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Ying-Chieh Chen, Joseph B. Geddes III, Leilei Yin, Pierre Wiltzius,* and Paul V. Braun* The optical properties of a photonic crystal (PC) are governed by the periodicity of its lattice, geometry of its basis, and dielectric contrast of its constituents. Numerous advances in experimental fabrication and characterization of three-dimensional (3D) PCs with submicron morphology have been made since their inception,[1] along with theoretical prediction of their optical properties.[2] Their detailed morphology has typically been verified directly via electron microscopy of surfaces and cross sections,[3–5] and indirectly via optical spectroscopy and diffraction measurements,[6–9] but not holistically by direct electromagnetic 3D tomography at length scales substantially shorter than those of optical wavelengths. Here, 3D PCs fabricated by holographic optical lithography were imaged using hard X-ray microscopy. The large penetration depth of the X-rays allowed angle-resolved two-dimensional (2D) images to be analyzed to reconstruct the full 3D morphology of a holographic PC via computed tomography (CT). The reconstructed morphology was used both as a basis for optical reflectance spectra calculations, which compared closely to experimental measurements, and to validate a theoretical model of the PC structure. Fabrication of 3D PCs via multibeam interference lithography allows flexible control of their basis of periodic units.[10–12] Most theoretical proposed structures assume the basis follows the iso-intensity surface.[13,14] However practical issues such as shrinkage, photoresist resolution and absorption-generated intensity gradients can invalidate this assumption, and full modeling of the fabrication process has been reported.[14] Nevertheless, without appropriate means to inspect the actual fabricated structures on the micro- and nanoscales, it is difficult to obtain the necessary information to verify or modify such a
Dr. Y.-C. Chen, Dr. J. B. Geddes III, Prof. P. V. Braun Department of Materials Science and Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801, USA E-mail: [email protected] Dr. Y.-C. Chen, Dr. J. B. Geddes III, Dr. L. Yin, Prof. P. V. Braun Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign Urbana, IL 61801, USA Prof. P. Wiltzius Division of Mathematical, Life, and Physical Sciences University of California Santa Barbara, Santa Barbara, CA 93106, USA E-mail: [email protected] Prof. P. V. Braun Frederick Seitz Materials Research Laboratory University of Illinois at Urbana-Champaign Urbana, IL 61801, USA
DOI: 10.1002/adma.201200411
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model. This situation is quite unlike that for one-dimensional (1D) and 2D PCs, where the morphology can be completely characterized via scanning electron microscopy (SEM). We aimed to characterize an optical material whose properties depend on morphology with characteristic length scales that are subwavelength for the optical bandwidth of interest. Therefore, absent suitable superresolution optical techniques,[15,16] which are typically more appropriate for weakly scattering samples, and not high refractive index contrast PCs, one requires short wavelength electromagnetic (X-ray) or matter (electron) waves to achieve the required resolution. Given the penetration depth for electrons is much less than size of the 3D samples we wish to study, we have two possible practical strategies. The first is to destructively characterize the sample using focused ion beam (FIB) milling to reveal subsequent cross sections of the sample, along with scanning electron microscopy to image each cross section. Artifact generation during FIB milling will always be a concern with this approach, and the actual volume of the sample imaged is quite small. The second is to use X-ray CT to image the entire sample volume via phase or absorption contrast. X-ray CT is an imaging technique used primarily in the medical field, recent improvements to which have opened up new opportunities in other disciplines, particularly biological and materials science.[17] X-rays possess short wavelengths enabling high resolution and exhibit deeper penetration depths than electrons. Thus, 2D angle-resolved X-ray images can be reconstructed to full 3D images via CT.[18] This technique is especially useful for nondestructive imaging of the interiors of optically opaque objects. Here, we report imaging SU-8 polymer PCs fabricated by holographic lithography (i.e., multibeam optical interference) with hard X-ray CT with a laboratory-based microscope system (nanoXCT, Xradia, Pleasanton, CA, USA).[19] The imaged samples are PCs fabricated with the polymer photoresist SU-8 (MicroChem, Newton, MA, USA) following the procedure developed previously.[20] The glass substrate on which the holographic PC was fabricated was etched away with hydrofluoric acid to minimize the X-ray absorption. Both phase contrast and absorption contrast modes were performed. For an as-fabricated polymer holographic PC sample, phase contrast mode is sufficient to resolve the periodicity, as shown in Figure 1. However, material boundary artifacts caused by the non-monochromatic and non-parallel light source make this particular image unsuitable for quantitative analysis. Nevertheless, the phase contrast image is sufficient to reveal some morphological details of the as-prepared SU-8 polymer sample directly. In order to study the real-space geometry of holographic PCs in a quantitative way, we turn to the absorption contrast alternative. X-ray absorption scales as the third power of the atomic number. The constituents of both air and SU-8 polymer possess
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X-Ray Computed Tomography of Holographically Fabricated Three-Dimensional Photonic Crystals
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Figure 1. Phase contrast X-ray CT images of a polymer holographic PC: a,b) cross-sections and c) a reconstructed 3D structure.
