Fabrication and optical characterization of a high-quality fcc-opal-based photonic crystal grown by the vertical convective self-assembly method

Objective: Fabrication and optical characterization of close-packed 225 nm SiO 2 -based colloidal crystals . Materials and methods: The vertical convective self-assembly method is used to grow high-quality 225 nm close-packed SiO 2 -based colloidal crystals. An annealing process (550°C) is made in order to improve the mechanical stability of the sample. Optical characterization is done by angle-r esolved transmission spectroscopy (A-RTS) and structural characterization by Scanning Electron Microscopy (SEM). Results: Both, A-RTS and SEM, show that with the vertical convective self-assembly method, with the appropriate parameters of temperature of evaporation (60°C), volume fraction of the colloidal suspension (0.2% w/w) and acidity (pH=6), highly ordered close packed face centered cubic (fcc ) SiO 2 based colloidal crystals are obtained. Conclusions: The growth of high-quality (long range order and defect-free) face centered cubic opalbased photonic crystals is reported.


Introduction
Photonic meta-materials, artificially engineered materials in which their optical properties are unattainable with naturally occurring materials, attract a great deal of attention mainly because of their ability to control the way in which the electromagnetic radiation interacts with them and, also, because they represent one of the most important examples of the so-called emerging technologies in the fields of electronics and optoelectronics (1).A particular kind of photonic meta-materials are the close-packed 3D colloidal crystals: periodic arrangement (face centered cubic (fcc) and/or hexagonal close packed (hcp) stacking lattice) of mono-disperse silica or polystyrene nano-spheres with diameters within the wavelength range of visible light in which many novel optical phenomena, that are strongly dependent of the sphere-packing symmetry, are observed (2).One of the most important optical characteristics in a SiO 2 -based colloidal crystal, which can be detected directly by the A-RTS, is the presence of stop bands in which propagation of light is allowed only in certain crystallographic directions.Scattering of light, therefore, follows the Bragg's law, in the same sense that X-rays are diffracted by a family of planes of the atomic crystals.These novel optical phenomena foster a great number of potential applications in advanced optical devices such as waveguides (3), sensors (4), lenses (5) and low threshold lasers (6,7).
Although the detailed growth mechanism of these colloidal crystals is not known (8), upon both thermodynamic studies and experimental results it is well known that under the appropriate conditions, colloidal particles assemble spontaneously into ordered structures (9), giving place to the called self-assembly methods.Although numerous selfassembly methods have been employed to make such 3D colloidal crystals (sedimentation (10,11), electrophoresis (12), and spin coating (13), mainly), the low control over the growth parameters results in a variety of defects in such a way that the controlled and uniform growth of 3D colloidal crystals remained to be developed.However, the controlled evaporation-induced self-assembly vertical deposition method, in which capillary forces produce large high-ordered opal films due to the directional nature of the substrate/colloidal suspension interface, has shown to be one of the more efficient methods (14,15).The present work reports the growth of long-ordered 225 nm fcc-SiO 2 -based colloidal crystals from self-assembly vertical deposition method on a hydrophilic glass substrate, evaporation temperature of 60°C, volume fraction of the colloidal suspension of 0.2% w/w, pH of 6 and annealing of 550C.The paper is organized as follows.In section 2 the experimental details (materials, instrumentation and procedures) are presented.In section 3, a structural analysis from the SEM images of the structure is provided.Optical properties, from A-RTS, of the opal films will be obtained showing the existence of a stop band, typical in the optical behavior of light in photonic crystals, which follows the Bragg's law.

Materials and methods
Mono-disperse colloidal SiO 2 spheres with a nominal diameter of 250nm (Ångström Spheres® 0.25 µm silica spheres: SIOP025-01-100G) were assembled on a soda lime float glass substrate (Knittel standard microscope slides) by self-assembly vertical deposition.The glass substrate was cleaned ultrasonically with acetone (Merck, GR for analysis), ethanol (Merck, absolute GR for analysis), and fully rinsed with deionized water (Milli-Q water, 0.056 µS⋅cm -1 ) followed by drying under a flow of nitrogen gas before use.In order to make the surface hydrophilic, the glass substrate was etched by immersion in piranha solution (a solution containing sulfuric acid (Merck H 2 SO 4 , 95-97%) and hydrogen peroxide (Carlo Erba H 2 O 2 , solution 30% m/m in water) of 3:1 in volume) for 30 min followed by rinsing with deionized water and dried with nitrogen.The hydrophilic substrate was immersed vertically into a vial (25mL) containing a diluted solution of SiO 2 spheres, used as received from the supplier (Ångström Spheres®), of 0.2% w/w in 20mL of deionized water.The acidity of the solution was controlled by using adequate amounts of chlorohydric acid (HCl) and Sodium hydroxide (NaOH) in order to obtain a pH of 6.
The vial was then placed in a vibration-free temperature controlled chamber (Terrigeno furnace mod.L2) programmed to heat at 60 0 C for 25h.Two type K thermocouples were placed into the chamber in order to monitor the distribution and eventual changes of temperatures over the time as in figure 1. Thermocouple 1 was in the air, T ref in figure 1, and thermocouple 2 was dipping in the suspension, T in figure 1. Finally the deposited film was annealed at 550 0 C for 2h (Terrigeno furnace Mod.L2) in order to improve the mechanical stability of the sample.
Optical properties, which determine the presence of a stop band in the dispersion relation of the structure, were studied by means of A-RTS measurements in the UV-Visible range.The impinging light (Newport 6333 Quartz Halogen Lamp) was focused to a spot of 3.0mm 2 , the transmitted light was collected by a monochromator (Acton research spectral pro 775), detected by a photomultiplier tube (77342 Side-on Oriel PMT) and sent to a Lock-in amplifier (Stanford Research Systems SR830).Scanning Electron Microscope (SEM) was used to carry out a structural characterization of the sample (JEOL, Mod.JSM 6490-LV operated at 20 kV).The sample was coated with gold to enhance the conductivity and avoid possible charging.

