Open Access
Add to BibSonomyAbstract
The composition, the structure and the optical properties of mesostructured hybrid silica films elaborated by sol-gel routine are studied versus the temperature of the post treatment by comparing ellipsometric measurements, atomic force microscopy and electronic microscopy characterizations, X-ray diffraction and thermal analysis. This paper shows that the refractive index variation is a combination between the structure contraction, the solvent evaporation, the silica wall condensation and the pyrolysis of the copolymer. We also investigate the optical properties of thermally grown silver nanoparticles in the mesotructured films and we demonstrate that these properties depend on the optical properties of the host matrix and on the silver concentration profile in the film.
©2011 Optical Society of America
1. Introduction
Because of various applications in microelectronics [1,2], in catalysis [3], or for optical coatings [4,5], chemical sensors [6] or host matrices for metallic and semiconductor nanoparticles growth [7–9], the synthesis of porous materials has become an important research field in the last few years. Sol-gel routine is used to elaborate mesoporous silica thin films with 2D or 3D hexagonal and cubic mesostructures [10]. These films are prepared by surfactant template methods in which an organic micellar mesophase self-organizes in the silica network during the deposition [11]. The formed mesostructure depends essentially on the surfactant nature and on the silica/surfactant ratio. The mesoporous silica films are obtained after removing the surfactant by calcination. Mesoporous thin films synthesized from non-ionic triblock co-polymer surfactants are interesting materials as they have high degree of ordering [12,13]. Moreover, this type of surfactant is both low cost and environmentally benign [14,15]. The refractive index of mesoporous silica films mainly depends on the film porosity and can be tuned by varying the molecular weight of the triblock copolymer [16]. A low refractive index film can then be obtained with a high molecular weight copolymer like Pluronic F127 (PEO106-PPO70-PEO106). Muro and associates have recently reported an increase of the porosity and a refractive index decrease, when raising the F127 concentration in a silica sol [17].
The use of such mesoporous films as host matrices for in situ growth of metal nanoparticles has been investigated for the control of the surface plasmon resonance (SPR). The latter leads to an absorption band in the UV/visible spectrum whose position and shape depend on the nanoparticles size and shape, the refractive index of the host matrix [18,19] and the interparticle distance [20,21]. We have recently demonstrated that mesostructured silica films doped with a silver salt could be used to control the growth of silver nanoparticles thanks to an in situ chemical [22] or photo-chemical [23] reduction of silver ions. Mesoporous titanium dioxide films were also used to limit the growth of silver nanoparticles to the pore size under laser illumination [24]. Unlike the two previous reduction methods, the thermal growth of silver nanoparticles is known to generate greater nanoparticle sizes than the pore size [25].
Although spectroscopic ellipsometry is known to be an efficient tool to follow the chemical [26,27] or the physical [27–29] growth of silver nanoparticles on a substrate, to date, no work was reported on a complete spectroscopic ellipsometric characterization of the optical properties of silver nanoparticles embedded in a mesostructured silica film. Such nanocomposite films may present singular properties like anisotropy or graded index that need cross investigations to attest the results.
To our knowledge, this paper reports the first complete ellipsometric characterisation of mesoporous materials loaded with thermally grown silver nanoparticles. We firstly characterize the changes in mesostructured silica thin films without silver during calcination of F127 copolymer. The mesostructure, the compression in the normal direction, the chemical composition of the films are measured as well as their refractive index. The modelling of the ellipsometric parameters is correlated to the different results obtained on the films. Secondly, we demonstrate the capabilities of spectroscopic ellipsometry to investigate the optical properties of mesostructured silica films containing thermally grown silver nanoparticles. Our interpretations are also based on the characterization of the opto-geometrical matrix parameters and the silver location in the film thickness. This kind of material offers a great interest for the achievement of optical components based on low refractive index or on SPR.
2. Synthesis
All reactants are used as received from Sigma Aldrich Inc.. In our typical synthesis, 4 g of tetraetoxysilane (TEOS) are mixed with 1.76 g of hydrochloride acid HCl (0.055M). This solution is stirred 30 min. Then, 1.14 g of the tribloc copolymer F127 dissolved in 18 mg of ethanol are added to the initial solution. The sol is stirred 15 min. Finally, 1.7 g of silver nitrate are added in the sol and the sol is mixed during 15 min. This addition of silver nitrate is omitted for elaborating undoped films. Each film is deposited by dip-coating with a 3.5 cm/min speed rate on a clean glass substrate or on a thermanox substrate, for TEM measurements, in a clean room class 1000 and under a yellow light in order to prevent the photoreduction of silver salt when it is added. The humidity rate and the temperature are respectively fixed at 50 ± 5% and 21 ± 1°C in order to insure a better repeatability of the synthesis. Each film is transparent, crack-free and of good optical quality. Films are then directly heated 30 min in air at a temperature comprised between 100°C and 400°C.