low atomic numbers, and their absorption contrast is not strong enough to produce suitable images for 3D reconstruction and analysis. Typically, OsO4 or RuO4 are used to stain a polymer to enhance the image contrast;[21,22] however we found these stains swell SU-8 polymer and distort the PC. Atomic layer deposition (ALD) has been shown to be a reliable infiltration technique for SU-8 polymer PCs and synthetic opals.[23–25] We selected hafnium dioxide (HfO2) as our infiltration material: hafnium has a high atomic number of 72, the ALD technique for HfO2 is well developed, and the process can be done at relatively low temperatures of 125 °C (Cambridge Nanotech, Cambridge, MA, USA). We first deposited 10 nm of Al2O3 at 85 °C to prevent
deformation of the SU-8 structure during the 125 °C deposition of HfO2. That subsequent deposition totaled 163 nm of HfO2, as measured by ellipsometry. This infiltration process produced a conformal HfO2 shell surrounding the SU-8 polymer region of the PC. Figure 2a–c shows electron microscopy images of the sample before ALD infiltration. Figure 2d,e shows SEM images of cross sections of the infiltrated PC prepared by FIB milling. Figure 2f shows corresponding normal incidence optical spectra before and after ALD infiltration. Notice the main reflectance peak at longer wavelengths (≈70% at ≈1300 nm for uninfiltrated sample), as well as several other reflectance peaks at shorter wavelengths resulted from the highly periodic morphology of the holographic PC, even after undergoing shrinkage during post baking and subsequent development. We observed the main reflectance peak position at several times during the infiltration process and noted that it was red shifted as expected due to the HfO2 infilling to a final position of ≈1600 nm, indicating retention of periodicity. The magnitude of the main reflectance peak decreased somewhat to ≈60% upon infiltration. X-ray transmission images were collected at 0.5° intervals from 0.0° through 180°. Four selected images, each taken at a different angle and each exhibiting a different periodic pattern, are shown in Figure 3. At 0°, the hexagonal patterns corresponded to the A-B-C stacking of face-centered cubic lattice in the 111 plane. The periodicity was measured as a/√3 = 510 nm, where a is the hexagonal periodicity of the top view of the 111 plane feature (884 nm). At 90° cross-section, we can clearly see that the PC possessed 14 layers and again exhibited A-B-C stacking order. The three circular black features were gold particles used for alignment. One defect caused either by dust or bubbles in the film can be clearly seen (white
Figure 2. a–c) SEM images of a SU-8 polymer PC. d,e) SEM cross-sectional images of the HfO2-infiltrated PC, as prepared via FIB milling. f) Reflectance spectra at normal incidence for PC before and after HfO2 infiltration. Different lines denote spectra measured from different regions of the PC.
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λ B = 2ne d,
(1)
where d is the structural period of the PC along the direction of interest, with 2 1/2 ne = f a (na )2 + f b np (2)
Figure 3. X-ray transmission microscopy images of HfO2-infiltrated SU-8 polymer PC collected at various viewing angles.
spot) in the 0° image. Detection of buried defects illustrates two advantages of X-ray CT; the technique is able to generate a full 3D reconstruction of the structure, including defects, and is non-destructive. To detect buried defects via SEM, one must prepare a series of cross sections by FIB milling and characterize them, which is a tedious process that destroys the sample. Moreover, the minimum size of defect detectable in this manner is governed by the thickness of each slice of the sample cut by FIB milling, whereas the minimum defect size detectable by X-ray CT is governed by the resolution of the instrument. One could also map engineered defects, such as resonators or waveguides via X-ray CT, which obviates any need to fill the PC with index matching fluid and a fluorescent dye. The transmission images were transformed to absorption images and reconstructed via algorithms built into the nanoXCT software. Figure 4a shows three intersecting cross sections of the reconstructed structure. The image only shows the HfO2 shell due to the low X-ray absorptivity of both air and SU-8 polymer. However it is easy to discern these two materials because the HfO2 layer separates the air and polymer regions. All three material regions are continuous. As shown in Figure 4b, the reconstructed structure was then binarized to identify the polymer region by using human judgment and imaging software (Amira, Visage Imaging, San Diego, CA, USA). This analysis allowed us to observe arbitrary cross-sections throughout the real-space fabricated structure in a more flexible
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and non-destructive manner than preparing successive cross sections via FIB milling and observing them by SEM. We computed the expected reflectance of the SU-8 polymer PC. The Bragg wavelength λB is given by the equation
being its effective refractive index, fa and fp the volume fractions, and na and np the refractive indices, respectively, of the air and polymer constituents. The reconstructed PC had a polymer filling fraction of 40%, which compared closely with the estimated values obtained from spectra and the SEM measured layer spacing, using Bragg reflection and effective medium calculations for the refractive index. Layer spacing was measured using the reconstructed structure. The SEM top view periodicity, as seen in Figure 2b, was used to calibrate lengths for the 3D X-ray CT image, with each square pixel calculated to have an average width of 32.7 nm, and the layer spacing of the scanned PC was found to be 513 nm. We used the 1D transfer matrix method to compute the reflectance spectra for the reconstructed structure,[20] a fair approximation for PCs possessing low dielectric contrast because the contribution of diffraction from obliquely propagating modes is small. Each 1D slice of the effective refractive index for the modeled and reconstructed structures had the filling fraction shown in Figure 4d. Also included in the calculation were both an air halfspace in which the incident and reflected waves propagate and a substrate that consisted of a 750 nm thick SU-8 adhesion layer and glass halfspace (not shown). The reflectance spectra for the measured and reconstructed structures showed a close match between their main peaks in center wavelength, bandwidth, or magnitude. Spectra for these two cases (modeled case to be discussed following) show other high energy peaks at similar locations. Differences are mostly likely due to the measurement and the X-ray CT scan not being taken at the exact same spot on the sample. Additionally, differences in surface termination and filling fraction variations throughout the thickness of the PC contribute to the variation of background fringes and high order peaks. We compared cubical regions in the interiors of the reconstructed structure and the modeled structure; the latter was taken to exhibit uniform shrinkage along the thickness direction, similar to previous work.[20] The model considered four interfering plane waves in SU-8 photoresist in an umbrella configuration, with the central wave circularly polarized and the three oblique waves linearly polarized in their incident planes; their vacuum wavelength was 532 nm. The photoresist had a refractive index of 1.607 before development and 1.57 afterward, as determined by previous measurements.[20] We assessed similarities and differences between the two reconstruction and modeling processes. Figure 5a shows the modeled structure (red), the reconstructed structure (blue), and their comparison. The modeled structure was constructed to match both the overall filling fraction of the middle portion of
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Figure 4. a) X-ray CT absorption cross-sectional images of HfO2-infiltrated SU-8 polymer PC. b) X-ray CT reconstructed structure (purple) found by identifying polymer regions in such cross-sectional images. c) Measured reflectance spectra of the polymer PC (solid black), transfer matrix calculations of spectra for modeled structure (dot-dashed red) and reconstructed structure (dashed blue). d) Effective refractive index variation for modeled and reconstructed structures (air halfspaces, adhesion layers, and substrates not shown).
