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J. Phys. Chem. C 2007, 111, 182-187
Real-Time Spectroscopic Ellipsometry of Silver Nanoparticle Formation in Poly(Vinyl Alcohol) Thin Films T. W. H. Oates* and E. Christalle Institute of Ion Beam Physics and Materials Research, Forschungszentrum Dresden-Rossendorf, BautznerLandstrasse 128, 01328 Dresden, Germany ReceiVed: August 7, 2006; In Final Form: October 6, 2006
Silver nanoparticle formation in poly(vinyl alcohol) thin films is analyzed in real time by spectroscopic ellipsometry. Modeling the data using the Maxwell-Garnett theory shows that the silver content predicted by the model depends of the film thickness. This is conjectured to be due to the absence of plasmon resonances in very small particles affecting the model. The size dependence of the free electron relaxation frequency is used to analyze the particle size during nucleation and growth. Evaporation of the polymer matrix is also monitored by real time ellipsometry and the plasmon resonance is observed to shift from 3.0 to 2.2 eV as the particles are liberated from the polymer. The particle density on the surface can be controlled by the silver concentration and the initial polymer thickness. The exposed particles are easily imaged with scanning electron microscopy, and the particle sizes are compared to the parameters predicted from the Maxwell-Garnett theory.
Introduction Polymer-metal nanoparticle composites are a promising class of material for a diverse range of novel applications, from sensors to optical devices.1 One of the main advantages of embedding nanoparticles in a polymer matrix is the coagulation inhibition provided by the polymer, thereby maintaining isolated particles. Recently it has been shown that by evaporation of the polymer at intermediate temperatures, the nanoparticles can be left dispersed on the substrate surface, with control over the particle density imparted by the polymer thickness.2,3 Polymer matrices have also been used to control the formation of nanoparticle structures, including the interparticle spacing and complex 3-D structures.4 Adjusting the interparticle distance by expansion and contraction of a temperature responsive polymer membrane is another novel feature available to such systems.5 Monitoring the formation of such composites using noninvasive optical techniques is a highly desirable objective. Most applications of noble metal nanoparticles, from photonic devices to sensors,6 utilize the plasmon polariton resonances inherent in the particle. For metallic particles that are small compared to the wavelength, incident electromagnetic radiation excites a collective oscillation of the conduction electrons which polarize the particle. The surface charge creates a restoring force and a resonance occurs, the frequency of which depends primarily on the size and electron density of the particle and the polarizability of the embedding medium. At resonance, strong light scattering occurs and the electric field in the vicinity of the particle is strongly enhanced. For noble metal particles embedded in a nonabsorbing dielectric the resonance generally occurs in the visible part of the spectrum, creating intense red and yellow optical materials, as observed in noble metalcontaining “stained” glasses. The strong electric fields in the vicinity of the particle are primarily responsible for a significant increase in the Raman scattering cross-sections of molecules * To whom correspondence should be addressed. E-mail: t.oates@ fz-rossendorf.de.
