Fast Microscopic Method for Large Scale Determination of Structure

Jan 21, 2006 - color coding for regions of different structures, morphologies, and layer numbers results. Incoherently scattering defect structures, h...
3 downloads 0 Views 4MB Size
Download PDF
1828

Langmuir 2006, 22, 1828-1838

Fast Microscopic Method for Large Scale Determination of Structure, Morphology, and Quality of Thin Colloidal Crystals H. J. Scho¨pe,* A. Barreira Fontecha, H. Ko¨nig, J. Marques Hueso, and R. Biehl† Institut f. Physik, Johannes Gutenberg UniVersita¨t Mainz, D-55099 Mainz, Germany ReceiVed September 13, 2005. In Final Form: December 15, 2005 We present a novel fast microscopic method to analyze the crystal structures of air-dried or suspended colloidal multilayer systems. Once typical lattice spacings of such films are in the range of visible light, characteristic Bragg scattering patterns are observed. If in microscopic observations these are excluded from image construction, a unique color coding for regions of different structures, morphologies, and layer numbers results. Incoherently scattering defect structures, however, may not be excluded from image construction and thus remain visible with high resolution.

Introduction Colloidal multilayer systems are fascinating and useful objects of intense interest in material research. They are fascinating for their sparkling opalescence, visible even for moderately ordered monolayer systems, but of fully developed beauty for multilayer structures. In this they are similar to natural thin ordered structures, as realized in butterfly wings and peacock feathers. On the fundamental science side, they display an intriguing richness of crystalline structures as a function of overall structural height1 and the details of particle interactions.2 On the other hand, they are useful as coatings and show a high potential for smart optical applications ranging from filters and gratings to sensors and photonic materials.3 Their manufacture, however, still presents some practical challenges. Polycrystalline samples of small scale crystalline order are readily obtained simply from drying a drop of a colloidal suspension on a smooth substrate. The making of large scale (mm2-cm2), defect free single-crystal films, is much more delicate, as many parameters of the drying process (like humidity, wetting properties, particle and salt concentration, temperature, etc.) have to be optimized. Methods applied to date range from sedimentation crystallization4 through colloidal epitaxy,5 spin-coating,6 electro-deposition,7 and physical confinement,8 to several methods of controlled drying exploiting capillary forces and convective self-assembly.9,10,11 In suspended systems (e.g., confined between parallel glass plates) large scale single crystals may be grown through the application of shear12 * To whom correspondence should be addressed. E-mail: [email protected]. † Institut f. Festko ¨ rperforschung, Forschungszentrum Ju¨lich GmbH, D52425 Ju¨lich, Germany. (1) Murray, C. MRS Bull. 1998, 23, 33. (2) Barreira Fontecha, A.; Scho¨pe, H. J.; Ko¨nig, H.; Palberg, T.; Messina, R.; Lo¨wen, H. J. Phys.: Condens. Matter 2005, 17, in press. A comparative study on the phase behaviour of highly charged colloidal spheres in a confining wedge geometry. (3) Special issue on photonic materials AdV. Mater 2001, 13, 6. (4) Miguez, H.; Meseguer, F.; Lopez, C.; Blanco, A.; Moya, J. S.; Requena, J.; Mifsud, A.; Fornes, V. AdV. Mater. 1998, 10, 480. (5) van Blaaderen, A.; Ruel, R.; Wiltzius, P. Nature 1997, 385, 321. (6) Winzer, M.; Kleiber, M.; Dix, N.; Wiesendanger, R. Appl. Phys. A 1996, 63, 617. (7) Bo¨hmer, M. Langmuir 1996, 12, 5747. (8) Kamp, U.; Kiatev, V.; von Freymann, G.; Ozin, G. A.; Mabury, S. A. AdV. Mater. 2005, 17, 438. (9) Denkov, N. D.; Velvev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Nature 1993, 36, 126. (10) Dimitrov, A. S.; Nagayama, K. Chem. Phys. Lett. 1995, 243, 462. (11) Dimitrov A. S.; Nagayama, K. Langmuir 1996, 12, 1303. (12) Biehl, R.; Palberg, T. Proc. R. Chem. Soc. Faraday Discuss. 2003, 123, 133.