the reconstructed structure (40%) to within 1% and matched the distance between two peaks in the graph of the filling fraction. In the comparison, gray regions indicate where both structures are polymer and transparent regions indicate where both structures are air; the unmatched regions are indicated by their original colors. As the figure shows, the two structures were highly correlated overall. By taking the number of the matching voxels (gray and transparent) and dividing it by the total number of voxels in the cubical region, we found that the volumetric overlap between the two structures was 85%. The differences between the reconstructed and modeled structures must then arise from differences between the experimental and modeling process. One amongst these is the assumption in the model that the developing resist shrunk uniformly in one direction perpendicular to the substrate. We found that the modeled structure must be shrunk by 55% from its original interference pattern to match the reconstructed structure. Overall high fidelity of the modeled structure as compared to the reconstructed one suggests that most of the shrinkage comes from material loss during development, which is known to occur in SU-8.[26–28] Nevertheless, stresses in the film must 2866
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also create some non-uniform shrinkage perpendicular to the plane of the substrate, and some lateral deformation parallel to that plane. That the former is so can be seen in Figure 5b, where the troughs in plot of filling fraction are truncated or flattened in the modeled as compared to the reconstructed structure. Some of the latter differences can be seen in Figure 5a. Optical spectra were calculated for the modeled structure and compared to those computed for the reconstructed structure, as shown in Figure 4c. The main reflectance peak height from the modeled structure was lower than that for predicted spectra of the reconstructed structure, despite the modeled structure exhibiting perfect regularity. On plotting the filling fraction slices perpendicular to the normal direction for each structure, we can see that the reconstructed structure has larger variation in filling fraction than the modeled structure, as demonstrated in Figure 5b. This difference explains why the reflectance of the reconstructed structure is higher than the modeled structure. The mismatch between the two spectra reflects that differences exist between the model and the fabricated structure and it is important to image the fabricated structure in real space in order to accurately study the optical behavior of the PC.
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COMMUNICATION Figure 5. a) Comparison between modeled and reconstructed structure in the interior of the PC. In the comparison, red indicates polymer in the model structure, blue indicates polymer in the reconstructed structure, and gray indicates polymer common to both structures; transparent regions indicate where both structures are air. The data cubes contain 513 voxels, with each voxel 32.7 nm per side. b) Comparison between filling fractions of modeled (red) and reconstructed (blue) structures in the middle of the PC.
In conclusion, we have demonstrated real-space 3D imaging of holographically defined PCs via X-ray CT on a HfO2 infilled SU-8-based PC sample. To the best of our knowledge, this study is the first use of X-ray CT to characterize the morphology of a 3D PC. The reconstructed structure used for calculation of reflectance spectra agreed with the measured spectra. The geometry of the reconstructed structure was compared with the previously reported modeled structure. The two structures exhibited 85% geometric agreement between them, and the observable differences explained the relatively higher reflectance spectra displayed by the reconstructed structure over the modeled structure. By using X-ray tomography to measure the fabricated PC, it is now possible to investigate the deformation process from an as-made PC through processing. Several factors were considered to account for this deformation and may include crosslink density variations and material loss during development. This improved understanding of the correlation between the interference pattern and final fabricated PC structure can facilitate the design of PCs, including
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those containing engineered embedded defects, for photonic applications.