3. Characterisation
The mesostructure of the film is characterized by X-ray diffraction with a Philips Xpert Pro diffractometer equipped with a monochromator and using the Cu Kα radiation. Transmission electron microscopy (TEM) pictures are recorded with a TOPCON EM002B transmission electrons microscope operating at 200 kV. The samples for TEM observations of film top views were prepared by scrapping the films. For TEM observations of the film cross sections, slices were cut by ultramicrotomy in films deposited on a thermanox substrate. In both cases, pieces of film were collected on a holey comb cabon TEM grid. The topography of the film surface is obtained thanks to a Philipps FEI NovaNanoSEM scanning electron microscope (SEM) operating at 15 kV or by using a 5500 atomic force microscope (AFM) from Agilent technologies in taping mode. Absorption spectra are recorded with a UV/Visible Perkin Elmer lambda900 spectrophotometer. The spectroscopic ellipsometric measurements were carried out using a UVISEL Jobin Yvon ellipsometer. The incident angle is fixed at 60°. The wavelength range used is 300 nm-800 nm. The glass substrate back surface of each sample characterized by ellipsometry is roughened to eliminate back reflection during ellipsometric measurements. The film thickness is measured with a DekTak mechanical profilometer.
The porosity of the mesoporous thin films is deduced from the variation of their refractive index versus the relative pressure of water vapour using a SOPRA ES4G ellipsometer. The wavelength and the incidence angle are 632.8 nm and 70°, respectively. Thermogravitometric analysis (TGA) data and thermal differential analysis (TDA) data are recorded with a Pyrus Perkin Elmer analyzer, in ambient air, with a heating rate of 10°C/min from room temperature to 450°C. The infrared spectra are measured in transmission thanks to a FT-NIR Perkin Elmer Spectrum One spectrophotometer. The wave number ranges from 1900 cm−1 to 4000 cm−1, it is limited by the absorption of the glass substrate.
4. Results and discussions
4.1 Undoped films
TEM images of the untreated and undoped films clearly show that the film is made of juxtaposed domains with different nanoorganizations and orientations (Fig. 1a ). According to previous works [16,30,31], copolymers with high ethylene oxide/propylene oxide (EO/PO) ratio (>1.5) such as F127 are known to form preferentially cubic micellar structures. Many domains observed on our films have the same symmetry corresponding to the cubic phase oriented along the axis <110>, <100> or <111>, and in each case, the lattice parameter in a plane parallel to the surface plane is a// = 14.8 nm. This organization comes from the phase separation between the inorganic silica matrix and the organic F127 tribloc copolymer [11], which forms micelles that appear brighter than the silica walls on the SEM and TEM pictures. The average micelles diameter is estimated to 7.4 nm ± 0.3nm from TEM characterizations.
Fig. 1 (a) TEM pictures of an untreated mesostructured thin film and SEM pictures of an untreated film surface (b) before and (c) after annealing at 400°C.
The mesostructure is also clearly observed on the SEM pictures of the untreated film surface (Fig. 1b). The micelles diameter and the lattice parameter of the mesostructure estimated in the surface plane from Fig. 1b to within the SEM resolution are similar to that determined from the TEM characterizations. After heat treatment at 400°C these parameters are kept constant in the surface plane (Fig. 1c), which is consistent with results previously reported in the literature [12,32]. The latter also report a film shrinkage in the direction perpendicular to the film surface. In order to characterize the lattice parameter in that normal direction, XRD measurements were carried out on untreated and annealed films from 100°C to 400°C (Fig. 2 ). The XRD patterns of all films show oscillations resulting from interferences between the incident wave and the reflected wave on the substrate. The pseudo-period of these oscillations can be used to roughly estimate the film thickness that is 160 nm ± 46 nm at 400°C. The diffraction angle attributed to diffraction on the {110} reticular plane of a phase is identified on all XRD patterns. It indicates that the periodic structure is conserved after the thermal treatment. Kitazawa et al. [16] have shown that a thermal post-treatment can induce structural modifications when the copolymer used has a low molecular weight, which, according to Losurdo et al. [33] is likely to be due to the generation of thicker silica walls during the phase separation in such a case. The XRD diffraction angles and the calculated lattice parameters a⊥ for each temperature are summarized in Table 1 . The lattice parameter a⊥ of an untreated film is 13.4 nm. It differs by about 10% from a// measured in the surface plane. This difference is caused by the anisotropic shrinkage of the mesostructure in the direction normal to the substrate plane that occurs during the drying step and that transforms spherical micelles into oblate ellipsoidal micelles [12,25].