or other external fields.13 Shear has also been applied to orient and anneal bulk colloidal crystals.14 AC electric fields applied perpendicular to the film assembly direction have also been successfully used in reducing the number of grains and enforcing a preferred orientation in drying monolayer systems.15 In Figure 1, we present an example of a dry colloidal crystal film made from PS590 polystyrene latex spheres in aqueous suspension prepared by vertical deposition. Note that the diffraction colors appear continuous in this image taken under divergent white light illumination, indicating the high degree of orientational ordering. However, the film still contains numerous crystalline defects, which may break the symmetry of the crystal and create defect states which can destroy the photonic band gap.16,17 The present paper deals with their analysis using a new, simple, fast microscopic method. Although progress in the direction of enhanced film qualities is rapid, the actual analysis of a film’s structure, stacking sequence, dislocation and defect concentration, etc. remains a tedious process. To reach a thorough characterization, large scale investigations such as light microscopy (yielding crack structure) and Bragg microscopy (yielding the orientation of crystal grains), mid scale methods such as high-resolution microscopy or force microscopy (yielding surface structure and quality on a particle level, defect statistics on small areas of 10 × 10µm2 to 500 × 500µm2), and light scattering (yielding the average crystal structure and orientation over the illuminated region) have to be combined with small scale methods, like force microscopic tomography (yielding the 3D-structure for embedded objects) or scanning electron microscopy (yielding the local structure of crystals, grain boundaries etc. only on the surface with high precision but low statistics). Therefore, there is a need for a method which would simultaneously provide information on small scale details over a large area. In the present paper, we shall introduce such a method, which is applicable to sufficiently transparent samples and for these is capable of yielding film height (in number of layers), crystal structure, layer stacking sequence, statistics of dislocations and other defects, as well as grain boundary thicknesses and, in many cases, grain orientations. (13) Sullivan, M.; Zhao, K.; Harrison, C.; Austin, R. H.; Megens, M.; Hollingsworth, A.; Russel, W. B.; Cheng, Z.; Mason, T.; Chaikin, P. M. J. Phys.: Condens. Matter 2003, 15, 11. (14) Dux, Chr.; Versmold, H. Phys. ReV. Lett. 1997, 78, 1811. (15) Scho¨pe, H. J. J. Phys. Condens. Matter 2003, 15, L533. (16) Vlasov, Y. A.; Astratov, V. N.; Baryshev, A. V.; Kaplyanskii, A. A.; Karimov, O. Z.; Liminov, M. F. Phys. ReV. E 2000, 61, 5784. (17) Wang, Z. L.; Chan, C. T.; Zhang, W. Y.; Chen, Z.; Ming, N. B.; Sheng, P. Phys. ReV. E 2003, 67, 016612.

10.1021/la0524972 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/21/2006

Fast Method for Photonic Crystal Quality Analysis

Langmuir, Vol. 22, No. 4, 2006 1829

Ei(r) ) E0 exp(ik‚r)

(2)

where the time dependence is omitted, as we consider elastic scattering only. Far from the sample, the superimposed scattered fields may again be considered as a plane wave. The difference between the incoming and scattered wave vectors defines the scattering vector

|q| ) |k0 - kS| ) (4πνS/λ) sin(Θ/2)

Figure 1. Crystalline colloidal thin film vertically drawn from an aqueous suspension of PS590 at 80% humidity, temperature 20.5 °C, particle number density 1 × 1017 m-3, salt concentration c ) 1 × 10-3M. Covered area 17 × 25 mm2. Note the continuous change of diffracted color indicating the near perfect crystal orientation of this film.

In principle, we perform a simple transmission microscopic experiment under parallel white light illumination with small numerical aperture. As will be shown in detail below, a color contrast is generated via the exclusion of Bragg scattered light from image construction. Since the scattering properties of different crystal structures and defects differ in a characteristic way, each image of regions of different structures will produce a different color. Calibration of the color-structure relation by high resolution methods has to be performed only once for a particular material and can then be used for other samples. The method should thus allow for fast, large scale serial investigations as performed in the control of (mass) production processes. The paper is organized as follows. We first recall some basic light scattering theory and apply it to microscopy. We then illustrate the method in detail using a number of air-dried samples and parallel-plate confined, suspended samples of different quality and optical properties. We conclude with a short discussion of the range of applicability and other performance criteria.

Light Scattering and Microscopy on Thin Colloidal Crystals Light Scattering.18-21 We consider a sample of N identical, nonadsorbing, spherical colloidal particles of radius a and of refractive index νP(λ), dispersed in a medium of refractive index νM(λ) (if a dry film is considered, νM ) 1). The index of refraction of the colloidal crystal is give as

νS ) xΦνP2 + (1 - Φ)νM2

(1)

where Φ is the packing or volume fraction of crystal. We further assume a locally homogeneous particle number density ni ) Ni/Vi within different scattering regions Vi (crystallite grains). All particles contained in the scattering volume VS ) ∑Vi centered around r0 ) (0,0,0) shall be illuminated by parallel white light of intensity I0(λ). We represent the illuminating beam as a superposition of plane waves of different wavelength λ. For each wave, we can write for the electric field (18) Dhont, J. K. G. An introduction to the dynamics of colloids; Elsevier: Amsterdam, 1996. (19) Berne, B. J.; Pecora, R. Dynamic Light Scattering; Wiley and Sons: New York, 1976. (20) Pusey, P. N. In Liquid freezing and the glass transition; Levesque, D., Hansen, J. P., Zinn-Justin, J., Eds.; Elsevier: Les Houches, 1991. (21) Scha¨tzel, K. AdV. Colloid Interface Sci. 1993, 46, 309.