Experimental Section Fabrication: The photoresist was composed of 0.0672 g cyclopentadienyl(fluorine)iron(II) hexafluorophosphate, 1.8422 g cyclopentanone, 0.0626 g dimethyl formamide (Sigma-Aldrich, St. Louis, MO, USA), and 19 g SU-8 2025. The solvent and photoacid generator were mixed for 1 h and the SU-8 2025 was then added before stirring the solution overnight. The substrate was a #2 cover glass, which was cleaned in order with soap and water, acetone, isopropyl alcohol, and then dried via compressed N2 stream. The adhesion layer was made by spin coating SU-8 2002 at 1000 rpm for 60 s, prebaking at 65 °C for 10 min and then 95 °C for 10 min, exposing with long-wave ultraviolet light from a lamp for 20 min, and postbaking at 95 °C for 20 min. The photoresist was spin-coated on the adhesion layer as per MicroChem suggestion: 500 rpm for 5 s with 100 rpm s−1 acceleration; then 2000 rpm for 30 s with 300 rpm s−1 acceleration. The sample was then pre-baked at 65 °C for 10 min and then 95 °C for 25 min, and allowed to cool for
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www.MaterialsViews.com 10 min. The photoresist was exposed for 0.5 s in a setup consisting of four beams in an umbrella configuration; the beams possessed 532 nm wavelength and were generated from a single 5.4 W laser beam (Verdi V5, Coherent, Santa Clara, CA, USA) with appropriate optics. The three p-polarized side beams were spaced 120° in azimuth and intercepted the circularly polarized vertical central beam at an angle of 43.7° in air; the intensity of the latter was 3.7 times greater than each of the former. Following exposure the sample was post-baked at 80 °C for 20 min in dry air at 1 atm in a vacuum oven, developed in propylene glycol methyl ether acetate for 1 h, rinsed in isopropyl alcohol for 10 min, then dried using critical point drying (Samdri 790, Tousimis, Rockville, MD, USA). Characterization: ALD of Al2O3 was performed at 85 °C by alternating 0.03 s pulses of deionized H2O and trimethylaluminum precursors, with 2 s exposure times and 65 s pump times for each, and 20 sccm N2 flow. ALD of HfO2 was performed at 125 °C by alternating 0.06 s pulses of deionized H2O followed by 125 s pump time, and 0.6 s pulses of tetrakis(dimethylamido)hafnium(IV) followed by 75 s pump time (0 s exposure times for both precursors; N2 flow was 20 sccm). An ≈1.5 mm portion of the cover slip substrate was removed by attaching a piece of Tygon tubing to its back with rapidly curing epoxy. This step made a vessel for etchant (20% hydrofluoric acid (aq), 80% isopropyl alcohol; changed twice over the ≈1 day etch time), which after having been stopped by the adhesion layer left a free-standing portion of the PC suspended across a hole in the substrate. The tubing and glue were then removed. One polymer sample of this kind (without ALD infiltration) was sent for phase contrast imaging by Xradia at angles from –70° to 70° at 0.25° intervals with a 8 keV (0.15 nm Cu rotation anode source, which was sufficient to identify the main features of the PC at 50 nm by 50 nm by 80 nm resolution, as shown by Figure 1); this imaging took 62 h to complete. Absorption contrast imaging was conducted on another sample using a nanoXCT-100 instrument; a piece of the sample was completely removed from the substrate and mounted to allow a full 180° scan at 0.5° intervals and accurate 3D reconstruction, along with several gold particles for registration. Modeling: A 1D transfer matrix method was used to compute the reflectance spectra for the reconstructed structure, including both an air halfspace in which the incident and reflected waves propagate, and a substrate that consisted of a 750 nm thick SU-8 adhesion layer and glass halfspace. Cubical regions in the interiors of the reconstructed structure and the modeled structure were compared; the latter was taken to exhibit uniform shrinkage along the thickness direction. The model considered four interfering plane waves in SU-8 photoresist in an umbrella configuration, with the central wave circularly polarized and the three oblique waves linearly polarized in their incident planes; the latter made an angle of 43.7° with the central wave in air and were evenly spaced in azimuth. The central wave possessed an intensity 3.7 times higher than each of the oblique waves; Fresnel reflections at the air/ photoresist interface were found to have little effect on the final structure and so were excluded from calculation. The photoresist had a refractive index of 1.607 before development and 1.57 afterward, as determined by previous measurements; the vacuum wavelength of the plane waves was 532 nm. The modeled intensity pattern was thresholded to find the polymer regions. The threshold intensity and shrinkage factor were chosen as explained in the main text.
Acknowledgements J.B.G. III gratefully acknowledges partial support of a Beckman Postdoctoral Fellowship. Sample fabrication was supported by the US
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Army Research Office Award #DAAD19-03-1-0227. Characterization and optical modeling was supported by the US Department of Energy Energy Frontier Research Center Award #SC0001293. The authors thank Xradia for providing phase contrast images of one sample. Received: January 30, 2012 Published online: May 2, 2012