Table 1. Lattice Parameter a⊥ in the Direction Perpendicular to the Film Surface Calculated from the XRD Diffraction Angle Measured after Heating the Films at Different Temperatures
According to the XRD patterns, the annealing at 100°C has no significant effect on the film mesostructure whereas the anisotropic shrinkage increases at higher temperature with a lattice parameter a⊥ decreasing by about 30% after a heat treatment at 400°C. This contraction factor is similar to that observed by S. Besson et al. [12] and Kho et al. [13]. Thus, the thermal post treatment induces an important shrinkage along the normal direction to the substrate that is linked to the thermal condensation of the silica network [34].
The film topography was measured by AFM on an untreated sample and samples annealed at 100°C, 200°C, 300°C or 400°C (Fig. 3 ). A fine roughness of low amplitude that is likely to correspond to the film mesostructure appears on the films surface from 200°C. However, the radius of curvature of the tip apex being of the order of magnitude of the pores radius after pyrolysis of the copolymer micelles, the AFM tip cannot give a faithful description of mesopores even after the thermal treatment at 400°C. Without heat treatment or after annealing at 100°C, the film surface is smoother at the nanometer scale and the high spatial frequencies are not observed anymore. In these cases the pores are filled with the copolymer and the topography signal does not distinguish the organic phase from the inorganic one. These AFM characterizations seem to indicate that the copolymer micelles located at the film-air interface degrade under heat treatment from 200°C. Such degradation does not occur when measuring the TDA-TGA spectra of the only F127 copolymer, in the form of powder (see later), but may be due to a surface effect as the copolymer is in the form of micelles in the silica film.
Fig. 3 AFM pictures of the surface of (a) an untreated thin film, and of films annealed at (b) 100°C, (c) 200°C, (d) 300°C and (e) 400°C.
The film porosity was also estimated from ellipsoporosimetry measurements after heat treatment at 400°C. Ellipsoporosimetry combines ellipsometry and water vapour adsorption and desorption and allows estimating the film porosity and the pore diameter from the variations of the refractive index with relative pressure [35]. The hysteresis loop of the insert in Fig. 4a , obtained after adsorption and desorption of water corresponds to a type IV adsorption desorption isotherm and is characteristic of a porous sample. According to the modelling described in [35] the porosity and the pore diameter of this film can be estimated from the hysteresis loop to 31% and 3-4 nm, respectively (Fig. 4b). A similar porosity is reported in the literature on a mesoporous thin film after calcination of the same copolymer [16]. The pore diameter estimated from ellipsoporosimetry is smaller than that estimated from SEM characterizations on the same sample (Fig. 1c). This difference results from the compression of the mesostructure during calcination that flattens the pores and reduces their average volume and to the fact that our modelling assumes the presence of spherical pores [12].
Fig. 4 (a) Ellipsoporosimetric measurements on a film annealed at 400°C and (b) pores radius distribution.
The changes in the film chemical composition with increasing temperature are evaluated by infrared spectroscopy in the light of the thermal analysis (DTA-TGA) of pure F127 triblock copolymer (Fig. 5a ). DTA and TGA curves recorded under ambient atmosphere exhibit a large exothermic peak centred at 390°C and a significant weight loss occurring from 350°C. Therefore, the copolymer template can be completely removed by calcination at 350°C or more [36]. The comparison of the infrared transmission spectra (Fig. 5b) of untreated films and annealed films at 400°C shows firstly the full disappearance of two absorption bands located at 2875 cm−1 and 2913 cm−1 and attributed to the stretching vibrations of the alkyl groups, and secondly the decrease of the absorption band centred at about 3350 cm−1 and due to the stretching vibration of the alcohol or silanol groups. The last band is also shifted toward 3600 cm−1 after heat treatment. This shift can be attributed to the modification of the OH vibrations frequency during the condensation of the silica walls. The persistence of the band indicates that silanol groups remain in the film and that the condensation of the silica network is incomplete. In addition, the disappearance of the two bands located around 2900 cm−1 results from the evaporation of residual solvent, the condensation of the silica network and the pyrolysis of F127 that is supposed to be complete according to DTA-TGA results. IR spectra show that no change occur when annealing the film for 1h instead of 30 min at 400°C. They confirm that the chemical composition of the film is stabilized after a 30 min-long heat treatment at 400°C.