Results and discussion
In the convective self-assembly method the weakly interacting SiO 2 colloidal spheres are crystallized near the moving contact line between the stationary substrate and the concave meniscus formed between the surface of the very low concentrated evaporating suspension and the hydrophilic substrate (Figure 1).The convective flow of solvent (deionized water in this case) through the interstitial sites induces lateral capillary forces that in turn cause an attractive interaction between the spheres in such a way that are pushed to the flat substrate, just as in the case of the dip coating technique (16).In general, there are many types of interactions between the spheres (mainly Van der Waals, Brownian and Coulomb interactions), however the capillary forces acting between the colloidal spheres are larger compared with them.For this reason, convective methods are sometimes known as self-assembly by capillary forces (17).The convective transfer of SiO 2 spheres from the solution to the hydrophilic substrate is forced primarily by the temperature dependent solvent evaporation.Taking into account that there is not a thermodynamic equilibrium between the solvent vapor pressure and the solution surface and supposing mechanical equilibrium, the solvent evaporation produces a pressure gradient that is compensated by a solvent influx from the bulk solution and a sphere flux that causes the accumulation of particles in the substrate, forming a disordered dense mono-layer.Then capillary pressure due to curvature of the liquid surface between neighboring spheres lead to specific crystallization during the dried process.One of the most important facts in the growth of high quality films by convective methods is the constancy of the particle volume fraction in the meniscus area that depends mainly of the sedimentation velocity (described by the Kynch theory ( 18)) and the solvent evaporation rate (v s and v w in figure 1, respectively).Due to that, the phase change of a solvent from its free surface occurs only under non-equilibrium conditions, the vertical convective method is a system that is not in thermodynamic equilibrium and, consequently, the parameters that govern the growth process were not completely understood.However, it is well known that if the environmental conditions like the suspension evaporation rate, the particle sedimentation velocity, the particle volume fraction in the solution and the shape of the meniscus are properly controlled, a thin film of (fcc/hcp) close-packed colloidal spheres is deposited on the substrate as the meniscus moves down it (19).Both stacking patterns (fcc and hcp) have identical packing densities ( = 74%) and coordination numbers (twelve).This is why, within the framework of photonic applications, the impact of the morphology on the optical properties of self-assembled colloidal crystals draws a lot of interest.From theoretical calculations (20), both structures are energetically similar, that is, the free energies (per particle) are the same within an uncertainty of no more than 2×10 -3 K B T (21).
In figure 2 the classical ABC notation is used to denote each possible position of the hexagonal close packed monolayer ( 22): A, B (displaced by (r, r√3/3, 0) from A), and C (displaced by (2r, 2r√3/3, 0) from A), where r is the radius of the spheres.In all cases the displacement is referred to the i, j, k unit vectors that define the coordinate system.If the stacking sequence is regular, the arrangement of spheres grown may be a [111]-fcc structure, with a repeated ABCABC… pattern (every third layer is the same), or a [001]-hcp structure, with a repeated ABAB… pattern (every other layer is the same) (23,24).The generic systems are described in figure 2. The [001]-hcp structure is shown, in a perpendicular view to the (100) plane, in figure 2a and the [111]-fcc structure is shown, in a projection perpendicular to the (111) plane, in figure 2b.The primitive vectors a 1 , a 2 , and a 3 , and the primitive cells are also shown.A typical scanning electron microscope (SEM) image of the SiO 2 opal-based photonic crystal made by the vertical convective self-assembly method at a growth temperature of 60°C, volume fraction of the colloidal suspension of 0.2% w/w, pH of 6 and annealing temperature of 550°C is shown in figure 3. The top surface (parallel to the substrate) of a high quality micro-colloidal crystal composed of 225 nm SiO 2 spheres with a distribution standard deviation less than 6% (Figure 3) assembled in a hexagonally close-packed ordered array is observed.In figure 3 the i direction (row of spheres) is parallel to the growth direc-tion of the crystal.From figure 2, at least three layers (ABC for fcc or ABA for hcp) must be considered in order to establish the 3D colloidal stacking pattern.In figure 4 a four layer top view SEM image (Figure 4a) is compared with a [111]-fcc stacking lattice model (Figure 4b).The ABCA pattern is observed indicating clearly that the colloidal crystal has a cubic structure.Confirming this result, figure 5a gives a cross-sectional view of the sample and figure 5b a simulation that shows the [01-1] direction of an fcc lattice.From figure 5 a [111]-fcc-stacking lattice of high quality with uniform thickness of 6.5µm is observed.
In order to investigate the angular-dependent spectral response of the transmitted intensity under excitation with visible light, in which the direction of the specular reflection of light from the sample surface and the direction of diffraction from the colloidal crystal coincide, of the 225 nm SiO 2 opal-based colloidal crystal, under the assumption of a perfect fcc stacking lattice, the Bragg formulation of diffraction is used.Since the wave-length of visible light (350-800 nm) is close to the lattice constant (a 0 = ∼ 350nm, for spheres with diameter of 250 nm), the geometry of the diffraction conditions is very similar to the one that occurs in X-ray diffraction by an atomic crystal in which, for certain sharply defined wavelengths and incident directions, intense peaks (first order Bragg peaks) of scattered radiation are observed due to the interaction of light with a periodic dielectric permittivity.
In the Bragg description of the diffraction of radiation by a crystal, two assumptions are made: i) Radiation is specularly reflected by a family of planes in the structure and ii) the reflected rays interfere constructively when the condition [1] is satisfied, where λ max is the wavelength of the first-order diffraction peak, d is the distance between reflecting adjacent planes ([111] planes for an fcc structure with d = and [001] planes for a hcp structure with d = ), θ is the angle between the incident light beam and the normal to the surface of the sample ([111] direction for fcc and [001] direction for hcp) and is the effective refractive index of the material [2] where n SiO2 is the refractive index of the SiO 2 (n SiO2 = 1.45, for silica bulk), n air is the refractive index of air (nair = 1.0), f SiO2 is the filling factor of the silica (f SiO2 = = 74%, for both, fcc and hcp structures) and f air is the filling factor of the voids (f air = 26%).Due to the fact that inter-planar distances (distance between [111] planes in fcc and between [001] planes in hcp) are the same in both stacking lattices (d = ), it is clear that the determination of an fcc or hcp stacking lattice cannot be done from the Bragg's formula.However, from figures 5 and 6 an fcc-stacking lattice can be deduced.
When non polarized light with wavelength of 450-650 nm impinges parallel to the surface of the substrate (the [111] direction of the 225 nm fcc-SiO 2 based photonic crystal, as is shown in figure 2) a strong absorption band, a narrow photonic stop band, centered on 505 nm and with a Full-Width at Half-Maximum (FWHM) of 40 nm is observed (Figure 6) in contrast with the transmittance spectrum of amorphous SiO 2 (sample grown at a temperature of 60°C, volume fraction of the colloidal suspension of 0.1% w/w, pH of 9 and annealing temperature of 550°C in which ordering was not observed).Following the Bragg's law, the wavelength of the stop band can be tuned by tilting the {111} surface of the colloidal crystal relative to the incident light.The wavelength (λ max ) of the first-order diffraction peak as a function of the incidence angle is shown in  figure 6 by means of the angle-resolved transmission spectra, and a plot of sin 2 (φ) vs λ 2 following the Bragg equation is shown in figure 7. From a linear fit to the experimental data, the values n eff = 1.34 ± 0.5% and r = 115 nm ± 1% are obtained in extremely high agreement with the theoretical value of the effective refractive index and, on the other hand, with the measurement of the diameter of the spheres done by SEM (Figure 3).