absorbed on the particle surface, forming the basis of surfaceenhanced Raman spectroscopy (SERS).7 The optical properties of nanoparticles provide an insight into their size and structure. Mie theory describes the size-dependent light scattering and absorption of small metal particles, taking into account the inherent dielectric properties of the particle.8 For particles smaller than the mean free path of electrons in the bulk material (a few tens of nanometres in metals) the dielectric function of the metal becomes size dependent due to increased electron scattering from the particle surface.9 This feature is considered an intrinsic size effect, as compared to the extrinsic size effects of the Mie theory. Further effects are observed for much smaller particles. For example the conduction band becomes increasingly quantized10 and the lattice parameters decrease with decreasing size due to an increased surface to volume ratio.11 Optical absorption spectroscopy is most commonly used to characterize the plasmon resonance of composite films and the resonance energy and broadening are often quoted. Important information on the particle properties can be obtained by fitting the resonance with physical models, including possible quantisation effects for very small particles.12 The size-dependent dielectric constants are also an indicator of the average particle size.13 For thin composite films, spectroscopic ellipsometry (SE) is an excellent technique for measuring the optical properties and, with appropriate modeling, can simultaneously determine the film thickness, and hence the dielectric constants, with a single measurement. Recent advances in hardware make it possible to observe in real-time the formation of nanoparticles in situ.3,14 The aim of the work presented here is twofold. First, the realtime analysis, using spectroscopic ellipsometry, of the formation of silver nanoparticles in poly(vinyl alcohol) films by temperature-induced reduction and diffusion of silver ions is performed. Physical parameters are extracted by modeling the data using an effective medium approximation. Second, the controlled evaporation of the polymer matrix is performed with the assistance of real-time spectroscopic ellipsometry. By use of
10.1021/jp065081l CCC: $37.00 © 2007 American Chemical Society Published on Web 11/22/2006
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J. Phys. Chem. C, Vol. 111, No. 1, 2007 183
TABLE 1: Experimental, Fitted, and Measured Parameters for the Samples Cured at 150 °C exptl parameters
fitted parameters
measd parameters
sample
Ag concn (mg mL-1)
spin frequency (rpm)
thickness (nm)
silver volume (%)
Γ (eV)
MSE
avg radius (nm)
SD (nm)
A B C D E F
6.6 6.6 6.6 11 11 11
4000 2000 1000 4000 2000 1000
41 57 85 48 59 92
0.76 1.14 1.53 2.36 2.66 2.75
0.38 0.46 0.51 0.50 0.56 0.52
6.1 9.1 14.9 10.1 12.9 38.9
4.7 5.1 7.8 5.5 4.7 6.2
1.8 1.5 4.0 2.0 2.0 3.0
films of different thicknesses, the density of nanoparticles on the substrate surface can be controlled. The exposed particles are then imaged by scanning electron microscopy (SEM) and the observed nanoparticles compared with the ellipsometric parameters. Experimental Section Poly(vinyl alcohol) (PVOH) containing silver nanoparticles is a polymer/metal-nanoparticle composite noted for its ease of preparation using environmentally friendly precursors. An aqueous solution of silver nitrate and PVOH produces silver nanoparticles when heated via a polyol reduction of the silver ions and subsequent diffusion, nucleation, and growth. In such a case the polymer acts as both the reducing agent and the host matrix. The reduction step is also possible either in the solution stage or after casting of the polymer. Lin et al. recently demonstrated PVOH-Ag to be ideal for SERS substrates when combined with poly(γ-glutamic acid) as a stabilizer of the nanoparticles reduced in the solution stage.15 Porel et al. have recently reported the application of PVOH-Ag as an optical limiter, including an extensive TEM investigation of the particle size as a function of the processing temperature and silver ion concentration.16 The method of reducing the silver ions in the solid polymer film is repeated here. PVOH (87-89% hydrolyzed, average MW 13 000-23 000, Sigma Aldrich) was dissolved in deionized water and mixed with an aqueous solution of silver nitrate (99.9999%, Sigma Aldrich). The final PVOH concentration was 33 mg/mL. Final concentrations of silver nitrate were 6.6 and 11 mg/mL. After 1 h mixing the solutions were spun onto silicon substrates with a 2-nm native oxide surface layer, at frequencies of 1000, 2000, or 4000 rpm for 30 s, forming polymer films approximately 90, 60, and 40 nm thick, respectively. The substrates were aligned in reflection mode in the beam of a J.A. Woollam M2000 rotating compensator spectroscopic ellipsometer, with a boralectric heater