Fig. 5 (a) DTA/TGA of pure F127 tribloc copolymer and (b) IR transmission spectra of the film as deposited and after annealing at 400°C for 30 min and 1h.
The changes in the chemical composition during the thermal treatment significantly affect the opto-geometrical properties of the film. Spectroscopic ellipsometry [37] was used to measure the film thickness and refractive index after different heat treatments. The results (Fig. 6 ) show that the mesostructured film behaves as an isotropic homogeneous layer after annealing up to 300°C and as an anisotropic homogeneous layer at higher temperatures. For the isotropic films the refractive index is estimated by fitting the results with a Lorentz dispersion law [38]:
where εs is the permittivity of the film at high wavelength, and ω and ωt are the frequency of light and the resonance frequency, respectively. In the case of anisotropic films, the birefringence is assumed to be uniaxial with an optical axis perpendicular to the film surface. The ordinary no and extraordinary ne refractive indexes are both modelled with Eq. (1). Whatever the calcination temperature the films are transparent in the visible range and the extinction coefficient is supposed to be null. The estimation of the refractive index relies on the minimization of a mean square error (MSE) function giving the distance between the experimental and the simulated ellipsometric parameters. The use of a Levenberg Marquardt algorithm allows optimizing three parameters simultaneously, εs, ωt, and the film thickness d [39]. The optimized results shown in Fig. 6 correspond to MSE smaller than 0.7 for the isotropic films and smaller than 0.2 for the anisotropic ones. This low MSE values confirm that considering our films, made of self-assembled copolymer micelles in a silica network, as homogeneous films is coherent. Such films do not scatter light, the micelles are much smaller than the visible wavelengths and the dielectric contrast inside the film is not high.The estimated refractive index of the film without annealing or after annealing up to 100°C (Fig. 6), 1.480 at 500 nm wavelength, is very close to that of silica [40]. This refractive index abruptly decreases with the annealing temperature between 100°C and 200°C where it falls to 1.399 at 500nm, then it slightly decreases down to 1.382 for a temperature reaching 300°C and falls again abruptly between 300°C and 350°C. The lower refractive index values are obtained at 400°C where n0 = 1.285 and ne = 1.270, corresponding to a negative birefringence. At the same time, during the temperature increase the film thickness progressively decreases by 37%, as also observed by profilometric measurements (Table 2 ). This shrinkage is in agreement with the contraction of 30% of the film structure previously observed by XRD.
Table 2. Film Thickness Estimated from Ellipsometric and Profilometric Measurements after Heating the Films at Different Temperatures
The first fall in refractive index between 100°C and 200°C is most probably due to the evaporation of residual solvent that creates microporosity in the film. It must also be related to the fact that nanoscale porosity appears on the surface topography (Fig. 3c) from 200°C. It could then also correspond to the formation of mesopores near the top surface of the film. The second fall observed between 300°C and 350°C is attributed to the pyrolysis of the copolymer (Fig. 5a). The latter leads to the formation of a mesoporous silica film whose refractive index depends on the air volume ratio. The observed birefringence from such temperature was also reported by Peiris et al. [41] who concluded that higher the surfactant concentration in the sol greater the birefringence.
4.2 Silver containing films
The mesostructured silica films doped with silver nitrate underwent the same heat treatment than the undoped films, which led to the formation of silver nanoparticles on top of the copolymer degradation. The initially colourless films take a yellowish color characteristic of the surface plasmon resonance of silver nanoparticles [25] from 120°C. This temperature is the same as that reported for the thermal growth of silver nanoparticles in a polystyrene film [42]. The SPR band observed on the absorbance spectra of Fig. 7 has growing amplitude with increasing temperature up to 200°C, which results from the rise of the nanoparticles concentration and size. Then, from 200°C to 400°C the amplitude of the SPR band decreases so far as to disappear. The nanoparticles are indeed likely to be reoxidized at such high temperatures as already reported in silica films [43]. It can be noted here that the absorbance level, given by –log (1-A-R), A being the absorption coefficient and R the reflection coefficient of the film, after calcination at 400°C is smaller than that of the untreated film. After calcinations at 400°C, the film is mesoporous and has a low effective index. It behaves like an antireflection coating, with lower R and then lower absorbance than the initial film. Such a film is transparent and colourless and cannot be coloured again by annealing at 200°C or at any temperature below 550°C.