Conclusions
Fabrication of high quality 230 nm fcc-SiO 2 opal based photonic crystals by the vertical convective self-assembly method is reported with the following growth parameters: volume fraction = 0.2%, pH = 6, evaporation temperature = 60°C, and annealing temperature = 550°C for 2 hours.SEM images of different areas of the film show that the stacking pattern is fcc.However, there are several observed imperfections of the film such as: point defects, dislocations and cracks.The particle size obtained using the Bragg condition is in excellent agree-ment with the particle size measured by SEM as well as the effective refractive index.

Figure 1 .
Figure 1.Schematic diagram of the vertical convective self-assembly setup.The inset shows the solvent temperature at T ref =60°C.The water and spheres fluxes in the vicinity of the hydrophilic substrate as well as the surface tension are shown.

Figure 2 . 6 π√Figure 3 .
Figure 2. Schematic diagram of the [001]-hcp (a) and [111]-fcc (b) stacking pattern on mono-disperse spheres in a perpendicular view to the growth direction.The primitive vectors (a 1 , a 2 , a 3 ) and the primitive cell are shown in each case.

Figure 4 .
Figure 4. a) A perpendicular SEM image of a 230 nm SiO2 based colloidal crystal.b) Computer simulation of an fcc stacking lattice that has been trimmed to show the arrangements of spheres similar to those observed in a).The letters (ABCA…) show the stacking pattern typical of an fcc structure.

Figure 7 .
Figure 7. UV-VIS Angle-resolved transmission spectra of the film measured with the incident light forming an angle ϕ respect to the normal of the substrate.