NANO LETTERS
Template-Assisted Growth of Nominally Cubic (100)-Oriented Three-Dimensional Crack-Free Photonic Crystals
2005 Vol. 5, No. 12 2646-2650
Chongjun Jin,† Martyn A. McLachlan,‡ David W. McComb,‡ Richard M. De La Rue,† and Nigel P. Johnson*,† Department of Electronics & Electrical Engineering, UniVersity of Glasgow, Glasgow, G12 8LT, U.K., and Department of Materials, Imperial College London, London, SW7 2AZ, U.K. Received September 25, 2005; Revised Manuscript Received October 20, 2005
ABSTRACT Three-dimensional (3D) photonic crystals (PhCs) are now beginning to acquire functionality via the use of dopants and heterostructures. However, the self-organized fabrication of large-area single crystals that are free of cracks and stacking faults has remained a challenge. We demonstrate a technology for the fabrication of (100)-oriented thin film 3D opal PhCs that exhibit no cracks over areas having no intrinsic size limit via a modified template-assisted colloidal self-assembly approach onto a patterned substrate.This technology potentially makes available large area regions of single photonic crystal, which can be used for optoelectronic devices.
Introduction. Three-dimensional (3D) periodic photonic crystals (PhCs) offer an excellent tool for the manipulation of photons and addressing key issues in the fields of quantum optics,1-3 integrated optoelectronic devices,1-3 and metamaterials.4,5 The functionality of 3D PhCs has also been increased with the use of dopants6 and heterostructures.7 Various methods for the fabrication of 3D PhCs have been proposed and demonstrated including colloidal selfassembly8-13 and optical and electron-beam lithography (EBL) combined with a variety of etching methods.14-19 Among these fabrication methods, the colloidal self-assembly approach is comparatively straightforward and economical. In this process, a monodisperse colloid is dried or deposited on a substrate, producing a face-centered cubic (fcc) crystal. Various approaches have been developed based on the selfassembly approach aided by gravitational force,20 electrochemical assistance,21 capillary action,8 and fluidic cell confinement.22 For the 3D PhCs fabricated via a colloidal self-assembly route, there are two types of unintentional defects that may be considered critical in the sense that they disrupt the propagation of light through the structure. The defects that require consideration are stacking faults and macroscopic cracks. In the former, the stacking of close-packed planes in the crystal is varied between the energetically favored facecentered cubic (fcc) stacking and hexagonal close packing * Corresponding author. E-mail:
[email protected]. † University of Glasgow. ‡ Imperial College London. 10.1021/nl051905j CCC: $30.25 Published on Web 11/10/2005
© 2005 American Chemical Society
(hcp). However, the differences in the free energies of the fcc structure and hcp structure are small, approximately 0.005RT (calculated for the hard-sphere model),23 which means that stacking faults are likely to occur. Macroscopic cracking is caused by a reduction in the center-to-center distance between the spheres as the growth progresses from wet to dry conditions for either silica spheres or polystyrene spheres.8,24 We have demonstrated previously25,26 that both the size and spacings between cracks can be roughly controlled but not eliminated for polystyrene spheres. Under self-assembly conditions, we have demonstrated the formation of single domains exceeding 1 mm in length and 500 µm in width;26 however, such structures are formed when the thickness of the film is many hundreds of sphere layers thick. For a thin film that is composed of only several tens of layers of spheres, the films are dominated by microscopic cracks that occur in the close-packed 〈110〉 directions, implying major limitations for application in integrated devices. There have been many suggestions postulated for the reduction of these cracks, for example, optimization of the growth conditions26,27 and annealing the spheres before growing the crystals.28 The latter addresses the shrinkage of the spheres upon drying but not their reduced separation. Here we show how the use of template-assisted colloidal self-assembly (originally proposed to control both crystal structure and orientation) can eliminate cracks. This method, known as colloidal epitaxy,10 is closely analogous to conventional liquid-phase epitaxy for atomic crystals. A variety of template structures have now been
Figure 1. SEM images of a template on a silicon substrate. (a) Top view of the template. (b) Tilted view of the template at 30°.