Fig. 7 Absorbance spectra of mesostructured silica films doped with silver salt after thermal reduction at temperatures ranging from room temperature to 400°C.
The formation of silver nanoparticles between 120°C and 200°C as well as their disappearance at 400°C are confirmed by TEM characterizations of the films (Fig. 8 ). High-resolution TEM images (insert in Fig. 8a) show that the nanoparticles are crystallised in the typical fcc symmetry of bulk silver. TEM pictures of the film cross section after annealing at 160°C (Fig. 8a) show that the silver-nanoparticle distribution is not homogeneous in the film depth. Even if silver nanoparticles grow within the whole film, they mostly concentrate at the film-substrate interface. Near this interface, their size exceeds the copolymer micelle size with a mean diameter of 11 nm with a standard deviation of 7 nm. Therefore, we cannot conclude as we did previously when using a chemical reduction [22], or an optical reduction [23] process that the silica walls of the mesostructured films act as molds for the nanoparticles growth.
Fig. 8 TEM pictures of mesostructured silica films doped with silver salt and annealed (a) at 160°C or (b) at 400°C during 30min.
Silver diffusion towards the sample substrate was better evidenced by Rutherford Backscattering Spectrometry (RBS) measurements. The experimental conditions are presented in a previous paper [22]. Before heat treatment, silver (in the form of silver nitrate) is distributed in the whole film thickness with however higher concentration near the film-air interface. After annealing at 200°C, the concentration gradient is completely reversed with a higher concentration near the film-substrate interface consistent with the TEM observations showing silver nanoparticles concentrated near the substrate. RBS data processing (Fig. 9b ) also evidence the diffusion of a part of silver inside the substrate. After annealing at 400°C, silver has completely disappeared from the film to diffuse in the substrate where it is diluted. Such observations were also reported on silver containing silica films annealed at similar temperatures and were attributed to an interdiffusion between Ag in the film and Na in the glass substrate [43].
Fig. 9 (a) RBS spectra and (b) calculated distributions of silver in the film depth for different annealing temperatures. The films are deposited on glass substrates.
Removing Na from the substrate by using quartz instead of glass substrates, we indeed thickness (Fig. 10 ) and that only a low decrease of the SPR band occurs after annealing at 400°C (not shown). Therefore, interdiffusion between Ag and Na is likely to occur in our film also. The latter may explain the stability of the colourless film (on glass) annealed at 400°C since sodium likely increases the stability of silver oxide at high temperature [43].
Fig. 10 (a) RBS spectra and (b) calculated distributions of silver in the film depth for different annealing temperatures. The films are deposited on silica substrates.
Ellipsometric measurements were performed on a sample annealed at 200°C. Because of the presence of silver nanoparticles, the film effective index was modelled using the Maxwell Garnett theory [44]. In this effective medium approximation the film refractive index is calculated from the refractive indexes of silver nanoparticles and of the hybrid silica matrix as a function of filling factor q. As previously, Eq. (1) is used to describe the refractive index of the hybrid matrix including silica and copolymer and Eq. (2), below, describes the nanoparticle refractive index according to the Drude model [45]:
where ε∞ represents the contribution of the interband transitions in the visible range, Γ is the free-electrons relaxation rate, ωp the plasmon frequency and ω the light frequency. Moreover, in the light of TEM (Fig. 8a) and RBS (Fig. 9) characterizations, the film is assumed to be made of two sub-layers of unknown thickness and filling factor. Therefore the minimization of the MSE function relies here on the optimization of 9 parameters: two thicknesses and filling factors, εs and ωt for the dielectric matrix and the three parameters of the Drude model ε∞, Γ and ωp. The refractive indexes obtained after fitting the ellipsometric data are shown in Fig. 6 and Fig. 11 and correspond to a MSE of 0.04. The optimized fit leads to a 88 nm-thick top layer composed of 0.2% of silver and a 8 nm-thick bottom layer composed of 11.5% of silver. The total film thickness deduced from ellipsometry measurements is in accordance with that estimated from profilometric measurements on the same sample (90 ± 14 nm). Since TEM characterizations on the cross-section need to deposit the films on polymer substrates the film thickness changes in that case and cannot be compared with the other results. The bottom layer thickness corresponds to the height of the nanoparticles located at the film-substrate interface according to TEM characterizations (Fig. 8a).Fig. 11 Dispersion laws of the complex effective index of (a) the top layer and (b) the bottom layer of the silver containing films after annealing at 200°C.
