 0.1 nm) tip-sample separation approximation.

(D3)

where ∆f is the MCT detector bandwidth. Practically all near-field features vanish at z > 2 nm, so we can estimate the signal to be proportional to the difference between two extreme phases. We calculated the signal variability for the peak phases between zero and the phase (φL) corresponding to the tip’s separation from the surface:

(

φL ) arccos 1 -

)

sp z0

(D4)

For a bandwidth less than 700 kHz, the contribution of the transient modes becomes very significant, and a good fit to the experimental data can be achieved only for increasingly large set-point values (Figures D4 and D5). The increase in bandwidth above 800900 kHz has very little effect on the theoretical plots or the best-fit set point values. Acknowledgment. We gratefully acknowledge support from the NSF (CHE-0404579), ARO (W911NF-04-100191), ONR (N00014-05-10765), CRC Program (202483), NSERC (312497), and NIH (R21-EB003101). Supporting Information Available: Molecular crystal structure, ν(CO) region assignment correlation for Fe2(CO)9, far-field infrared spectra, and broadband infrared near-field imaging. This material is available free of charge via the Internet at http://pubs.acs.org. LA0625594