proposed for initiation of template-directed 3D PhC growth including square periodic arrays of holes,10,29 square periodic pyramidally shaped arrays,30-32 grooves,30 square twodimensional gratings,33 and pillars.34 In addition, all of the methods discussed previously, that is those used for untemplated colloidal self-assembly, can be adapted for templatedirected growth. Among these methods, the colloidal selfassembly technique with a capillary force is the most advantageous for template-assisted growth because the growth of uniform layers with thicknesses that can be controlled accurately is possible. However, to the best of our knowledge, only two or three layers of spheres have been aligned well into (100) orientation by using colloidal epitaxy. When more layers of spheres are deposited onto the template, the crystal growth tends to reorient toward (111) planes34 and forms a structure with a coexistence of the (100) and (111) orientations. Zhang and co-workers report that only 10-40% of the template area can maintain the (100) orientation.33 In this letter, we present a method for the formation of high-quality (100)-oriented thin PhC films that are free of cracks, with no obvious limit to the opal film area, by using a modified template-assisted colloidal self-assembly method with the aid of capillary and gravitational forces. We outline the theory behind the method and describe potential applications for structures formed by this approach. Experimental Section. A scanning electron microscope (SEM) image of a typical (100)-patterned template is shown in Figure 1a. The patterns were written on a silicon wafer and defined in a layer of hydrogen silsesquioxane resist (HSQ, Dow Corning Fox 14) using electron beam lithography (EBL). The HSQ resist was then developed in a solution of tetramethylammonium hydroxide, forming the periodic pillars of HSQ. The templates were subsequently heated in a furnace at 400 °C for 1 h to consolidate the HSQ pillars with the underlying silicon wafer.35 During the course of this study, we investigated a number of sphere diameters and pillar spacings. The pillar spacings used were 308, 312, 316, and 320 nm at a constant height of 160 nm. The pillars were tapered slightly (see Figure 1b), forming a well between adjacent pillars for the deposited sphere to rest in. In this paper, for all but one case the polystyrene sphere diameter was fixed at 299 nm (σ 1.4%). Two different surface conditions were also studied: first with plain HSQ pillars on the silicon surface and, second, with the HSQ pillars coated with an approximately 5-nm-thick layer of gold/palladium. Nano Lett., Vol. 5, No. 12, 2005
There are three critical factors that must be controlled simultaneously to ensure high quality (100)-oriented structures. First, it was found that if the angle between the substrate and horizontal is near 90°, then (100) and (111) opals coexist on the template. These conditions are not favorable for templated assisted growth. This finding is similar to those in previous reports.33,34 Here we employ a combination of gravitational and capillary forces by orientating the templated substrate at shallower angles than those reported in previous work. The angle between substrate and horizontal should be maintained between 45° and 60°. Second, we have controlled the growth environment to ensure that the energetically unfavorable (100) orientation is formed, in preference to the favored (111) orientation. We have identified the optimum conditions for the growth of (111)oriented crystals (with no template) previously, and the temperature identified was 65 °C. However, use of a high temperature is not favorable for the growth of (100)-oriented photonic crystals. If the temperature is reduced to 40 °C, then we have found that the opal always reorients to the (111) direction when more than five layers of spheres are grown on the template. This behavior is also similar to that described in previous reports.34 In this study, we have discovered that if the temperature is reduced to around 24 °C and the colloidal concentration is reduced to 0.01-0.05%, then both the (100) and (111) orientations may coexist even on the flat surface without the template, as shown in Figure 2a. Finally, it is vital that when the templated surface is present, enough time is available for the spheres deposited from the colloid to arrange themselves into the positions defined by the template. In our case, it is important that the growth rate (as measured by the evaporation rate of the solution) is slow, around 1 mm/day, to ensure that the growth is guided by the template. Under these conditions, the relative humidity is between 32 and 40%. This result is very different from previous work, where the growth rate was approximately 10 times higher, at around 10-15 mm/day. Our growth method also has similarities with techniques such as graphoepitaxy,36 in which a “seed” surface enables growth in a particular orientation. A (100)-oriented crystal grown under the conditions described above is shown in Figure 2b, c, and e. Parts b, c, and e of Figure 2 show SEM images of the (100)-oriented crystals produced using template-directed growth. The standard deviation on the sphere diameter is extremely narrow, at around 1.4%. However, this level of size dispersion still gives rise to defects (including those caused by the presence of occasional abnormally small or 2647
Figure 2. SEM images of a (100)-oriented crystal grown by the template-assisted colloidal self-assembly method. (a) Crystal formed out the templated area with (111) and (100) orientations present. (b) SEM picture of the crystal on the template with a 308-nm period. (c) Tilted view of SEM picture of the (100)-oriented crystal at an angle of 30°. (d) The (100)-oriented crystal made from the spheres with a standard deviation of 2.72%. (e) A large scale view of the crystal without cracks. The inset shows a magnified view with arrows indicating the abnormally large and small spheres.
large spheres), as observed on the top surface of the crystal (see the inset in Figure 2e). For larger deviations in the sphere size, more serious defects occur and affect the quality of the crystal significantly. For example, Figure 2d shows template-assisted growth of polystyrene spheres with a standard deviation of 2.7% (diameter 301 nm). The growth environment and template spacings used were the same as those described in Figure 2c. Under the growth conditions described, the surface condition appears to have little impact: (100)-oriented 3D crystals could be grown equally well on either the HSQ surface, as prepared, or with the addition of a thin (around 5 nm) Au/Pd metallic layer. 2648
The most striking feature is that crystal films grown on the template do not contain cracks. A (100)-oriented crystal (Figure 2e) with more than 10 layers was produced over an area 800 × 800 µm2. This area was determined solely by the field size used in the EBL pattern generation process, and the optical micrograph in Figure 3 shows the boundary between the patterned and unpatterned areas. In contrast, cracks were observed for all areas greater than 10 × 10 µm2 in the (111)-oriented crystal (see Figure 2a) that grows on the unpatterned template areas of the same sample. Such crack formation has been reported previously.8 Nano Lett., Vol. 5, No. 12, 2005
Figure 3. Optical image of showing boundary of templated area and cracks outside the templated area.