acting as the sample stage. The substrates were heated to either 120 or 150 °C (maximum deviation of 3 °C) for up to 1 h with simultaneous acquisition of real-time ellipsometric data. The samples were then heated to 350 °C to evaporate the polymer matrix, leaving the particles on the substrate surface. Finally, SEM images of the particles on the substrate surface were obtained. Table 1 shows the experimental parameters for the samples cured at 150 °C, along with the modeled and measured parameters determined as described below. Results and Discussion I. SEM. SEM images of nanoparticle-containing polymer composites could not resolve the nanoparticles due to substrate charging. By evaporation of the polymer, the nanoparticles were exposed and could thus be resolved, albeit deposited on the substrate surface. Figure 1 shows the SEM images of the samples cured at 150 °C, after the evaporation of the polymer,
with histograms of the particle radii included. The average particle radius and standard deviation are reported in Table 1. It can be seen from the images that the area density of the particles increases with increasing silver ion concentration and film thickness, except for sample C. By use of real time ellipsometry, the polymer evaporation was stopped when the plasmon resonance shifted starkly (described in detail below), indicating that the particles were no longer enshrouded in polymer material. That a small amount of polymer remains at least partially surrounding the particles is clearly seen in most of the SEM images. The notable difference is in the structure of sample C, due to overheating. The polymer is entirely removed and the particles have fused together, forming substantially larger particles with non-spherical shapes. It is therefore critical to optimize the evaporation process, with the aid of real time ellipsometry, to avoid overheating, not only for SEM imaging but also if the structure of the particles in the polymer is to be maintained (e.g., for nanorods). In sample F, and to some degree in sample E, fusing of the particles has taken place within the polymer due to the high particle density. It is surmised that the particles have fused during the polymer evaporation stage. Histograms of the particle sizes show that the narrowest size distribution is for sample B, although as discussed the data from C is not indicative of the particle size in the polymer matrix. On the other hand, the exact determination of the particle boundary was hindered by the remaining polymer, and a number of smaller particles are quite probably overlooked for this same reason. On the whole the observed particle sizes are around twice that observed by Porel et al.,16 although the curing temperatures here are roughly twice as high. II. Ellipsometric Analysis. Ellipsometric data is generally represented by the parameters Y and D, defined as the ratio of Fresnel reflection coefficients R ˜ p and R ˜ s for p- and s-polarized light, respectively
R ˜p ) tan Ψei∆ R ˜s
(1)
Real-time data contains spectroscopic data in the range from 1.3 to 3.35 eV, averaged over 50 scans resulting in a data point every 11.4 s. Figure 2 shows typical Ψ and ∆ as a function of photon energy at 10-min intervals during curing at 120 °C. The imaginary part of the dielectric function, determined using the model discussed below, is also shown. The plasmon resonance at 3.0 eV is obvious. After 1 h the resonance peak is still increasing, indicating that the nanoparticle formation is still occurring. For samples cured at 150 °C the ellipsometric data stabilized after around 10 min indicating completion of the nanoparticle formation in the polymer. To analyze the ellipsometric data we use the Maxwell-Garnett effective medium theory (MGT)17 to determine the effective complex dielectric function, ˜ , of the film. The theory has been used previously to model similar metal polymer composites.12
184 J. Phys. Chem. C, Vol. 111, No. 1, 2007
Oates and Christalle
Figure 1. SEM images of samples cured at 150 °C after evaporation of the polymer. Histograms show particle radii to 20 nm. Average radii and standard deviations are listed in Table 1. The scale bar is 200 nm.
The model assumes a mixture of two distinct materials, each possessing the optical properties of the bulk material, and requires the particles dispersed in the host material do not interact with one another. This can be accommodated by keeping the fill factor low. For the case of noble metal nanoparticles the MGT is analogous to the Mie theory (the solution to Maxwell’s equations for spherical particles) in the quasistatic limit.10 The quasistatic limit denotes that the particles are much smaller than the wavelength of light in which case the dipolar plasmon resonance dominates and higher order multipoles can be neglected. For visible wavelengths the particles should be smaller than 20 nm.