[1] K. A. Arpin, A. Mihi, H. T. Johnson, A. J. Baca, J. A. Rogers, J. A. Lewis, P. V. Braun, Adv. Mater. 2010, 22, 1084. [2] J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed., Princeton University Press, Princeton, NJ 2008, Ch. 6. [3] R. Rengarajan, D. Mittleman, C. Rich, V. Colvin, Phys. Rev. E 2005, 71, 016615. [4] X. Wang, J. F. Xu, H. M. Su, Z. H. Zeng, Y. L. Chen, Y. K. Pang, W. Y. Tam, Appl. Phys. Lett. 2003, 82, 2212. [5] Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, Y. L. Chen, Appl. Phys. Lett. 2005, 87, 061103. ¨ ¨ [6] I. I. Tarhan, G. H. Watson, Phys. Rev. Lett. 1996, 76, 315. [7] L. Wu, Y. Zhong, C. T. Chan, K. S. Wong, G. P. Wang, Appl. Phys. Lett. 2005, 86, 241102. [8] J. Chen, W. Jiang, X. Chen, L. Wang, S. Zhang, R. T. Chen, Appl. Phys. Lett. 2006, 90, 093102. [9] D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning, A. J. Turberfield, Opt. Quant. Electron. 2002, 34, 3. [10] L. Z. Cai, X. L. Yang, Y. R. Wang, Opt. Lett. 2002, 27, 900. [11] J.-H. Jang, C. K. Ullal, M. Maldovan, T. Gorishnyy, S. Kooi, C. Y. Koh, E. L. Thomas, Adv. Funct. Mater. 2007, 17, 3027. [12] J. H. Moon, J. Ford, S. Yang, Polym. Adv. Technol. 2006, 17, 83. [13] C. K. Ullal, M. Maldovan, M. Wohlgemuth, E. L. Thomas, C. A. White, S. Yang, J. Opt. Soc. Am. A 2003, 20, 948. [14] R. C. Rumpf, E. G. Johnson, J. Opt. Soc. Am. A 2004, 21, 1703. [15] J. B. Pawley, in Handbook of Biological Confocal Microscopy, 3rd Ed. (Ed: J. B. Pawley), Springer, New York 2006, Ch. 2. [16] B. Huang, Curr. Opin. Chem. Biol. 2010, 14, 10. [17] D. Sayre, H. N. Chapman, Acta Cryst. 1995, A51, 237. [18] A. M. Cormack, Phys. Med. Biol. 1973, 18, 195. [19] M. Feser, J. Gelb, H. Chang, H. Cui, F. Duewer, S. H. Lau, A. Tkachuk, W. Yun, Meas. Sci. Technol. 2008, 19, 094001. [20] Y. C. Chen, J. B. Geddes III, J. T. Lee, P. V. Braun, P. Wiltzius, Appl. Phys. Lett. 2007, 91, 241103. [21] K. Kato, Polym. Eng. Sci. 1967, 7, 38. [22] J. S. Trent, J. I. Scheinbeim, P. R. Couchman, Macromolecules 1983, 16, 589. [23] J. S. King, E. Graugnard, O. M. Roch, D. N. Sharp, J. Scrimgeour, R. G. Denning, A. J. Turberfield, C. J. Summers, Adv. Mater. 2006, 18, 1561. [24] A. Brzezinski, Y.-C. Chen, P. Wiltzius, P. V. Braun, J. Mater. Chem. 2009, 19, 9126. [25] M. Knez, K. Nielsch, L. Niinstö, Adv. Mater. 2007, 19, 3425. [26] D. C. Meisel, M. Diem, M. Deubel, F. Pérez-Willard, S. Linden, D. Gerthsen, K. Busch, M. Wegener, Adv. Mater. 2006, 18, 2964. [27] X. Zhu, Y. Xu, S. Yang, Opt. Express 2007, 15, 16546. [28] R. G. Denning, C. F. Blanford, H. Urban, H. Bharag, D. N. Sharp, A. J. Turberfield, Adv. Funct. Mater. 2011, 21, 1593.
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Ying-Chieh Chen, Joseph B. Geddes III, Leilei Yin, Pierre Wiltzius,* and Paul V. Braun* The optical properties of a photonic crystal (PC) are governed by the periodicity of its lattice, geometry of its basis, and dielectric contrast of its constituents. Numerous advances in experimental fabrication and characterization of three-dimensional (3D) PCs with submicron morphology have been made since their inception,[1] along with theoretical prediction of their optical properties.[2] Their detailed morphology has typically been verified directly via electron microscopy of surfaces and cross sections,[3–5] and indirectly via optical spectroscopy and diffraction measurements,[6–9] but not holistically by direct electromagnetic 3D tomography at length scales substantially shorter than those of optical wavelengths. Here, 3D PCs fabricated by holographic optical lithography were imaged using hard X-ray microscopy. The large penetration depth of the X-rays allowed angle-resolved two-dimensional (2D) images to be analyzed to reconstruct the full 3D morphology of a holographic PC via computed tomography (CT). The reconstructed morphology was used both as a basis for optical reflectance spectra calculations, which compared closely to experimental measurements, and to validate a theoretical model of the PC structure. Fabrication of 3D PCs via multibeam interference lithography allows flexible control of their basis of periodic units.[10–12] Most theoretical proposed structures assume the basis follows the iso-intensity surface.[13,14] However practical issues such as shrinkage, photoresist resolution and absorption-generated intensity gradients can invalidate this assumption, and full modeling of the fabrication process has been reported.[14] Nevertheless, without appropriate means to inspect the actual fabricated structures on the micro- and nanoscales, it is difficult to obtain the necessary information to verify or modify such a
Dr. Y.-C. Chen, Dr. J. B. Geddes III, Prof. P. V. Braun Department of Materials Science and Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801, USA E-mail: [email protected] Dr. Y.-C. Chen, Dr. J. B. Geddes III, Dr. L. Yin, Prof. P. V. Braun Beckman Institute for Advanced Science and Technology University of Illinois at Urbana-Champaign Urbana, IL 61801, USA Prof. P. Wiltzius Division of Mathematical, Life, and Physical Sciences University of California Santa Barbara, Santa Barbara, CA 93106, USA E-mail: [email protected] Prof. P. V. Braun Frederick Seitz Materials Research Laboratory University of Illinois at Urbana-Champaign Urbana, IL 61801, USA
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model. This situation is quite unlike that for one-dimensional (1D) and 2D PCs, where the morphology can be completely characterized via scanning electron microscopy (SEM). We aimed to characterize an optical material whose properties depend on morphology with characteristic length scales that are subwavelength for the optical bandwidth of interest. Therefore, absent suitable superresolution optical techniques,[15,16] which are typically more appropriate for weakly scattering samples, and not high refractive index contrast PCs, one requires short wavelength electromagnetic (X-ray) or matter (electron) waves to achieve the required resolution. Given the penetration depth for electrons is much less than size of the 3D samples we wish to study, we have two possible practical strategies. The first is to destructively characterize the sample using focused ion beam (FIB) milling to reveal subsequent cross sections of the sample, along with scanning electron microscopy to image each cross section. Artifact generation during FIB milling will always be a concern with this approach, and the actual volume of the sample imaged is quite small. The second is to use X-ray CT to image the entire sample volume via phase or absorption contrast. X-ray CT is an imaging technique used primarily in the medical field, recent improvements to which have opened up new opportunities in other disciplines, particularly biological and materials science.