Cracking on untemplated substrates is caused by shrinkage of the sphere center-to-center spacing or lattice constant when the structure dries. This can arise from individual spheres shrinking and/or the removal of solvent between the spheres. In the case where the domains adhere to the substrate when drying, tensile stress in the crystal is relieved by the formation of cracks. For the templated case, the spheres in the bottom layer stay in their initial positions when the crystal dries out because displacement of the spheres is restricted by the pillars. Subsequent layers are constrained with the same inplane lattice constant by the spheres beneath, resulting in non-close-packed face-centered structures being formed, with a small regular array of gaps between spheres, as shown in Figure 2b and e. With the sacrifice of a close-packed structure, a slightly non-close-packed crack-free photonic crystal is formed by our method. On close inspection of the enlarged image of Figure 2b, some position deviation exists (the gap between in-plane spheres is slightly different). This position deviation can be up to 1.5% of the lattice constant from the mean position and is comparable to the deviation of sphere size. A position deviation of 1.5% does not seriously affect the band-gap of the opal.37 Furthermore, the position deviation is caused mainly by the randomness in the sphere size, in our case. The formation of crack-free PhC films made by the modified template-assisted method is the most significant phenomenon in our experiments because nearly perfect millimeter-scale 3D photonic single-crystal films can be obtained using this approach, with the potential for much larger areas. Thus, we have achieved templatedirected growth on (100)-orientated surfaces in which stacking faults are eliminated and with the additional benefit of the crystal being crack-free. The optical measurement and simulation results show that there is a band gap in the 〈100〉 direction.38 Further numerical simulations reveal that silicon inverse structures produced from our polymer opal would show a full band-gap between the eighth and ninth bands.38 The growth regime has been confirmed for several different pillar spacings in the range from 308 to 320 nm. Using spheres of a diameter of 299 nm and with the pillar spacing up to 7% larger than the sphere size, the crystal remains well-ordered. Nano Lett., Vol. 5, No. 12, 2005
Figure 4. Reflection spectrum of the (100)-oriented opal grown on a template with a pillar spacing of 308 nm.
The effect of the angle on the growth of opal also seems quite significant. For example, for a 90° angle, only a small number of (100)-oriented layers of spheres could be obtained, and for a 45° angle, a (100)-oriented opal with over 20 layers of spheres could be fabricated. This behavior could be caused by the spheres deposition speed on the template, which is related strongly to the growth angle, the number of layers, and the length of the meniscus as well as the evaporation rate of the solution. These results need to be investigated further. However, it is clear that only a small number of layers of spheres could be obtained for a 90° growth angle, in agreement with reference 34. The optical reflection spectrum shown in Figure 4 for (100) opal grown on a template with a pillar spacing of 308 nm corresponds to the (200) spacing because reflection from the (100) planes is forbidden by symmetry. The reflection peak corresponding to the photonic-crystal stop band for the (100) orientation has its peak at 576 nm. When compared to the center of the stop band for a cubic closed-packed (fcc) structure with the same sphere diameter, 299 nm, which would be at 607 nm, the center of the stop band has been shifted to a shorter wavelength. This shift is caused by the reduction of the interplanar spacing that accompanies the formation of a non-close-packed structure. Furthermore, Fabry-Perot (F-P) resonant peaks caused by the finite thickness of the crystal film are clearly evident in this spectrum, and the separation of the F-P resonances is consistent with the number of layers. The number of layers of spheres can be found from the following equation neff(N - 1)/L + 2n0L0 ) λ1λ2/2(λ1 - λ2) where L0 is the thickness of the boundary layer and is half of the sphere diameter, L0 ) 149.5 nm. Because this layer is composed only of half spheres (not in contact with other spheres), the effective refractive index of the boundary layer, n0, is less than for the other layers, that is, n0 ) 1.2909. N is the number of layers, and L is the thickness of a single layer, with L ) 204.86 nm. neff is the effective refractive index of a single layer, neff ) 1.4248, and λ1 and λ2 are adjacent F-P reflection peaks. The F-P peaks naturally 2649
broaden at longer wavelengths. Thus, the five well-defined peaks at wavelengths shorter than the reflection peak of the stop band, which were used to calculate the number of layers. The average number of layers of spheres grown on the template is around 23. Conclusions. We have demonstrated the growth of (100)orientated 3D PhCs on EBL patterned substrates. The thickness of these crystals exceeds 20 layers. The role of the template is critical in directing the growth, as shown by regions outside the templated area where both (111) and (100) orientations coexist. It is found that the size-deviation of the spheres, growth angle, and growth rate are important parameters. For the size-deviation of the spheres, the smaller the deviation the more ordered the crystals. The growth rate is a vital factor because it determines the ability of the spheres to organize themselves in the (100) orientation. It is remarkable that no cracks appear in the (100)-oriented crystals using this technology. For future high density integrated optoelectronic devices, it is vital that critical defects are minimized. In principle, a single-crystal film could be grown free of stacking faults and cracks over an area determined only by the size of the template, which could be particularly valuable for optoelectronic devices integrated in 3D photonic crystal films.
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