(3)

where Θ is the scattering angle. The particle scattering amplitude at zero wave vector is given by the difference between the dielectric function of particles P and the surrounding medium M, normalized by the dielectric function of the sample S, times the particle volume: b(0) ) ((P - M)/S) (4/3)πa3. The particle form factor P(q) ) b(q)2/b(0)2 (normalized by b(0)2 so that in P(0) ) 1) describes the angle and wavelength dependence of single particle scattering and can be calculated from Mie theory. For spherical objects, the scattering of unpolarized light is symmetric about the optical axis, and thus, P(q) ) P(q). P(q) shows a characteristic series of minima resulting from destructive intraparticle interference. Note that, in an experiment performed on a single sphere species with white light composed of different wavelengths λ, the minima coincide in q space (except for small effects of the dispersion in the refractive indices of solvent and particles), but plotted versus Θ one observes shift of the minima toward larger angles with increasing wavelength. Restricting ourselves to single scattering events only, the intensity scattered coherently at each wavelength may be written as a sum over all crystalline regions I

ICOH(q) )

∑i Ci P(q) S(q)i

(4)

where the constant Ci

Ci )

I0

Ni k04 b(0)2

(4πRD)2

(5)

comprises the geometry of the scattering experiment and the optical properties of the particle material. Note the k4 dependence of C as the scattered intensity is much larger for shorter wavelength. Here I0 ) 1/2(S0/µSµ0)1/2 E02 is the incident intensity, µS the magnetic permeability of the solvent, and RD is the distance between scattering region Vi and the detector. The static structure factor S(q) is derived via the squared modulus of the Fourier transform of the real space distribution of particles F(r). It contains all the information about the particle positions rj and is in general defined as

S(q)i ≡

1

N

N

∑ ∑〈exp(iq(rj - rk))〉

N j)1 k)1

(6)

where the brackets 〈...〉 denote the ensemble average over Vi. For crystalline order, F(r) is a periodic function. In reciprocal space, this corresponds to a set of reciprocal lattice vectors Ghkl ) hb1 + kb2 + lb3 forming the reciprocal lattice (where h, k, and l are the Miller indices). From the squared modulus of the Fourier transform of F(r) an ideal crystalline structure factor S0C(q) may be derived. For the infinite crystal, this is a set of delta functions. Intensity is observed whenever q ) Ghkl, i.e., when the Ewald sphere intersects with reciprocal lattice points. For lattices with more than one lattice point per unit cell (like bcc or fcc), selection rules determine the h, k, and l for which scattering

1830 Langmuir, Vol. 22, No. 4, 2006

Scho¨pe et al.

is observed. In general, at fixed incident beam, wavelength, and sample orientation, only a few Bragg reflections emerge from the sample. This is different for two cases. If a crystal is small in one or more dimensions or if stacking faults are present, a considerable finite broadening of the bragg peaks is observed so that intensity is also present at q * Ghkl . The first point is well-known, e.g., in a powder scattering experiment the width of a bragg peak and the average crystal size L is connected via ∆qfwhm ) 2πKhkl/L, where ∆qfwhm is the full width at half-maximum of the bragg peak and Khkl is the Scherrer constant. In the case of microscopy on colloidal crystals in thin films, the smallest dimension is normal to the substrate (we define the x1 and x2 direction parallel to the substrate and x3 perpendicular to the substrate) and finite size broadening is most pronounced along the direction of the incoming beam. The presence of stacking faults in an fcc or an hcp crystal which has been discussed in detail by Pusey et al.22 will also cause a broadening. The statistics of stacking faults are described by a parameter R which gives the probability that an fcc stacking (ABCABC...) remains unchanged. Thus, R ) 1 corresponds to fcc and R ) 0 corresponds to hcp, whereas all randomly hexagonal stacked crystals have values between. Considering a close packed film crystal with a close packed plane parallel to the substrate, the occurrence of stacking faults leads to a redistribution of intensity into the reciprocal space between the original reciprocal lattice points along the q direction perpendicular to the hexagonal layers. In the extreme case of one hexagonal layer, a system of hexagonally arranged Bragg rods (h,k) is formed in the reciprocal space with constant thickness which means that there is a constant intensity along the rods and Bragg scattering is observed for any wavelength. For a series of hexagonal layers, the intensity is modulated along the rods as a function of the number of layers and of the stacking sequence. The influence of the stacking sequence and the layer number of oriented thin crystals on the scattering pattern and the scattered intensity can be illustrated in a nice way following Loose and Ackerson.23 The crystalline structure factor can be separated in a layer formfactor |F(q)|2 and a stacking structure factor ST(q)

S(q) )

1 M

|F(q) |2ST(q) ) 1 M

‚

1

xNL

NL

∑ p)1

M

p

eiks12 〈

M

eik(R ∑ ∑ n)1 m)1

m-R n) 3

3

〉 (7)

where M is the number of layers, NL is the number of particles in a layer, sp12 is a two-dimensional particle position vector inside the mth layer, the index p enumerates the particle position in the layer, and Rm3 is the position vector along the stacking axis. The layer form factor describes the interparticle interference stemming from one hexagonal layer, whereas the stacking structure factor describes the influence of the stacking sequence and the layer number. Equation 7 can be rewritten as

(

M-f 2 cos(f(q12 + q3)∆r) S(q) ) |F(q)|2 1 + f)1 M M

∑

)

(8)

which means that the structure factor is given as a weighted sum of the averaged phase factors of all layers with respect to the (22) Martelozzo, V. C.; Schofield, A. B.; Poon, W. C. K.; Pusey, P. N. Phys. ReV. E 2002, 66, 021408 Part 1. (23) Loose, W.; Ackerson, B. J. J. Chem. Phys. 1994, 101, 7211.