[17] X-rays possess short wavelengths enabling high resolution and exhibit deeper penetration depths than electrons. Thus, 2D angle-resolved X-ray images can be reconstructed to full 3D images via CT.[18] This technique is especially useful for nondestructive imaging of the interiors of optically opaque objects. Here, we report imaging SU-8 polymer PCs fabricated by holographic lithography (i.e., multibeam optical interference) with hard X-ray CT with a laboratory-based microscope system (nanoXCT, Xradia, Pleasanton, CA, USA).[19] The imaged samples are PCs fabricated with the polymer photoresist SU-8 (MicroChem, Newton, MA, USA) following the procedure developed previously.[20] The glass substrate on which the holographic PC was fabricated was etched away with hydrofluoric acid to minimize the X-ray absorption. Both phase contrast and absorption contrast modes were performed. For an as-fabricated polymer holographic PC sample, phase contrast mode is sufficient to resolve the periodicity, as shown in Figure 1. However, material boundary artifacts caused by the non-monochromatic and non-parallel light source make this particular image unsuitable for quantitative analysis. Nevertheless, the phase contrast image is sufficient to reveal some morphological details of the as-prepared SU-8 polymer sample directly. In order to study the real-space geometry of holographic PCs in a quantitative way, we turn to the absorption contrast alternative. X-ray absorption scales as the third power of the atomic number. The constituents of both air and SU-8 polymer possess
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X-Ray Computed Tomography of Holographically Fabricated Three-Dimensional Photonic Crystals
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Figure 1. Phase contrast X-ray CT images of a polymer holographic PC: a,b) cross-sections and c) a reconstructed 3D structure.
low atomic numbers, and their absorption contrast is not strong enough to produce suitable images for 3D reconstruction and analysis. Typically, OsO4 or RuO4 are used to stain a polymer to enhance the image contrast;[21,22] however we found these stains swell SU-8 polymer and distort the PC. Atomic layer deposition (ALD) has been shown to be a reliable infiltration technique for SU-8 polymer PCs and synthetic opals.[23–25] We selected hafnium dioxide (HfO2) as our infiltration material: hafnium has a high atomic number of 72, the ALD technique for HfO2 is well developed, and the process can be done at relatively low temperatures of 125 °C (Cambridge Nanotech, Cambridge, MA, USA). We first deposited 10 nm of Al2O3 at 85 °C to prevent
deformation of the SU-8 structure during the 125 °C deposition of HfO2. That subsequent deposition totaled 163 nm of HfO2, as measured by ellipsometry. This infiltration process produced a conformal HfO2 shell surrounding the SU-8 polymer region of the PC. Figure 2a–c shows electron microscopy images of the sample before ALD infiltration. Figure 2d,e shows SEM images of cross sections of the infiltrated PC prepared by FIB milling. Figure 2f shows corresponding normal incidence optical spectra before and after ALD infiltration. Notice the main reflectance peak at longer wavelengths (≈70% at ≈1300 nm for uninfiltrated sample), as well as several other reflectance peaks at shorter wavelengths resulted from the highly periodic morphology of the holographic PC, even after undergoing shrinkage during post baking and subsequent development. We observed the main reflectance peak position at several times during the infiltration process and noted that it was red shifted as expected due to the HfO2 infilling to a final position of ≈1600 nm, indicating retention of periodicity. The magnitude of the main reflectance peak decreased somewhat to ≈60% upon infiltration. X-ray transmission images were collected at 0.5° intervals from 0.0° through 180°. Four selected images, each taken at a different angle and each exhibiting a different periodic pattern, are shown in Figure 3. At 0°, the hexagonal patterns corresponded to the A-B-C stacking of face-centered cubic lattice in the 111 plane. The periodicity was measured as a/√3 = 510 nm, where a is the hexagonal periodicity of the top view of the 111 plane feature (884 nm). At 90° cross-section, we can clearly see that the PC possessed 14 layers and again exhibited A-B-C stacking order. The three circular black features were gold particles used for alignment. One defect caused either by dust or bubbles in the film can be clearly seen (white
Figure 2. a–c) SEM images of a SU-8 polymer PC. d,e) SEM cross-sectional images of the HfO2-infiltrated PC, as prepared via FIB milling. f) Reflectance spectra at normal incidence for PC before and after HfO2 infiltration. Different lines denote spectra measured from different regions of the PC.
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λ B = 2ne d,
(1)
where d is the structural period of the PC along the direction of interest, with 2 1/2 ne = f a (na )2 + f b np (2)
Figure 3. X-ray transmission microscopy images of HfO2-infiltrated SU-8 polymer PC collected at various viewing angles.
