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Periodic patterning using aerial image modulation with optical lithography

[+] Author Affiliations
Boyan Penkov

Phoebus Optoelectronics, 12 Desbrosses Street, New York, New York 10013

Garry Bordonaro

Cornell University, Cornell NanoScale Science and Technology Facility, 250 Duffield Hall, Ithaca, New York 14850

Andrii B. Golovin

City College of New YorkDepartment of Electrical Engineering160 Convent Avenue, New York, New York 10013

Igor Bendoym

City College of New YorkDepartment of Electrical Engineering160 Convent Avenue, New York, New York 10013

Donald M. Tennant

Cornell University, Cornell NanoScale Science and Technology Facility, 250 Duffield Hall, Ithaca, New York 14850

David T. Crouse

City College of New YorkDepartment of Electrical Engineering160 Convent Avenue, New York, New York 10013

J. Micro/Nanolith. MEMS MOEMS. 12(3), 033009 (Aug 02, 2013). doi:10.1117/1.JMM.12.3.033009
History: Received March 31, 2013; Revised June 12, 2013; Accepted July 1, 2013
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Open Access Open Access

Abstract.  Photolithography for patterns with periodicity in the illumination plane (2.5-D lithography) has seen rapid advances over the past decade, with the introduction of holographic lithography and the further development of phase-contrast and grayscale photolithography methods. However, each of these techniques suffers from substantial difficulties preventing further integration into device fabrication: a lack of parallel processing capabilities and dimension limitations. Here, we present a demonstration of controlled layer topography through modulation of both the exposure dose and exposure focal plane yielding reproducible 2.5-D patterns which are applied to the further development of plasmonic gratings. This process is entirely compatible with commercially available i-line photolithography and etch hardware, enabling a path to ready integration.

Figures in this Article

The controlled fabrication of surface topography—with nanoscale patterns more intricate than square-edged channels or gratings—has seen a recent rise in interest.1 In particular, controlled patterning of surfaces with limited, 2.5-dimensional (2.5-D) (for patterns with periodicity in the illumination plane) or complete [fully three-dimensional (3-D)] pattern variation normal to the wafer surface has seen increased demand.2 These structures find application in propagating plasmon-mode biosensors36 and assays that can control protein7 or block copolymer8 absorption.

However, no general and parallel fabrication technique has emerged to fill this need. Focused ion beam sputtering is well known;9 however, it presents clear integration difficulties since it is a serial, scanned-beam process. Conformal phase masks have been used to fabricate micron-thick layers with intricate 3-D structure,10,11 yet are not capable of patterning a surface layer without first patterning the mask itself, and without taking advantage of an optical reduction factor. Interference lithography12 limits the feature size to between λ/2 and 3λ/2, placing severe constraints on final dimensions of devices made with conventional tools. Recent developments in spatially controlled deposition kinetics13 are promising, but limit materials and geometry. Grayscale14 and multilayer techniques15 limit feature sizes as well, and require expensive single mask or multiple mask sets.

In this work, a fabrication approach that does not suffer from these difficulties is presented. By controlling not just the exposure dose delivered, but also the illumination profile in the photoresist (the aerial image), periodic structures with a wide variety of profiles are fabricated. These structures are created using off-the-shelf hardware, operating with well-understood i-line illumination (λ=365nm) and with commercially available photoresists, and modeling the exposure with commercially supported codes. Examples of using this technique to fabricate structures with variation in size and curvature are demonstrated. Moreover, the approach is generalized not only to the fabrication of structures in photoresist, but also the etch transfer of those structures to an underlayer. This is accomplished by control of the aerial image; by modulating the exposure dose delivered, the image focus, and the postexposure conditions:16 the postexposure bake, spray development, and hard bake. The modified mask feature spacing controls the interaction between the focal plane and the aerial image; the dose and focus modulations change the absorbed axial image, and the development parameters control the kinetics of the development. Each of these can be simulated numerically to sufficient precision to reliably produce the desired 2.5-D pattern.

To develop an appropriate test structure, full-field finite-difference time domain (FDTD) simulations were performed in Lumerical FDTD. The desired image plane intensity was simulated with the PROLITH lithography simulation package, by KLA-Tencor. The design space under consideration consists of devices with sinusoidal or smoothly curved sidewall profiles, as depicted in Fig. 1. With a specific design in mind, PROLITH was used to calculate the desired photoresist image, taking into account the photoresist and anti-reflection layers, the substrate materials and variation in sidewall profile. The material parameters used came exclusively from the PROLITH database, with the exception of the data for the SPR-220 resist, which was supplied by the manufacturer. Having established a materials stack, iterations were performed over physically controllable inputs—the focus plane and optical dose delivered—to determine the experimental parameters.