The MGT is formulated as
˜ p - ˜ h ˜ - ˜ h )F ˜ + 2˜ h ˜ p + 2˜ h
(2)
where ˜ h and ˜ p are the host and particle dielectric functions, respectively, and F is the fill factor of the particles. To determine ˜ h, the polymer optical properties are modeled with a twoparameter nonabsorbing Cauchy model and fit to measurements of a polymer film without silver inclusions
n(λ) ) R +
β λ2
(3)
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J. Phys. Chem. C, Vol. 111, No. 1, 2007 185
Figure 3. Experimental and fitted data for samples A (circles), B (squares), and C (triangles). Also plotted is the imaginary part of the complex dielectric function from the fitted data showing the plasmon resonance at 3.0 eV. Figure 2. Ellipsometric data for particles forming in polymer at 120 °C. Also plotted is the imaginary part of the complex dielectric function from the fitted data showing the plasmon resonance at 3.0 eV.
where n is the refractive index, λ the wavelength of light, and R and β are fitting parameters. For ˜ p, the bulk silver dielectric function is used, modified to account for intrinsic size effects. In the visible spectrum the optical properties of silver can be broken down into the contribution from conduction electrons (intraband transitions) and transitions of d-shell electrons to the conduction band (interband transitions). By assumption that the interband transitions below the bandedge (approx 3.6 eV) are frequency independent, they can be described by a constant offset to the real part of the dielectric function.18 Adding this to the electromagnetic response of conduction electrons, described well by the Drude model,19 we obtain a silver dielectric function
˜ (ω) ) ∞ -
ωp2 ω2 - iΓω
(4)
where ωp is the bulk plasma frequency, Γ is the free-electron relaxation frequency, and ∞ is the contribution from interband transitions. For particles smaller than the mean free path of electrons in the bulk, the free-electron relaxation frequency increases due to scattering from the particle surface, thereby dephasing the plasma oscillation and broadening the resonance. The increased broadening is proposed to be inversely proportional to the particle radius9
Γ ) ΓB +
Aνf R
(5)
where ΓB is the bulk free-electron relaxation frequency, νf is the Fermi velocity for silver (1.39 × 108 cm/s), and A is a constant of proportionality which must be determined by comparison with microstructural analysis. The parameters ∞, ωp, and ΓB for silver
were determined by fitting eq 4 to the data for bulk silver from20 (4.12, 9.18, and 0.022 eV, respectively). The above model was used in the ellipsometric data analysis program WVASE3221 to fit the experimental data. A regression analysis minimized the mean square error (MSE) between the fitted and experimental data. Correlation between fitting parameters was checked to ensure that the final values were unique. Figure 3 shows the ellipsometric data after 12 min for samples A, B, and C, cured at 150 °C. Fits to the data using the above formulism are also shown. Initially five variables were used in the fit: the two Cauchy parameters, Γ, F, and thickness. It was found for all samples that the fit could be significantly improved by adjusting either ∞ or ωp. Interestingly, when one of these parameters was allowed to vary they converged to a constant value for all samples measured: ∞ ) 4.9 ((0.1) and ωp ) 8.77 ((0.05) eV. If both parameters were set as variables a strong correlation was observed. There is some conjecture in the literature as to the uniformity of the interband transition contribution for very small particles;12 however, for particle sizes R > 1 nm there is expected to be little deviation in the value of ∞ from the bulk.22 Although changes in the lattice constant for smaller particles have been observed,11 there is little evidence to suggest a change in the plasma frequency for particles R > 1 nm. A change in the plasma frequency would imply a change in free electron density or the effective optical mass of the electrons for small particles. Since there is conjecture in the literature to suggest that ∞ may vary, the plasma frequency is fixed at the bulk value of 9.18 eV and ∞ is set to 4.9. Also shown in Figure 3 is the imaginary part of the dielectric function for the films taken from the fits showing the strong plasmon absorption peak at 3.0 eV. The fitted parameters for the six samples cured at 150 °C are listed in Table 1. The Cauchy parameters are not shown in the table as the variation from the bulk values was small for all samples (R ) 1.48 ((0.01), β ) 11 ((4) × 10-3). The trend of increasing film thickness with decreasing spin frequency is as expected. The variation in thickness between the two