spot) in the 0° image. Detection of buried defects illustrates two advantages of X-ray CT; the technique is able to generate a full 3D reconstruction of the structure, including defects, and is non-destructive. To detect buried defects via SEM, one must prepare a series of cross sections by FIB milling and characterize them, which is a tedious process that destroys the sample. Moreover, the minimum size of defect detectable in this manner is governed by the thickness of each slice of the sample cut by FIB milling, whereas the minimum defect size detectable by X-ray CT is governed by the resolution of the instrument. One could also map engineered defects, such as resonators or waveguides via X-ray CT, which obviates any need to fill the PC with index matching fluid and a fluorescent dye. The transmission images were transformed to absorption images and reconstructed via algorithms built into the nanoXCT software. Figure 4a shows three intersecting cross sections of the reconstructed structure. The image only shows the HfO2 shell due to the low X-ray absorptivity of both air and SU-8 polymer. However it is easy to discern these two materials because the HfO2 layer separates the air and polymer regions. All three material regions are continuous. As shown in Figure 4b, the reconstructed structure was then binarized to identify the polymer region by using human judgment and imaging software (Amira, Visage Imaging, San Diego, CA, USA). This analysis allowed us to observe arbitrary cross-sections throughout the real-space fabricated structure in a more flexible
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and non-destructive manner than preparing successive cross sections via FIB milling and observing them by SEM. We computed the expected reflectance of the SU-8 polymer PC. The Bragg wavelength λB is given by the equation
being its effective refractive index, fa and fp the volume fractions, and na and np the refractive indices, respectively, of the air and polymer constituents. The reconstructed PC had a polymer filling fraction of 40%, which compared closely with the estimated values obtained from spectra and the SEM measured layer spacing, using Bragg reflection and effective medium calculations for the refractive index. Layer spacing was measured using the reconstructed structure. The SEM top view periodicity, as seen in Figure 2b, was used to calibrate lengths for the 3D X-ray CT image, with each square pixel calculated to have an average width of 32.7 nm, and the layer spacing of the scanned PC was found to be 513 nm. We used the 1D transfer matrix method to compute the reflectance spectra for the reconstructed structure,[20] a fair approximation for PCs possessing low dielectric contrast because the contribution of diffraction from obliquely propagating modes is small. Each 1D slice of the effective refractive index for the modeled and reconstructed structures had the filling fraction shown in Figure 4d. Also included in the calculation were both an air halfspace in which the incident and reflected waves propagate and a substrate that consisted of a 750 nm thick SU-8 adhesion layer and glass halfspace (not shown). The reflectance spectra for the measured and reconstructed structures showed a close match between their main peaks in center wavelength, bandwidth, or magnitude. Spectra for these two cases (modeled case to be discussed following) show other high energy peaks at similar locations. Differences are mostly likely due to the measurement and the X-ray CT scan not being taken at the exact same spot on the sample. Additionally, differences in surface termination and filling fraction variations throughout the thickness of the PC contribute to the variation of background fringes and high order peaks. We compared cubical regions in the interiors of the reconstructed structure and the modeled structure; the latter was taken to exhibit uniform shrinkage along the thickness direction, similar to previous work.[20] The model considered four interfering plane waves in SU-8 photoresist in an umbrella configuration, with the central wave circularly polarized and the three oblique waves linearly polarized in their incident planes; their vacuum wavelength was 532 nm. The photoresist had a refractive index of 1.607 before development and 1.57 afterward, as determined by previous measurements.[20] We assessed similarities and differences between the two reconstruction and modeling processes. Figure 5a shows the modeled structure (red), the reconstructed structure (blue), and their comparison. The modeled structure was constructed to match both the overall filling fraction of the middle portion of
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Figure 4. a) X-ray CT absorption cross-sectional images of HfO2-infiltrated SU-8 polymer PC. b) X-ray CT reconstructed structure (purple) found by identifying polymer regions in such cross-sectional images. c) Measured reflectance spectra of the polymer PC (solid black), transfer matrix calculations of spectra for modeled structure (dot-dashed red) and reconstructed structure (dashed blue). d) Effective refractive index variation for modeled and reconstructed structures (air halfspaces, adhesion layers, and substrates not shown).
the reconstructed structure (40%) to within 1% and matched the distance between two peaks in the graph of the filling fraction. In the comparison, gray regions indicate where both structures are polymer and transparent regions indicate where both structures are air; the unmatched regions are indicated by their original colors. As the figure shows, the two structures were highly correlated overall. By taking the number of the matching voxels (gray and transparent) and dividing it by the total number of voxels in the cubical region, we found that the volumetric overlap between the two structures was 85%. The differences between the reconstructed and modeled structures must then arise from differences between the experimental and modeling process. One amongst these is the assumption in the model that the developing resist shrunk uniformly in one direction perpendicular to the substrate. We found that the modeled structure must be shrunk by 55% from its original interference pattern to match the reconstructed structure. Overall high fidelity of the modeled structure as compared to the reconstructed one suggests that most of the shrinkage comes from material loss during development, which is known to occur in SU-8.[26–28] Nevertheless, stresses in the film must 2866
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also create some non-uniform shrinkage perpendicular to the plane of the substrate, and some lateral deformation parallel to that plane. That the former is so can be seen in Figure 5b, where the troughs in plot of filling fraction are truncated or flattened in the modeled as compared to the reconstructed structure. Some of the latter differences can be seen in Figure 5a. Optical spectra were calculated for the modeled structure and compared to those computed for the reconstructed structure, as shown in Figure 4c. The main reflectance peak height from the modeled structure was lower than that for predicted spectra of the reconstructed structure, despite the modeled structure exhibiting perfect regularity. On plotting the filling fraction slices perpendicular to the normal direction for each structure, we can see that the reconstructed structure has larger variation in filling fraction than the modeled structure, as demonstrated in Figure 5b. This difference explains why the reflectance of the reconstructed structure is higher than the modeled structure. The mismatch between the two spectra reflects that differences exist between the model and the fabricated structure and it is important to image the fabricated structure in real space in order to accurately study the optical behavior of the PC.