Graphic Jump LocationF1 :

Overlays of the developed results against the PROLITH simulation target for a number of designs. From left to right, the dose increases from 50 to 80mJcm2; from bottom to top, the focus offset (measured toward the optical system) increases from 1.2 to 0.3 μm. The PROLITH simulation yields the expected sinusoidal pattern with a reasonable fabrication window; perturbations around the best achievable value degrade the aerial image variation.

To verify these results experimentally, the appropriate photoresist thickness for the design feature size and depth was calculated. Typically, the simulation optical stack consists of a constant 165 nm layer of Brewer Science XHRi-16c anti-reflective coating (ARC) beneath the Megaposit SPR-220 photoresist, with a thickness of 2μm. A line-space grating of 400 nm lines with 500 nm spaces was used, operating at the linear resolution limit of i-line lithography. This mask was used to fabricate metal-dielectric structures in which plasmon resonances, discussed below, were observed.

Bare silicon wafers (with Miller indices 100) were coated with the photoresist stack. Manufacturer suggested solvent bake times for each layer were used; in the case of SPR-220: 90°C for 60 s. The wafers were exposed using a GCA Autostep 200 i-line wafer stepper, using a numerical aperture of 0.45 (σ=0.5). The tool dose was verified before each batch: values of 10mJcm2 are typical, corresponding to exposure times of 0.04s. A combined focus-exposure matrix, with focus offset values suggested by simulation, was developed to optimize exposure; each die was exposed once. Depending on desired geometry, focus offset values were between 300  nm and 1.5 μm. Wafers were then postbaked and developed in accordance with simulated parameters, with typical values near the manufacturer suggestions for postbake (110°C for 60 s on hot-plate) and spray developed for 60 s in AZ 726 MIF.

Having developed the optical process, an etch process was developed17 to transfer the resultant sinusoidal geometry into the underlayer: in this case, the bulk silicon wafer. A reactive ion etch process was used, with CF4 as the etchant and CHF3 to increase selectivity to photoresist, in a 51 flow ratio. The forward power was 150 W and the chamber pressure was 40 mtorr.

The reflectivity, at variable angle of incidence, was characterized by an optical setup contained a tungsten–halogen source, Horiba iHR550 infrared monochromator, collimating silver mirror, polarizing prism, focusing silver mirror, and silicon photodetector. The measurements were performed using a linearly polarized collimated beam with a spectral range spanning 400 to 1100 nm. Collected data was normalized against the reflection of a flat silver mirror.

Exposure Simulations

The PROLITH simulation yields the expected sinusoidal pattern with a reasonable fabrication window; perturbations around the best achievable value degrade the aerial image quality linearly and controllably. Physical inputs of reasonable photoresist and ARC layers, reasonable mask sizes and development times yield a variety of sinusoidal patterns; thus, there is an acceptable tolerance in process and equipment variation.

Iterations over the line and space width of the mask yielded changes in the structure size while still operating in the near-field approximation. Beyond 700nm, the simulated exposures converged back to near-vertical sidewall profiles, as expected. The region of interest in this work remains with mask feature sizes approaching the illumination wavelength.

Iterations over the dose begin from half the typical value expected for full exposure; iterations for focus begin from t/2, where t is the thickness of the optical stack—2.16μm for the example developed here. This coarse iterative simulation elucidates typical behavior for a photoresist stack; the photoresist profile is then fine-tuned by iterating predominantly over dose close to the desired profile.

Moreover, multiple exposures, at varying focal planes, were considered in simulation. These enabled additional parameters to capture a broader array of exposure profiles at the expense of alignment accuracy and multipass exposure. The criteria used to judge the success of the simulations were the fidelity of the output to the intended geometry of the structure: the top CD size, bottom CD size, pattern height, space width, pattern curvature were taken into consideration.

It is important to underscore that the values discussed above are all approximate, and should be used as reasonable initial setting for subsequent experiments. For a given process target, accurate and exact values are produced by running a full simulation against the desired geometry. Modulation of dose and mask linewidth can be used as coarse adjustments to the eventual geometry, while focus offset acts as a much more sensitive perturbation.