The refractive index of the host matrix reported on Fig. 6 is slightly higher than the refractive index of an undoped film treated at the same temperature. This little difference can be due to the presence of silver nitrate in the sol, which modified the gelification conditions of the sol by increasing its viscosity [43] and consequently its refractive index. Moreover, the growth of silver nanoparticles in the film can strained the silica walls and consequently can slightly increase their refractive index.
The complex effective indexes of both layers are plotted on the Fig. 11. Due to the low concentration of silver nanoparticles in the top layer, the real part of its effective refractive index is relatively similar to the refractive index of the host matrix excepted near the resonance. The real part of the effective refractive index of the bottom layer has a sigmoidal shape that varies by 0.5 between near UV and red leading to a strong dispersion of light. The SPR band of silver nanoparticles (imaginary part of the effective refractive index) strongly differs in amplitude between the two sub-layers due to the large difference in silver content and is centred at 448 nm and 465 nm in the top and bottom layer, respectively. As the matrix refractive index is identical for both sub-layers, the redshift of the SPR band of the bottom layer is attributed to higher silver-nanoparticles mean diameter in keeping with TEM observations (Fig. 8a).
Finally, the recovering of the film effective refractive index from ellipsometric measurements when the film is nanostructured and leads to involve many parameters in the modelling is not a priori easy and sure. But, the combination of characterization techniques allowed us to establish an appropriate modelling that gives coherent results. The latter may be useful for developing optical devices based on silver nanoparticles
5. Conclusion
The optical properties of mesostructured silica thin films were directly correlated to their composition and structural properties. Under increasing temperature, the film refractive index decreases from 1.47 to 1.27 and becomes anisotropic. Used as a host matrix for the silver nanoparticles growth the film exhibits two different complex refractive index values depending on the depth. Silver is indeed largely concentrated in the film depth as confirmed by RBS measurements.
Acknowledgments
This work is supported by the region Rhône Alpes and ANR in the framework of JCJC 10 1002 project (UPCOLOR). We thank S. Reynaud and F. Vocanson from Hubert Curien Laboratory (LHC), Saint-Etienne France, for the AFM characterizations and the IR spectra, respectively. We also thank Aziz Boukenter from LHC for fruitful discussions.
References and links
1. C. Jin, S. Lin, and J. T. Wetzel, “Evaluation of ultra-low-k dielectric materials for advanced interconnects,” J. Electron. Mater. 30(4), 284–289 (2001). [CrossRef]
2. K. Maex, M. R. Baklanov, D. Shamiryan, F. Lacopi, S. H. Brongersma, and Z. S. Yanovitskaya, “Low dielectric constant materials for microelectronics,” J. Appl. Phys. 93(11), 8793–8841 (2003). [CrossRef]
3. S. Kataoka, A. Endo, M. Oyama, and T. Ohmori, “Enzymatic reactions inside a microreactor with a mesoporous silica catalyst support layer,” Appl. Catal. A Gen. 359(1-2), 108–112 (2009). [CrossRef]
4. B. J. Scott, G. Wirnsberger, and G. D. Stucky, “Mesoporous and mesostructured materials for optical applications,” Chem. Mater. 13(10), 3140–3150 (2001). [CrossRef]
5. B. B. Troitskii, V. N. Denisova, M. A. Novikova, M. A. Lopatin, L. V. Khokhlova, and A. E. Golubev, “Deposition of thin antireflection coatings based on mesoporous silicon dioxide by the sol-gel method in the presence of carbochain polymers and statistical copolymers,” Russ. J. Appl. Chem. 81(8), 1441–1445 (2008). [CrossRef]
6. J. Melde, B. J. Johnson, and P. T. Charles, “Mesoporous silicate materials in sensing,” Sensors (Basel Switzerland) 8(8), 5202–5228 (2008). [CrossRef]
7. T. Gacoin, S. Besson, and J.-P. Boilot, “Organized mesoporous silica films as templates for the elaboration of organized nanoparticle networks,” J. Phys. Condens. Matter 18(13), S85–S95 (2006). [CrossRef]