186 J. Phys. Chem. C, Vol. 111, No. 1, 2007 concentrations for a given spin frequency may be attributed to a slight change in the concentration of the PVOH increasing the viscosity of the 11 mg mL-1 solution. The increase in silver content with film thickness is not expected and occurs for both concentrations. We would expect that the silver volume fraction should be constant for a given silver ion concentration. It is informative to estimate the silver volume content from the chemical concentrations. Under the assumption that the silver and polymer have the density of the bulk materials, a maximum possible silver volume content of 0.72% is calculated for the 6.6 mg mL-1 AgNO3 solution. This is comparable to that determined for the thinnest film using the MGT but below that for the thicker films. From the SEM images we can estimate the volume fraction by the following assumptions. First we assume that the film thickness from the ellipsometry is correct and we can calculate the film volume in the image (630 nm × 440 nm × thickness). Next we assume the particles are spherical and we can make an estimate of the silver volume content in the film by calculating particle volumes from the measured radii. This approach gives a silver volume fraction of 1.4% for sample A and 1.0% for sample B. These values are likely an underestimate since a number of particles on the image boundary, and also very small particles not resolved in the SEM image have not been included in the count. While within the range of the MGT estimates they do not explain the increase in concentration of the fitted values. Since the SEM resolution is limited, it is possible that the samples contain a large number of smaller particles not observed in the micrographs. Thinner samples would have less volume for the nanoparticles to source mobile atoms, thereby reducing the average particle size. The relative contributions from particles of different sizes should be considered. It is well documented that very small particles exhibit a weak plasmon resonance due to Landau damping.23 In fact the resonance is not observed in particles smaller than 0.5 nm radius.24 In the limiting case that all particles are atoms there is obviously no plasmon resonance and the fill factor is estimated as zero, even though it may be the same as in a film with larger particles. This would contribute to an underestimation of the silver volume, and the deviation would increase for thinner films. The fill factor from the model should therefore be quoted with caution when studying nanoparticulate films. III. Real-Time Results. Kreibig showed that if the final average particle size is known the broadening can be related back to the size during the particle formation.22 This has been again recently exploited to determine the particle size by optical measurements.3,13 The method requires a small distribution of particle sizes, ideally monodisperse; however, for a mildly disperse distribution it provides a unique method to observe the particle growth kinetics in real time. While the method assumes the particles are spherical single crystals, it should also be noted that the broadening also arises from scattering at grain boundaries and defects, with point defects dominant over grain boundaries.25 From Table 1 we see that the broadening increases with increasing film thickness for the 6.6 g mL-1 films, indicating a smaller particle size in the thicker films. The SEM images are inconclusive in supporting this result. For the 11 mg mL-1 films this trend is not present and may be complicated by coalesced particles forming polycrystallites. Compared to the bulk value of 0.022 eV, it is clear that the scattering is highly enhanced in small particles. By determining A in eq 5 from the final particle size in the micrographs, the real-time data can be used to look at the growth kinetics of the particles during curing. The parameter A is
Oates and Christalle
Figure 4. Real-time data showing the growth of the nanoparticles at curing temperatures of 120 °C (circles) and 150 °C (triangles). The silver content increases as the particles begin to exhibit metallic behavior. The free-electron relaxation frequency, Γ, is size dependent and has been scaled from the final average particle size to give the average particle radius in real time.