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In conclusion, we have demonstrated real-space 3D imaging of holographically defined PCs via X-ray CT on a HfO2 infilled SU-8-based PC sample. To the best of our knowledge, this study is the first use of X-ray CT to characterize the morphology of a 3D PC. The reconstructed structure used for calculation of reflectance spectra agreed with the measured spectra. The geometry of the reconstructed structure was compared with the previously reported modeled structure. The two structures exhibited 85% geometric agreement between them, and the observable differences explained the relatively higher reflectance spectra displayed by the reconstructed structure over the modeled structure. By using X-ray tomography to measure the fabricated PC, it is now possible to investigate the deformation process from an as-made PC through processing. Several factors were considered to account for this deformation and may include crosslink density variations and material loss during development. This improved understanding of the correlation between the interference pattern and final fabricated PC structure can facilitate the design of PCs, including
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those containing engineered embedded defects, for photonic applications.
Experimental Section Fabrication: The photoresist was composed of 0.0672 g cyclopentadienyl(fluorine)iron(II) hexafluorophosphate, 1.8422 g cyclopentanone, 0.0626 g dimethyl formamide (Sigma-Aldrich, St. Louis, MO, USA), and 19 g SU-8 2025. The solvent and photoacid generator were mixed for 1 h and the SU-8 2025 was then added before stirring the solution overnight. The substrate was a #2 cover glass, which was cleaned in order with soap and water, acetone, isopropyl alcohol, and then dried via compressed N2 stream. The adhesion layer was made by spin coating SU-8 2002 at 1000 rpm for 60 s, prebaking at 65 °C for 10 min and then 95 °C for 10 min, exposing with long-wave ultraviolet light from a lamp for 20 min, and postbaking at 95 °C for 20 min. The photoresist was spin-coated on the adhesion layer as per MicroChem suggestion: 500 rpm for 5 s with 100 rpm s−1 acceleration; then 2000 rpm for 30 s with 300 rpm s−1 acceleration. The sample was then pre-baked at 65 °C for 10 min and then 95 °C for 25 min, and allowed to cool for
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www.MaterialsViews.com 10 min. The photoresist was exposed for 0.5 s in a setup consisting of four beams in an umbrella configuration; the beams possessed 532 nm wavelength and were generated from a single 5.4 W laser beam (Verdi V5, Coherent, Santa Clara, CA, USA) with appropriate optics. The three p-polarized side beams were spaced 120° in azimuth and intercepted the circularly polarized vertical central beam at an angle of 43.7° in air; the intensity of the latter was 3.7 times greater than each of the former. Following exposure the sample was post-baked at 80 °C for 20 min in dry air at 1 atm in a vacuum oven, developed in propylene glycol methyl ether acetate for 1 h, rinsed in isopropyl alcohol for 10 min, then dried using critical point drying (Samdri 790, Tousimis, Rockville, MD, USA). Characterization: ALD of Al2O3 was performed at 85 °C by alternating 0.03 s pulses of deionized H2O and trimethylaluminum precursors, with 2 s exposure times and 65 s pump times for each, and 20 sccm N2 flow. ALD of HfO2 was performed at 125 °C by alternating 0.06 s pulses of deionized H2O followed by 125 s pump time, and 0.6 s pulses of tetrakis(dimethylamido)hafnium(IV) followed by 75 s pump time (0 s exposure times for both precursors; N2 flow was 20 sccm). An ≈1.5 mm portion of the cover slip substrate was removed by attaching a piece of Tygon tubing to its back with rapidly curing epoxy. This step made a vessel for etchant (20% hydrofluoric acid (aq), 80% isopropyl alcohol; changed twice over the ≈1 day etch time), which after having been stopped by the adhesion layer left a free-standing portion of the PC suspended across a hole in the substrate. The tubing and glue were then removed. One polymer sample of this kind (without ALD infiltration) was sent for phase contrast imaging by Xradia at angles from –70° to 70° at 0.25° intervals with a 8 keV (0.15 nm Cu rotation anode source, which was sufficient to identify the main features of the PC at 50 nm by 50 nm by 80 nm resolution, as shown by Figure 1); this imaging took 62 h to complete. Absorption contrast imaging was conducted on another sample using a nanoXCT-100 instrument; a piece of the sample was completely removed from the substrate and mounted to allow a full 180° scan at 0.5° intervals and accurate 3D reconstruction, along with several gold particles for registration. Modeling: A 1D transfer matrix method was used to compute the reflectance spectra for the reconstructed structure, including both an air halfspace in which the incident and reflected waves propagate, and a substrate that consisted of a 750 nm thick SU-8 adhesion layer and glass halfspace. Cubical regions in the interiors of the reconstructed structure and the modeled structure were compared; the latter was taken to exhibit uniform shrinkage along the thickness direction. The model considered four interfering plane waves in SU-8 photoresist in an umbrella configuration, with the central wave circularly polarized and the three oblique waves linearly polarized in their incident planes; the latter made an angle of 43.7° with the central wave in air and were evenly spaced in azimuth. The central wave possessed an intensity 3.7 times higher than each of the oblique waves; Fresnel reflections at the air/ photoresist interface were found to have little effect on the final structure and so were excluded from calculation. The photoresist had a refractive index of 1.607 before development and 1.57 afterward, as determined by previous measurements; the vacuum wavelength of the plane waves was 532 nm. The modeled intensity pattern was thresholded to find the polymer regions. The threshold intensity and shrinkage factor were chosen as explained in the main text.
Acknowledgements J.B.G. III gratefully acknowledges partial support of a Beckman Postdoctoral Fellowship. Sample fabrication was supported by the US
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Army Research Office Award #DAAD19-03-1-0227. Characterization and optical modeling was supported by the US Department of Energy Energy Frontier Research Center Award #SC0001293. The authors thank Xradia for providing phase contrast images of one sample. Received: January 30, 2012 Published online: May 2, 2012
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