Photonic crystals (PC) have emerged as important types of structures for light manipulation. Ultimate control of light is possible by creating PCs with a complete three dimensional (3D) gap [1, 2]. This has proven to be a considerable challenge in the visible and ultraviolet frequencies mainly due to complications in integrating transparent, high refractive index (n) materials with fabrication techniques to create ~ 100nm features with long range translational order. In this letter, we demonstrate a nano-lithography approach based on a multilevel electron beam direct write and physical vapor deposition, to fabricate four-layer titania woodpile PCs that potentially exhibit complete 3D gap at visible wavelengths. We achieved a short wavelength bandedge of 525nm with a 300nm lattice constant PC. Due to the nanoscale precision and capability for defect control, the nanolithography approach represents an important step toward novel visible photonic devices for lighting, lasers, sensing and biophotonics.
© 2007 Optical Society of America
Complete 3D gap PCs such as the “woodpile” lattice can alter light-matter interactions, many of which occur at optical frequencies, in interesting and fundamental ways. Large lattice constant structures (> 3μm) can be fabricated using contact photolithography  yielding bandgap in the mid-infrared. Structures with bandgap in the near-infrared require even smaller dimensions and have been fabricated from silicon  using high precision step and repeat aligners and gallium arsenide  using wafer fusion, targeting the optical communication wavelengths (λ ~ 1.5μm). Both of these approaches, while yielding wafer scale 3D PCs, are generally quite complex and restrictive. Alternative nano-fabrication methods have also been explored [6, 7, 8, 9] to fabricate 3D PCs, some of which show great promise. However, further progress still needs to be made from the standpoint of precision, defect control and engineering, and incorporation of high index materials.
A major advantage of 3DPCs with visible bandgaps is the availability of highly efficient nanoscale light sources such as semiconductor quantum dots (e.g. CdSe, CdSe) and dyes. By incorporating such light sources at specific locations within 3D PCs, their emission properties can be suitably manipulated by the photonic bandstructure to improve efficiency and to tune the emission profile, potentially enabling novel applications in lighting, displays, lasing and sensing. However, fabrication of complete gap 3D PCs in the visible, poses two significant challenges: choice of a suitable material with high refractive index and transparency, and patterning of structures with desired nanoscale periodicity (< 500nm) and symmetry. Titanium dioxide (TiO2) has a high refractive index (nanatase ~ 2.5;nrutile ~ 2.8) with negligible absorption at visible wavelengths . This is an important advantage over metals which despite their high refractive index suffer large absorption at visible wavelengths. TiO2 has been used for infiltration of 3D PC templates [11, 12] including inverse opal PCs [13, 14, 15, 16]. However, the FCC symmetry of most inverse opals requires a refractive index contrast of n > 2.9 to create a complete 3D gap between higher order bands, which are more sensitive to disorder inherent in self-assembled opal templates . Nevertheless, higher refractive index material, like Sb 2 S 3 (n ~ 3.4) have been infiltrated into opal PCs for bandgap around 750nm wavelength . In contrast, the woodpile lattice structure is shown to open a complete 3D gap for a refractive index contrast of just over 2.0 . We decided to use reactively sputter deposited amorphous TiO2 (n ~ 2.3 as measured by ellipsometry) as the high index material, because it has a well controlled anisotropic dry etch profile with good selectivity to the e-beam resist mask. This property allows for the definition of nanometer sized features in TiO2 films, thus enabling fabrication of visible PCs using woodpile lattices. The photonic band structure in Fig. 1(a) calculated for the corresponding woodpile lattice within the first Brillouin zone shown in Fig. 1(b) exhibits a complete 3D bandgap between reduced frequencies () of 0.4300 to 0.4462 with a gap/midgap ratio of 3.7%, where “a” is the lattice constant of the woodpile structure indicated in Fig. 1(c). This implies a wavelength gap of 15-25nm approaching the emission linewidths of green and red emitting monodisperse quantum dots and light emitting diodes. This will enable us to explore the effect of complete bandgap on phenomena such as band edge emission enhancement, emission lifetime increase in the gap as well as line narrowing effects of nanocavities. For instance, even with a moderate quality factors of a few hundreds achievable by 1-2 unit cell (9-17 layers) confinement , emission linewidths can be reduced to ~ 5 – 6nm which are well within the bandgap size.