8. S. Besson, T. Gacoin, C. Ricolleau, C. Jacquiod, and J.-P. Boilot, “3D quantum dot lattice inside mesoporous silica films,” Nano Lett. 2(4), 409–414 (2002). [CrossRef]
9. C. Renard, C. Ricolleau, E. Fort, S. Besson, T. Gacoin, and J.-P. Boilot, “Coupled technique to produce two-dimensional superlattices of nanoparticles,” Appl. Phys. Lett. 80(2), 300–302 (2002). [CrossRef]
10. S. Besson, T. Gacoin, C. Ricolleau, C. Jacquiod, and J. P. Boilot, “Phase diagram for mesoporous CTAB–silica films prepared under dynamic conditions,” J. Mater. Chem. 13(2), 404–409 (2003). [CrossRef]
11. C. J. Brinker, Y. Lu, A. Sellinger, and H. Fan, “Evaporation-induced self-assembly: nanostructures made easy,” Adv. Mater. (Deerfield Beach Fla.) 11(7), 579–585 (1999). [CrossRef]
12. S. Besson, C. Ricolleau, T. Gacoin, C. Jacquiod, and J.-P. Boilot, “Highly ordered orthorhombic mesoporous silica films,” Microporous Mesoporous Mater. 60(1-3), 43–49 (2003). [CrossRef]
13. C. W. Koh, U. H. Lee, J. K. Song, H. R. Lee, M. H. Kim, M. Suh, and Y. U. Kwon, “Mesoporous titania thin film with highly ordered and fully accessible vertical pores and crystalline walls,” Chem. Asian J. 3(5), 862–867 (2008). [CrossRef] [PubMed]
14. P. Kipkemboi, A. Fogden, V. Alfredsson, and K. Flodström, “Triblock copolymers as templates in mesoporous silica formation: structural dependence on polymer chain length and synthesis temperature,” Langmuir 17(17), 5398–5402 (2001). [CrossRef]
15. D. Zhao, Q. Huo, J. Feng, B. F. Chmelka, and G. D. Stucky, “Nonionic triblock and star diblock copolymer and oligomeric surfactant syntheses of highly ordered, hydrothermally stable, mesoporous silica structures,” J. Am. Chem. Soc. 120(24), 6024–6036 (1998). [CrossRef]
16. N. Kitazawa, H. Namba, M. Aono, and Y. Watanabe, “Sol-gel derived mesoporous silica films using amphiphilic triblock copolymers,” J. Non-Cryst. Solids 332(1-3), 199–206 (2003). [CrossRef]
17. T. Maruo, S. Tanaka, N. Nishiyama, K.- Motoda, K. Funayama, Y. Egashira, and K. Ueyama, “Low-index mesoporous silica films modified with trimethylethoxysilane,” Colloids Surf. A Physicochem. Eng. Asp. 318(1-3), 84–87 (2008). [CrossRef]
18. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
19. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003). [CrossRef]
20. H. Portalès, N. Pinna, and M.-P. Pileni, “Optical response of ultrafine spherical silver nanoparticles arranged in hexagonal planar arrays studied by the DDA method,” J. Phys. Chem. A 113(16), 4094–4099 (2009). [CrossRef] [PubMed]
21. L. Bois, F. Chassagneux, C. Desroches, Y. Battie, N. Destouches, N. Gilon, S. Parola, and O. Stéphan, “Electroless growth of silver nanoparticles into mesostructured silica block copolymer films,” Langmuir 26(11), 8729–8736 (2010). [CrossRef] [PubMed]
22. Y. Battie, N. Destouches, L. Bois, F. Chassagneux, N. Moncoffre, N. Toulhoat, D. Jamon, Y. Ouerdane, S. Parola, and A. Boukenter, “Generation of an ordered layer of silver nanoparticles in mesostructured dielectric films,” J. Nanopart. Res. 12(3), 1073–1082 (2010). [CrossRef]
23. Y. Battie, N. Destouches, L. Bois, F. Chassagneux, A. Tishchenko, S. Parola, and A. Boukenter, “Growth mechanisms and kinetics of photo-induced silver nanoparticles in mesostructured hybrid silica films under UV or visible illumination,” J. Phys. Chem. C 114(19), 8679–8687 (2010). [CrossRef]
24. N. Crespo-Monteiro, N. Destouches, L. Bois, F. Chassagneux, S. Reynaud, and T. Fournel, “Reversible and irreversible laser microinscription on silver-containing mesoporous titania films,” Adv. Mater. (Deerfield Beach Fla.) 22(29), 3166–3170 (2010). [CrossRef] [PubMed]
25. L. Bois, F. Chassagneux, S. Parola, F. Bessueille, Y. Battie, N. Destouches, A. Boukenter, N. Moncoffre, and N. Toulhoat, “Growth of ordered silver nanoparticles in silica film mesostructured with a triblock copolymer PEO—PPO—PEO,” J. Solid State Chem. 182(7), 1700–1707 (2009). [CrossRef]
26. A. J. de Vries, E. S. Kooij, H. Wormeester, A. A. Mewe, and B. Poelsema, “Ellipsometric study of percolation in electroless deposited silver films,” J. Appl. Phys. 101(5), 053703 (2007). [CrossRef]
27. H. Pan, S. H. Ko, and C. P. Grigoropoulos, “Thermal sintering of solution-deposited nanoparticle silver ink films characterized by spectroscopic ellipsometry,” Appl. Phys. (Berl.) 93, 234104 (2008).