Figure 2. (a) Changes in the structure of Bragg rods/spots in reciprocal space with decreasing number of hexagonal layers with fcc stacking. (b) Changes in the structure of Bragg rods/spots in reciprocal space with changing stacking probability R. Note that once R differs from 1 or 0, there is a finite intensity observed between the fcc and hcp lattice points.

reference layer. When the illuminating beam is perpendicular to the hexagonal layer, q12 denotes the component of the scattering vector parallel to the layer and q3 the component perpendicular to the layer. ∆r is the connecting vector between two layers. Figure 2a shows the stacking structure factor for different numbers of layers. For one layer, the scattered intensity is constant, and for two layers, it is modulated by a cosine. With increasing layer number the intensity modulation of the rods becomes more and more pronounced. By rewriting eq 7 in the following form S(q) |F(q)|2

)

( 2h 3- k)] 2h - k 2h - k 2(1 - 2R)(1 - cos q ) + 3R - 4R (-1) cos(2π cos(q ) + R cos(2π 6 ) 3 )

[

R(1 - R) 1 - cos 2π

2

/ 3

2

2

k

/ 3

2

(9) it is possible to describe the influence of the stacking sequence on the intensity distribution along the 3rd axis. q3* ) q32a(2/ 3)0.5 ) πl q3/q3 is the component of the scattering vector along the 3rd axis normalized with the spacing between two layers. Here h, k, and l are Miller indices for a hexagonal crystal based on a fcc unit cell.24 It is obvious that for rods with (h-k) ) 3n reciprocal lattice points on the rods occur, while for rods with (h-k) ) 3n ( 1 the intensity distribution along the rods depends (24) Heymann A. et al. J. Colloid Interface Sci. 1998, 207, 119.

Fast Method for Photonic Crystal Quality Analysis

Langmuir, Vol. 22, No. 4, 2006 1831

grains themselves, as well as defects, such as grain boundaries, dislocations, bad spots, or dust particles. These objects may in most cases be considered isolated with uncorrelated positions. Therefore, setting their S(q) ) 1, the scattered intensity may be written as

IINC(q) )

Figure 3. Reciprocal space for stacked hexagonal layers. Left: plane of the reciprocal space parallel to the layer surface (q12 plane) with hexagonally arranged Bragg rods for a system of hexagonal layers. Points are indexed in 2D hexagonal notation. Right: corresponding projection of the reciprocal space perpendicular to the q12-plane with reciprocal Bragg spots and rods. Symbols denote individual Bragg spots for fcc (three pointed star up or down according to the orientation on the left side drawing), hcp (/, blue) and common for both structures (/, red). The green dashed lines mark the direction of broadening for r-hcp structures. Also for low layer numbers all Bragg spots broaden along this direction indicated with the red dashed lines. The indicated circle is the Ewald sphere for λ ) 514 nm, νs ) 1.46, 2a ) 1000 nm, Φ ) 0.74. Scattered intensity is observed where the sphere cuts a point like or broadened Bragg spot or rod. Ewald spheres for different wavelengths will cut the same rod at different positions.

on the stacking. Figure 2b shows the intensity distribution along a (1,0) bragg rod. For the experiments reported below, the exact knowledge of S(q)i is not crucial. What is important, however, is the qualitative result, that for thin film crystals a considerable broadening along the q3 direction of reciprocal space is observed and this broadening is modified by the stacking sequence and the layer thickness. The consequence for light scattering with different wavelengths is illustrated qualitatively in Figure 3, when the illumination is perpendicular to the hexagonal layer. For bulk crystals, intensity is only observed if the Ewald sphere intersects with a reciprocal lattice point. Thus, in Figure 3, one would only observe the (022) Bragg reflection for the shown Ewald sphere (λ ) 514 nm, νs ) 1.46, 2a ) 1000 nm, Φ ) 0.74). If, however, stacking fault broadening occurs, there will be scattering observed also at the positions of the first-order Bragg reflections, whereas for finite size broadening, some intensity may also be observed for the second order. In the limit of a hexagonal monolayer, scattering of all reflections will result. Ewald spheres of other wavelengths intersect the bragg rods at different positions, and thus, different scattering intensities originate for multilayer systems because the intensity is modulated along the rods as shown above. A second mechanism for the wavelength-dependent scattering intensity is given by the fact that the cross section for single scattering is proportional to 1/λ4. So light with different colors is removed with different efficiency from the light passing through the sample. The discussion refers to crystals of a single orientation and structure. S(q) differs for differently structured or oriented crystallites. If particle positions in different regions are uncorrelated, in reciprocal space, a superposition of light scattered off all regions is observable. Equally important for the present paper is another contribution to the scattering in addition to that from periodic arrangements of particles in crystallites. Scattering will occur due to crystal

∑l ClP(q)l

(10)

Note that here the angular dependence of the scattered intensity is mainly due to the form anisotropy of the crystal grains and the defects. In general, these objects are larger than single particles and interparticle distances, and thus, their scattering pattern is located at smaller q compared to the q of the bragg-scattered light. In addition, they will scatter quite strongly. Even for a bad spot, where according to Babinet’s theorem the form factor is approximately identical to that of an isolated particle, the small q scattering is orders of magnitude larger than for a particle in a crystalline region, since for the former the structure factor is practically zero. In conclusion, the total scattered intensity, considering the contributions of all scatterers, is

IS ) ICOH(q) + IINC(q)

(11)