2. Multilevel electron beam fabrication
We use a multilevel electron beam direct write approach to achieve the required nanometer size lattice constants and feature sizes with precise alignment between the layers and with good compatibility with many materials. Previously, this approach has been demonstrated for the fabrication of near-IR prototype 3D PC devices using silicon [21, 22] and more recently using gold  with band edge approaching 650nm wavelength. Here we successfully fabricated 4 layers (one unit cell along the stacking direction) of a woodpile lattice PC in the visible, consisting of sputter deposited TiO2 rods with lattice constants from a = 300nm to 400nm and device size of 80μm × 80μm. First a set of gold alignment marks is patterned on to a Si substrate. 110 ± 5nm of TiO2 film is then deposited using a reactive radio frequency sputtering of a titanium target in an oxygen ambient on an unheated substrate based on a published procedure . A PMMA e-beam resist film is spin coated on the TiO2 film and patterned using electron beam direct write (JEOL-JBX5FE), referenced to the alignment mark followed by reactive ion etch (Plasmatherm) in a plasma chamber flowing CHF3 gas. This results in a periodic array of TiO2 rods. The etched region is backfilled with a low index e-beam evaporated SiO2 and followed by spin on glass, which is then planarized . The planarized spin on glass is etched back once again with reactive ion etch to expose the top of the TiO2 rod surface. We then deposit another layer of TiO2 film and repeat the above procedure to make the subsequent layers. The electron beam system scans the initial set of alignment marks to obtain a position reference thereby precisely aligning the subsequent levels to the previous ones. After the desired number of layers are fabricated, we remove the low index dielectric (SiO2) by immersing the samples in a buffered hydrofluoric acid solution for ~ 60s.
For the rest of the text we will refer to the devices by their lattice constants. The nominal rod width is d = 0.35 - 0.40a with a height h = 110 ± 5nm. We examined the cross section of a 400nm lattice spacing device with a scanning electron microscope (SEM) seen in Fig. 2(a) clearly showing the 4 individual layers. The “wavy” appearance of rods is due to a small overlap of the rods resulting from slight over-etching (~ 10 – 15%) in order to ensure the connectivity of TiO2 rods after the removal of the low index filler. Previous reports indicate that the photonic bandgap is not destroyed by small amount of overlap . Furthermore, such overlap can be minimized by carefully calibrating and controlling the etch parameters. Figure 2(b) shows an SEM image of 300nm device allowing us to observe the underlying layers due to the open woodpile structure, although they were progressively more blurred as we go from layer 4 (top layer) to layer 2. The offset between layer 2 and layer 4 was found to be 150 ± 10nm , demonstrating successful alignment between layers was achieved for the desired woodpile symmetry. The rods, in this case are only around 110nm wide which is one of the smallest dimensions for a woodpile lattice reported to date.
The woodpile structure which has a bandgap between the lower bands (2-3) is known to be highly tolerant to layer-to-layer misalignment that can result during fabrication. Previous theoretical studies  indicate that the gap can survive even with 20% disorder which amounts to ±60nm for a = 300nm. However, by repeatedly using sharply defined alignment marks during the patterning of each layer, positional accuracy to within ±20nm can be achieved. This enables the fabrication of additional unit cells as well as point and line defects to create devices with desired photonic response. Improvement in the TiO2 refractive index can further increase the bandap size (~ 6.4% for n = 2.5). This may be achieved through substrate heating during sputter deposition or by post process annealing to convert the amorphous TiO2 to a higher index (anatase/rutile) form. The woodpile structure can be fabricated with minimal modification to the above process.
3. Optical characterization using microspot spectroscopy
Figure 3(a) shows the devices exhibit bright coloration indicative of strong stop bands in the visible frequency. The 400nm device reflects orange light while the 300nm device reflects yellow light. The uniformity of the color across the device region for the 400nm device points to good structural uniformity. The 300nm device though mostly uniform in color displays some darker reddish regions in the middle and around the edges. Due to dose control limitations of our e-beam direct write system, the exposure is not simultaneously optimized for the different lattice constant devices on the same wafer. This can be solved by using separate exposures optimized for each lattice constant device. In order to characterize the bandgap, we performed microspot optical reflectance spectroscopy from 400 nm to 800 nm wavelengths on the devices by focusing the illumination with a microscope objective(NA = 0.25) with a spot size of ~ 25μm. Similar approach has been used previously to conduct single domain spectroscopy of self-assembled photonic crystals . This also allows us to measure the more uniform region of the 300nm device. The relatively small NA corresponds to near normal incidence along the stacking direction thus probing the directional gap at the X symmetry point. Figure 3(b) shows a typical reflectance spectra from 300nm and 400nm devices. Each device shows a reflectance maximum at longer wavelengths corresponding to lowest order stop band and additional features at shorter wavelengths corresponding to higher order stop bands. For the 400nm device the lowest stop band maximum appears at 670nm with a short wavelength minimum (band edge) at 620nm. By reducing the lattice constant to 300nm the corresponding values are blue shifted to 620nm and 525nm which is well into the middle of the visible spectrum. Thus, we have demonstrated the fabrication of 3D PCs with sufficiently small lattice constants to potentially modify emission characteristics of embedded visible light sources.