28. T. W. H. Oates, L. Ryves, and M. M. Bilek, “Dynamic spectroscopic ellipsometry determination of nanostructural changes in plasmonic silver films,” Opt. Express 15(24), 15987–15998 (2007). [CrossRef] [PubMed]
29. T. W. H. Oates, L. Ryves, and M. M. Bilek, “Dielectric functions of a growing silver film determined using dynamic in situ spectroscopic ellipsometry,” Opt. Express 16(4), 2302–2314 (2008). [CrossRef] [PubMed]
30. D. Zhao, D. Yang, N. Melosh, J. Feng, B. F. Chmelka, and G. D. Stucky, “Continuous mesoporous silica films with highly ordered large pore structures,” Adv. Mater. (Deerfield Beach Fla.) 10(16), 1380–1385 (1998). [CrossRef]
31. G. J. A. A. Soler Illia, E. L. Crepaldi, D. Grosso, D. Durand, and C. Sanchez, “Structural control in selk-standing mesostructured silica oriented membranes and xerogels,” Chem. Commun. 20, 2298–2299 (2002).
32. D. Grosso, G. J. de A. A. Soler-Illia, F. Babonneau, C. Sanchez, P.-A. Albouy, A. Brunet-Bruneau, and A. R. Balkenende, “Highly organized mesoporous titania thin films showing mono-oriented 2D hexagonal channels,” Adv. Mater. (Deerfield Beach Fla.) 13(14), 1085–1090 (2001). [CrossRef]
33. M. Losurdo, M. Giangregorio, G. Bruno, F. Poli, L. Armelao, and E. Tondello, “Porosity of mesoporous silica thin films: kinetics of the template removal process by ellipsometry,” Sens. Acutators B 126(1), 168–173 (2007). [CrossRef]
34. S. Besson, C. Ricolleau, T. Gacoin, C. Jacquiod, and J. P. Boilot, “A new 3D organization of mesopores in oriented CTAB silica films,” J. Phys. Chem. B 104(51), 12095–12097 (2000). [CrossRef]
35. M. R. Baklanov, K. P. Mogilnikov, V. G. Polovinkin, and F. N. Dultsev, “Determination of pore size distribution in thin films by ellipsometric porosimetry,” J. Vac. Sci. Technol. B 18(3), 1385–1391 (2000). [CrossRef]
36. C. Xue, B. Tu, and D. Zhao, “Evaporation-induced coating and self-assembly of ordered mesoporous carbon-silica composite monoliths with macroporous architecture on polyurethane foams,” Adv. Funct. Mater. 18(24), 3914–3921 (2008). [CrossRef]
37. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).
38. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
39. K. Levenberg, “A method for the solution of certain problems in least squares,” Q. Appl. Math. 2, 164–168 (1944).
40. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
41. F. C. Peiris, B. D. Hatton, G. A. Ozin, and D. D. Perovic, “Anisotropy in periodic mesoporous silica and organosilica films studied by generalized ellipsometry,” Appl. Phys. Lett. 87(24), 241902 (2005). [CrossRef]
42. T. W. Oates, “Real time spectroscopic ellipsometric of nanoparticle growth,” Appl. Phys. Lett. 88(21), 213115 (2006). [CrossRef]
43. W. Li, S. Seal, E. Megan, J. Ramsdell, K. Scammon, G. Lelong, L. Lachal, and K. A. Richardson, “Physical and optical properties of sol-gel nano-silver doped silica film on glass substrate as a function of heat-treatment temperature,” J. Appl. Phys. 93(12), 9553–9561 (2003). [CrossRef]
44. G. J. C. Maxwell, “Colours in metal glasses and metal,” Philos. Trans. R. Soc. London, Ser. A 3, 385–420 (1904).
45. P. K. L. Drude, “Zur elektronen theorie der metalle,” Annalen der Physik 306(3), 566–613 (1900). [CrossRef]