Microscopy. Microscopy as applied here is complementary to the above outlined light scattering experiments as it does not look at scattering patterns in detail but rather is concerned with the light left over. As in scattering experiments, the illumination is by parallel light, however of different wavelengths λ. The back focal plane of the objective contains the Fourier transform of the light scattered off the sample, i.e., it contains the low angle parts of the scattering pattern derived above. From this light, the image is constructed. In contrast to conventional scattering experiments, the collected light is restricted in Θ by the numerical aperture of the objective N.A. ) νO sin ΘMAX. Here νO is the refractive index adjacent to the objectives opening, and typically ranges from 1.5 for immersion oil to 1 for air. In most objectives, the N. A. is fixed, but with some, it may be varied through the use of a variable iris aperture stop at the back focal plane of the objective. In general, a large aperture allows one to sample large q and thus small length scales, and provides a high microscopic resolution. The range to be sampled for a good resolution of particle sizes should cover at least the first minimum in P(q). In crystalline, Bragg-scattering samples, the q range to be sampled to obtain a good resolution of individual particle positions should cover at least the set of lowest order Bragg peaks. For defects and crystal grains, the range to be sampled is considerably smaller, as these are usually much larger objects than particles. Note that at fixed numerical aperture the scattering pattern is cut off at different q for each wavelength λ. We are interested in the collected intensity used for image construction. It is therefore useful to discuss the scattered and transmitted intensity in terms of angles, wavelengths, and colors. Using white light illumination, the range of wavelengths is naturally restricted by the sensitivity of the detector, and the range of angles is restricted by the N.A. The intensity transmitted along the optical axis is λmax

ITR )

(I0(λ) - IS(λ,0° < Θ e 180°)) ∑ λ

(12)

min

The total collected intensity is then given as λmax Θmax

ICOLL )

(ITR(λ) + ICOH(λ,Θ) + IINC(λ,Θ)) ∑ ∑ λ Θ min

(13)

1832 Langmuir, Vol. 22, No. 4, 2006

Equation 13 provides the clue to the color contrast between grains of different crystalline order and layer number and in addition explains the excellent visibility of grain shapes and of the various defects. Let us assume that Bragg scattered light of the firstorder Bragg reflection is outside the q-range of the objective used (ΘBragg > ΘMAX). The color of I0 is white by definition. Also the color of grain shape and defect scattering is approximately white, as all Ewald spheres for different λ will intersect similarly with regions of finite P(q). For a monolayer structure with Bragg rods of constant thickness, all Ewald spheres for different λ do intersect the Bragg rods which leads to a homogeneous scattering of all colors. However, due to the restriction of the scattering angle to 180°, more Bragg reflections for blue than for red can be observed over the whole Θ range. Due to the fact that the cross-section for single light scattering is proportional to 1/λ4, blue is scattered with higher efficiency. In addition, the minima of the particle form factor are shifted to higher Θ with longer wavelength. As a result, the observed color of a monolayer in a low resolution microscopy experiment is yellow to orange. For a multilayer system, the nature of the crystalline structure factor plays an important role. Here the Bragg scattering process takes place with different efficiencies for different wavelengths as a function of the crystalline structure and the layer number as discussed in the section above. So the color detected in a low resolution microscopy picture of a multilayer system is determined by the particle size, the index of refraction of particles and surrounding medium, the crystalline structure, the layer number, and the numerical aperture. In dispersed samples, it is also a function of the particle concentration. By analyzing thin crystals made of monodisperse spherical colloids, a reproducible color coding is achieved for ΘMAX smaller than any first-order Bragg reflection. With such a color coding, the crystalline structure and the quality of thin crystals can be analyzed in a fast and easy way on a large length scale. This color coding has to be calibrated only once for the used system, as highlighted below. Experimental Section For the experiments on dried samples, commercial polystyrene (PS) spheres were used having nominal diameters of 220 nm (Lab code: PS220, Batch No. IDC Portland, OR), 590 nm (PS590; Batch No. PS-F-3390 Mycroparticles, Berlin, Germany), 653 nm (PS653; Cat. No. 5065A Duke Scientific, Palo Alto CA), and 1000 nm (PS1000; IDC, Portland OR). The polydispersity of all samples was below 6%. Original suspensions were mixed with distilled water to obtain a packing fraction of approximately 1%. The suspensions were thoroughly deionized with mixed bed ion-exchange resin (Amberlite UP 604, Rohm & Haas, France) and subsequently filtered to remove dust and ion exchange debris. If desired, a small amount of NaCl was added to the suspension to reduce the strong electrostatic interactions by screening. For the preparation of dried colloidal crystals the glass substrates were first cleaned, then left for some hours in a solution of sulfuric acid to obtain hydrophilic glass surfaces, rinsed with double distilled water, and finally dried in a free flowing dry argon stream. Most dry samples shown below were prepared either by placing a drop of suspension on the substrate and leaving it to dry under ambient conditions, or by vertical deposition onto a substrate dipped into the suspension and slowly pulled upward. Suspended crystallites were obtained in samples placed in wedge cells to sample different crystal thicknesses at identical suspension conditions. Wedge cells were made from standard microscopy slides of 1 mm thickness and lateral dimensions of 25 × 75 mm2. In the top plate there are two holes for filling the cell. At one end a (8 × 2)mm2 piece of 50 µm polycarbonate foil was placed between two slides to result in a wedge of small angle γ ≈ 0.04°. The cell was sealed with perfluorinated, water-insoluble vacuum grease (Glisseal, Bohrer, CH). The suspension was then brought into contact with one