4. Comparison to computational models
In order to get a better insight into the observed optical response, we compared the experimental data with results from finite difference time domain(FDTD) and plane wave expansion(PWE) calculations.
4.1. Finite difference time domain calculation (FDTD)
Simulated normal incidence reflectance spectra were calculated using a commercial FDTD software(OptiFDTD). To approximate our spectroscopy geometry of focused light source on a small sample, we utilized a supercell of five unit cells in the plane of the fabricated structure with perfectly matched layer boundary conditions. We discretized the structure on a15nm mesh and illuminated it with Gaussian source of width ~ 2a to maintain a tractable computational load. The experimental features typically agreed with the normal incidence FDTD prediction to within 5 – 10%. Figure 4(a) shows that for the 300nm device the reduced midgap frequency (ωred) from experiment was 0.492 compared to FDTD value of 0.508. The reflectance peak intensity was ~ 40% for both cases. Higher frequency features of the experimental spectra also exhibited a similar trend as the FDTD predictions. For the 400 nm device the midgap frequency of ωred = 0.590 matched closely with the corresponding FDTD value of 0.580 as seen in Fig. 4(b), while the peak intensity of 40% was lower than the calculated value of 48%. A similar trend in the higher frequency response for the experimental and FDTD data is again observed. Since the experimental data of the 400nm device spans a greater range of reduced frequency we are able to observe a greater number of higher frequency features. We attribute the observed discrepancy between the experimental and FDTD features to a combination of following factors. First, the experimental data contains reflectance from off-normal incidence angles which is not accounted for in the normal incidence FDTD model. Second, woodpile parameters (e.g. rod width, height, overlap) used as inputs for the FDTD model contain measurement uncertainties. Third, discretization of the structure in the FDTD domain space introduces additional approximations that may shift the calculated spectra. Nevertheless, the good match between experimental and simulated reflectance for a four layer TiO2 woodpile PC suggests that fabrication of additional unit cells by the multistep lithography technique will result in a stronger photonic response consistent with 3D bandgap.
4.2. Plane wave expansion (PWE)
We also compared the experimental response to bandstructure calculations along the stacking direction (ΓX〈). The bandstructure was calculated using PWE method [29, 30] with 240-480 plane waves. We found the theoretical midgap position for 300 nm device to be 0.432 and for 400nm device to be 0.546. The observed blue shift of the peak position by ~ 10 – 15% from the midgap can be attributed to having only 4 layers (i.e. one unit cell) of PC along the stacking direction, as adding more layers is shown to shift the peak towards longer wavelengths by that amount . Thus the PWE method, which is computationally less intensive than FDTD, gives a reasonably good estimate of the frequencies of the optical features. Finally, we note that the ratio of c to a is different for the 300nm device ( = 1.46) and the 400nm device ( = 1.1). PWE calculations indicates that the 300nm device is more likely to show a full 3D gap as the ratio is closer to the ideal value of √2. In this case, this could not be directly verified experimentally as there is only one unit cell along the vertical. However, our current spectroscopy setup which only probes the ΓX〈 pseudogap shows that the 300nm device does exhibit a significantly wider reflectance feature than the 400nm device, consistent with our expectations.
The individual devices that were fabricated here are only 80μm × 80μm in size. However, one can make larger areas if required by field stitching these individual patterns. The process developed here can also be easily transfered to a large volume lithographic fabrication such as nanoimprint lithography. In conclusion, we have demonstrated that by using a nano-lithographic approach we can fabricate an omni-directional gap 3D PC in the visible frequency, in particular a TiO2 based woodpile lattice with precise structural control to produce predictable optical response. By patterning mechanically robust multilayers of TiO2 rods with dimensions of ~ 100nm and periodicities < 500nm and with excellent alignment between layers, we have shown that multistep e-beam direct write process is suitable for fabrication of visible 3D PCs with large number of layers if necessary for 3D gap PC devices. In combination with the availability of strong visible light emitters such as quantum dots, dyes and LEDs, a systematic study of light emission in 3D PC environment is possible leading to novel photonic devices in the future.
We thank Aaron Gin for reviewing the manuscript and providing valuable suggestions. San-dia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.
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