specific to the embedding medium of the particles and must be evaluated by determining the average particle size. However once A is determined it should be applicable to all samples and particle sizes in the experiment. Samples A and B provide the best SEM images for the determination of A. From eq 5, values of 0.31 and 0.41 were determined for samples A and B respectively. It is clear from the deviation in the values that the uncertainties in this method are significant. Since A is a matrix dependent parameter it can only be compared qualitatively with literature values. Reviews found in the literature26 give theoretical values from 0.29 to 1, while experimental values from 0.15 to 3.6 have been reported.27 In Figure 4 the real time data for the nanoparticle growth for samples cured at 120 and 150 °C is shown. The silver content from the MGT is shown along with the particle radius, determined by scaling Γ using A ) 0.41. The inverse of Γ is also shown for reference. The difference in particle formation for the two temperatures is clear. Although the values for the silver content should be used with caution, as discussed previously, the qualitative values give important information on the growth kinetics of the particles. The results support the theory that the nanoparticle growth is mediated by temperatureinduced reduction of the silver ions, followed by migration, nucleation, and ripening. While the number of silver atoms (plus ions) is constant in the film, the model only accounts for particles exhibiting metallic behavior. Particles with a radius of less than 1 nm contribute insignificantly to the plasmon dispersion. This helps to explain why the values of the particle radii do not begin at zero. Figure 5 shows typical ellipsometric data at a number of stages during evaporation of the polymer. The most notable change occurs in the phase data, ∆, which shows a pronounced change as the polymer is removed from around the particles. Since the energy of the surface plasmon extends into the surrounding dielectric in the form of an evanescent wave, the polarizability of the surrounding medium is critical in determining the plasmon resonance frequency.10 The imaginary part of the dielectric function, scaled with the film thickness, is also shown for 0 and 35 min. The data is modeled at 0 min using
Ellipsometry of Silver Nanoparticle Formation
J. Phys. Chem. C, Vol. 111, No. 1, 2007 187 Evaporating of the polymer matrix after the particle formation, with the assistance of real-time SE, provides novel control over the concentration of the particles on the substrate surface and avoidance of overheating which leads to coalescence of the particles. SEM images of the particles also reveal that the particles are not randomly dispersed on the substrate, suggesting the polymer induces a degree of order in the particles, most likely during the evaporation phase. This may hold some promise for patterning of the nanoparticles on the substrate surface by manipulating the evaporation process. For practical applications, control of the plasmon resonance position is highly desirable.29 Controlled evaporation of the polymer matrix provides a novel method for changing the dielectric environment of the nanoparticles and therefore control over the plasmon resonance. Acknowledgment. This work was supported by a Marie Curie International Incoming Fellowship under the European Commission’s FP6 framework. References and Notes
Figure 5. Spectroscopic ellipsometric data showing the shift in the optical properties as the polymer matrix is evaporated from the nanoparticles. The imaginary part of the dielectric function for the initial and final data are shown scaled with film thickness. As the nanoparticles are exposed the plasmon resonance shifts markedly from 3.0 eV (0 min) to 2.2 eV (35 min).
the method outlined previously, while at 35 min, due to anisotropy of the embedding medium, a Lorentzian curve is used to fit the plasmon resonance (for particles exposed on a substrate surface a number of more complicated models have been proposed which take into account the particle-surface interaction and the asymmetry of the surrounding dielectric medium28). The MSE for the initial and final states were 3.5 and 8.0, respectively, indicating a good fit. The resonance shifts from 3.0 to 2.2 eV as the polymer is evaporated. Conclusion Spectroscopic ellipsometry is shown to be an excellent tool for the determination of the optical properties of metal nanoparticle/polymer composite thin films. Because of the simultaneous determination of the film thickness the dielectric constants of the film can be evaluated directly. Modeling the dielectric properties using the MGT gives an indication of the fill factor of the film; however, the accuracy of the fill factor depends on the film thickness. Including a size dependency for the broadening, Γ, is critical for nanoparticles below 10 nm radii; however, the accuracy of the fill factor is further compromised due to the exclusion of very small particles (R < 1 nm) from the model, since particles of these dimensions exhibit strong Landau damping. The size dependency of Γ provides a unique method to determine the average size of the particles and when combined with real-time SE reveals the particle size during the nucleation and growth phase.
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