Scho¨pe et al. of the openings and sucked in by capillary forces. This way bubble free samples are conveniently obtained. The cell was then completely sealed and mounted on the stage of an inverted microscope for observation (DMIRB, Leitz, Germany). Ko¨hler illumination with white light and different objectives was utilized: for high-resolution images in most cases the long distance objectives PL Fluotar L 63×/0.7 corr PH2 ∞/0.1-1.3/C and PL Floutar L 100/0.75 ∞/(Leitz, Germany) were used. The former was particularly useful for suspended samples; the latter, for dried films. We further employed the objective PL APO 100×/1.40-0.7 Oil ∞/0.17/D (Leitz, Germany) which allows for a variation of the N.A. For the large area surveys, standard 10×, 20×, and 40× objectives were used. Fourier images were obtained in the conoscopic mode using an additional Bertrand lens to image the back focal plane of the objectives. To ensure high quality digital imaging, we used a 3.5 Mpix color digital camera [OTX2, 3.3FZK, La Vision, Germany].

Results Fourier Microscopy. In what follows, we shall demonstrate the particulars and the performance of our new method in several examples of air-dried and suspended films. To show what kind of crystalline structures can occur in our samples, we first start with high-resolution real space microscopy and with the observation of the low q part of scattering patterns through the microscope. Figure 4 compares a series of high resolution real space images taken with the 63× objective at nearly closed condensor aperture with the scattering pattern obtained for the q range of 0 < q < 7.5µm-1 at λ ) 633 nm (ΘMAX ) 44.4°). Note the differences in the symmetry of scattering patterns reflecting the differences in crystal structure. The sequence of structures is found to be in good agreement with previous experimental investigations and theoretical expectations.1,2,25 In addition to phases of hexagonal symmetry (4) also the square (0), the rhomboedric (R), the buckling (B),26 and the prism phases (P)27,28 are obtained over large areas of several hundred square µm. Using the extended notation of Pieranski29 with the digit denoting the number of layers, the sequence of phases observed is 14, 1B, 20, 2R, 24, 2B, 30, 3P, 34, 3B, 40, 4P. In Figure 4, panels d and h, it is not possible to identify the symmetry of the 2D-scattering pattern because too many grains with different orientation in the plane perpendicular to the incoming beam are illuminated. Color Coding of Crystal Structures in Low Resolution Microscopy. Next we turn to the construction of real space and Fourier space images under conditions of varied aperture. Figure 5 shows a series of Fourier images with reduced diameter of the circular field stop located at the back focal plane of the 100× objective, for a dry sample prepared by simple drop drying. Here the border between 14 and 24 is observed. The two regions are separated by a small rim of square structure 20. Rhomboedric and buckling phases are missing due to the fast drying process with its strong capillary forces compressing the sample laterally into the most resistive structures. This and the occurrence of defects of various kinds are typical for the simple drop drying technique. At open field stop, the first-order diffraction pattern is collected completely. The real space image appears bluishwhite due to the presence of the blue dominated diffraction pattern in the back focal plane. With decreasing aperture diameter, the colors change through blue to violet as long as remainders of the first-order reflection are still collected. An abrupt color change (25) Messina, R.; Lo¨wen, H. Phys. ReV. Lett. 2003, 91, 146101. (26) Schmidt, M.; Lo¨wen, H. Phys. ReV. Lett. 1996, 76, 4552. (27) Neser, S.; Leiderer, P.; Palberg, T. Prog. Colloid Polym. Sci. 1997, 102, 1194. (28) Neser, S.; Bechinger, C.; Leiderer, P.; Palberg, T. Phys. ReV. Lett. 1997, 79, 2348. (29) Pieranski, P.; Strzlecki, L.; Pansu, B. Phys. ReV. Lett. 1983, 50, 900.

Fast Method for Photonic Crystal Quality Analysis

Langmuir, Vol. 22, No. 4, 2006 1833

Figure 4. (a-l) Real space images and Fourier images (low q scattering patterns) of wedge cell samples of PS1000 taken with the 63× objective. Image width 137.5 × 102.5 µm2. The insert in the real space pictures is a cut-out with higher magnification. With slit height increasing from 0 to 50 µm a characteristic sequence of structures is observed in good agreement with previous literature. (a) 14 (digit denoting the layer number, and the symbol giving the symmetry - here triangular/hexagonal); (b) 1B (buckling phase); (c) 20 (square); (d) 2R (rhomboedric); (e) 24; f) 2B; (g) 30; (h) 3P (prism); (i) 34; (j) 3B; (k) 40; (l) 4P. Note the strong differences in scattering patterns as the symmetry of the crystals is changed.

occurs once the reflection is completely excluded. Note further, that the information on the positions of individual particles is now lost. It is turned into a specific color coding: the monolayer region turns into a light ochre (Figure 5e, top), whereas the double layer region turns golden brown (Figure 5e, bottom); the square region retains a light bluish-violet appearance. Thus, the

best color contrast is achieved upon closure of the aperture to exclude first order Bragg reflections. Note, that at the same time the abundant defects become clearly visible and can be easily discriminated. Bad spots appear as small white circles; grain boundaries, as rows of dark spots. Dislocations appear as dark lines and indicate the orientation of individual grains.

1834 Langmuir, Vol. 22, No. 4, 2006

Scho¨pe et al.

Figure 5. Sequence of Fourier and real space images of a drop dried suspension of PS590. Image width 63.5 × 57.5µm2. In the Fourier images, the scattering patterns of all phases superimpose. From top to bottom the diameter of the field stop aperture is decreased stepwise. (a) N.A. ) 1.4; (b) N.A. ) 1.33; (c) N.A. ) 1.08; (d) N.A. ) 0.91; (e) N.A. ) 0.7. Note that the color of the real space images changes only gradually as long as the first-order Bragg reflections remain present in the collected light (a-d). A strong qualitative color contrast is visible in panel e, where the upper 14 region appears in a light ocher while the lower 24 region has turned golden brown. Both are separated by a small rim of 20 of light bluish-violet color. Note further the increased visibility of defects by closing the aperture in panel d and in particular panel e. See also Figure 6.

Fast Method for Photonic Crystal Quality Analysis

Langmuir, Vol. 22, No. 4, 2006 1835

Figure 6. (a-f) Real space images of different crystal structures of PS653 with open aperture and high-resolution panels a, c, and e and closed aperture and color coding panels b, d, and f. Image sizes 63.5 × 57.5 µm2. Layer height increases from left to right. In panels a and b, the transition from a submonolayer coverage to 2∆ is shown, in panels c and d, we show the sequence 14, 20, 24, 30, 34. In panels e and f, we show the sequence 34, 40, 44. In panels d and f, the stacking sequences are indicated.

In Figure 6a-f, we show the possibility of color coding areas of different structure. We compare real space images of PS653 layer structures taken at maximum and minimum apertures of the 100× objective. At maximum apertures, individual particles and their local arrangement are clearly visible, whereas for closed aperture, only defects are visible and crystalline areas appear uniformly color coded. In Figure 6, panels a and b, the transition from a submonolayer coverage to 24 is shown; in Figure 6, panels c and d, we show the sequence 14, 20, 24, 30, 34. In panels e and f, we show the sequence 3∆, 40, 44. Most important, 34 shows two different colors: dark ochre and aubergine. This is due to the differences in the stacking sequence: ABA vs ABC. Likewise in Figure 6, panels e and f, the 44 has three different

stacking permutations: ABAB, ABAC, and ABCA leading to three different colorings. The differences in color are due to the different scattered intensities for the respective structures, depending on λ and the details of Bragg peak broadening. This figure thus demonstrates the central feature of our method. An interesting feature is observed at the lower right corner of Figure 6, panels c and d, marked by the arrow. Here two dislocation lines cross. The first running from left to bottom right separates a grain in two regions of different stacking sequence. The second is oriented nearly perpendicular to the first and changes the color crossing it. Note again the different appearances of the rather irregular grain boundaries and the straight dislocation lines.

1836 Langmuir, Vol. 22, No. 4, 2006

Scho¨pe et al.

Figure 7. Electron micrograph of a two layer sample of PS590. One observes a near perfect single crystal with two dislocation lines separating two regions of different stacking sequence. The sequence can be identified by imaging the lower layer through the bad spots (I,II). The inserts show magnifications of these areas. The stacking sequence changes, indicating, that the dislocation concerns only the upper layer. In the regions III-V one observes a local decrease of order due to polydispersity.

Figure 9. Analysis of defects in two PS590 films grown vertically without (a) and with (b) an electric ac field applied during drying. Note the changes in the character and statistics of defects. In panel b, the density of grain boundaries and of dislocations is decreased, whereas the density of bad spot defects is slightly increased.

Figure 8. Electron micrograph of a crack border of a dry film of PS220 with 51 layers and two stacking faults at the positions indicated by the arrows. With the aid of electron microscopy the stacking sequence may be obtained.

Two questions remain before proceeding to defect characterization. How is the method calibrated and how universal is such a calibration? To obtain the color coding for a certain refractive index difference between particles and matrix one has to determine the system structures independently. For the dried samples this is rather unproblematic. In nearly all cases, transitions between different layer numbers NL occur in steps of one and within layers of triangular symmetry there are different stacking

possibilities resulting in NL - 1 different colors. To assign the different stacking sequences to the corresponding colors, however, one has to resort to a high resolution method. In real space, electron microscopy can be used. Figure 7 shows an image taken on PS653 in a two layer system. Two regions inside a crystal grain of constant orientation are separated by two dislocation lines. Through the upper layer bad spots (I,II) the arrangement of particles in the lower layer is visible and one may discriminate an AB stacking and an AC stacking. For larger layer numbers, one may resort to inspections of crack borders. The inspection of the crack border does not determine the structure inside the crystal which can change by dislocation and stacking faults, and so this method implies an unknown systematic error. Figure 8 shows the cliff of a relatively thick film of 51 layers PS220 with ABC stacking and 2 stacking faults at the indicated positions. The structure analysis in reciprocal space using light scattering techniques is more powerful. On one hand, laser light scattering can be used to obtain the full scattering pattern which can be analyzed in analogy to X-ray scattering patterns of atomic substances. By scanning the intensity along the bragg rods,14 the information about the stacking probability can be obtained. This method can also be used in Fourier microscopy. By analyzing the scattered intensity of a Bragg peak I(λ) along the scattering angle Θ, the intensity distribution along the Bragg rod can be obtained after correction with the particle form factor. This low cost approach is quite effective and fast. Only one sample of the

Fast Method for Photonic Crystal Quality Analysis

Langmuir, Vol. 22, No. 4, 2006 1837

Figure 10. Example for large scale analysis performed with the 10×/0.25 objective. Multilayer film grown from a drop of PS590 on a slightly tilted substrate (angle to horizontal γ ) 7°). The field of view is 800 × 1200µm. In the image, the high side during the growth process is at the bottom side; thus, the film had grown from bottom to top starting with a bilayer. Note the uniformity of color of the bilayer. Grain boundaries are nicely visible even in this low magnification up to seven layer structures. This magnification is perfectly suited for large scale stacking analysis. Defect analysis (bad spots and dislocations) can be performed by zooming in during image analysis.

used particles size has to be calibrated to analyze the quality of the other samples. The situation is different for suspended samples, here Bragg scattering, or, for special systems, confocal microscopy, can be used. Such systems are not close packed, so the first maximum of S(q) depends on the particle concentration, whereas the minima in P(q) depends on the particle size. Here each sample has to be calibrated anew to obtain the color code. This sounds tedious, but in practice, it is aided by the fact that for slight changes of the refractive indices the color coding changes gradually. In addition, the selection rules for stacking sequences are retained. Defect Analysis. To illustrate the defect analysis, we chose the exemplary comparison of films growing with and without a shearing electric field applied perpendicular to the growth front.15 We are interested in the influence of the electric field on the kind and density of defects. We therefore observed regions of PS590 monolayer films with closed aperture, using the 100× objective. Figure 9 shows the resulting monolayers. In Figure 9a, the monolayer was grown without external field, and in Figure 9b, it was prepared under an electric ac-field (500V/cm at 10 Hz) and otherwise identical conditions concerning humidity (80%), temperature (20.5 °C), particle concentration (5 × 1018 m-3), salt concentration (5 µM) etc. Dislocations are visible as straight dark lines, whereas the grain boundaries are clearly visible as irregular rows of dark points. In panel a, small dislocations are abundant and arranged at angles different from multiples of 60° indicating the presence of several crystal grains. With the field applied during growth (Figure 9b), no grain boundaries are present. Dislocations are fewer, larger, and properly oriented indicating the formation of a single crystal over the 47 × 81 µm2 field of view. The number of bad spot defects, however, is considerably larger than in the first case. Inspection of the growth process revealed that these emerge preferentially in the vicinity of annealing grain boundaries. There is another, as yet unidentified optical signature present in both images: certain small, isolated

regions of a few particle diameters in size are of a slightly brighter color than the surrounding areas. In Figure 9b, their number is decreased but their size increased. We do not know the origin of this effect. Possibly, there are some regions of less pronounced order, caused by polydispersity, like the region marked III-V in Figure 7, which coalesce during annealing under the shearing electric field.

Applications Finally, we shall apply the method to crystalline colloidal films. The image shown in Figure 10 is taken with a low magnification 10× objective. Here we see a dry multilayer system prepared by simple drop drying of a PS590 suspension on a slightly tilted substrate. The numbers of layers is growing from bottom to top starting with two layers. The grain boundaries and the stacking probability can be easily identified. The use of the 3.3 Mpix digital camera ensures that even small scale objects are not lost. The typical extent of a bad spot of 1 µm diameter is three pixels in these pictures. If smaller particles are investigated, we would use a 20× magnification objective. Depending on the length scale of interest, either the original pictures are used or a digital zoom can be performed using image analysis software. Thus, the color coding can be used to perform stacking and grain size analysis from large scale images, while sets of zoom images are used for defect analysis.

Conclusion We present a novel microscopic observation scheme suitable for fast, large and small scale analysis of colloidal crystal thin films. In particular, the structure and stacking sequence of hexagonally close packed structures are color coded, exploiting results from light scattering theory in the design of image construction. Equally, several different kinds of defects are made

1838 Langmuir, Vol. 22, No. 4, 2006

visible with characteristic signatures even in large scale images. The method can readily be combined with automated image processing and should turn out very useful in quality assessment for film formation. This feature may considerably accelerate the development and optimization of novel deposition techniques. It should also facilitate less tedious on-line product control. The method is not restricted to dry film applications. It therefore may find further interesting applications in fundamental research concerning the behavior of colloidal crystals in confinement.

Scho¨pe et al.

Acknowledgment. We are pleased to thank H. Lo¨wen for many helpful discussions on the phase behavior under confinement. This work was financially supported by the Deutsche Forschungsgemeinschaft (Pa459/8, Pa459/10, Pa459/12), the Sonderforschungsbereich TR6 TPD1, the Stiftung RheinlandPfalz fu¨r Innovation, the European Community (MRTN-CT2003504712), and the Materialwissentschaftliches Forschungszentrum (MWFZ) Mainz. This is gratefully acknowledged. LA0524972