Photoresist Patterning, Etch Transfer

Patterning photoresist using this technique yields a variety of controlled cross sectional profiles. Figure 2 shows a scanning electron microscopy (SEM) cross section of photoresist, exposed and developed according to a simulation tailored toward a sinusoidal image. The subfigures demonstrate other geometries that can be created with the above technique, similarly in photoresist. An asymmetrical grating is shown with a curved base and sharper tops. Moreover, a more extreme example is developed: an array of sharply tipped lines.

Graphic Jump LocationF2 :

A scanning electron microscopy (SEM) image of patterned photoresist using the controlled defocus lithography technique emphasizing the variety of producible patterns. An extreme example of aerial image modulation is visible in inset (a). Inset (b) is an edge-on sine wave pattern. Finally, we see an interim example of the possible gradation in inset (c).

Multiple iterations of this process yield reliable pattern generation and transfer, as demonstrated in Fig. 1. Using a dose–focus matrix for optimization, patterns that compare closely to those generated in simulations are produced.

While creating patterns in photoresist is useful, far greater utility lies in transferring these to underlayers and enabling deposition of a coating. In Fig. 3, the transfer of the photoresist pattern into the silicon substrate is demonstrated, along with a gold coating. Using the etch parameters described above, etch selectivity within 7% of unity is achieved, yielding minimal change in the photoresist aspect ratio.

Graphic Jump LocationF3 :

An edge-on (θ=10°) SEM image of a periodic pattern transferred into the substrate, and coated in 25 nm gold. The photoresist pattern, here, is taken from the sample shown in Fig. 2(c).

Narrowband Plasmon Resonance

We used this approach to construct a surface plasmon-based asymmetrical grating, with a decreased density of plasmon states near the grating edge, yielding particularly narrowband performance. Reflection spectra calculated by FDTD simulation are compared to experimental measurements. The reflectivity of the metal-dielectric sample in Fig. 3 was measured using normal incident angle of transverse magnetic polarized probing light, and is presented in Fig. 4.

Graphic Jump LocationF4 :

The measured p-polarized spectral reflectance (points), with the simulated spectral reluctance (solid curve), at normal incidence. The measured reflection minimum is at 911 nm, whereas the calculated reflection minimum is at 909 nm. This resonance is due to optical excitation of propagating plasmon modes along with the asymmetric curved surface. Below 800nm, diffraction losses decrease directional reflectivity.

The peaks, each indicating the incident illumination coupling into a surface mode, overlap to within Δλ=2nm. The sample demonstrated a narrow-band reflectivity minimum for the p-polarized probe field at the wavelength of 911 nm (Fig. 4). The minimum wavelength was blue-shifted with increasing angle of incidence. In contrast, the reflection of s-polarized light did not demonstrate any minimum of reflectivity at 911 nm or any other wavelength within the measurement range. The resonance is narrow, with a full-width at half-maximum of 19 nm, indicating a high-quality periodic structure.

Above, the fabrication of 2.5-D periodic structures using a one-step optical lithography process compatible with conventional i-line tools is demonstrated. Etch transfer of the shape, with high fidelity, into the underlying silicon is performed.

Limitations of this technique became evident during the development of this process. Image fidelity is affected by focus control. Moreover, technology transfer to industrial processes, using 200 mm substrates and with decreased tolerances for resist uniformity and wafer bow, may be challenging.

While this approach has been implemented before using electron-beam lithography,18 an approach using photolithography enables integration with a parallel workflow, and a reduction in fabrication cost. In the realm of all-optical techniques, the aerial image modulation approach enables topography patterning of feature sizes too large for holographic lithography and too small for grayscale approaches.

This work was performed in part at the Cornell NanoScale Science and Technology Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant No. ECS-0335765). We thank Meredith Metzler and Vince Genova for insight and assistance with the etch transfer development.

Watanabe  M., Mizukami  K., “Well-ordered wrinkling patterns on chemically oxidized poly(dimethylsiloxane) surfaces,” Macromolecules. 45, (17 ), 7128 –7134 (2012). 0024-9297 CrossRef
Fuchs  Y. et al., “Holographic molecularly imprinted polymers for label-free chemical sensing,” Adv. Mater.. 25, (4 ), 566 –570 (2012). 0935-9648 CrossRef
Fischer  B., Fischer  T. M., Knoll  W., “Dispersion of surface plasmons in rectangular, sinusoidal, and incoherent silver gratings,” J. Appl. Phys.. 75, (3 ), 1577 –1581 (1994). 0021-8979 CrossRef
Kitson  S. C. et al., “Surface profile dependence of surface plasmon band gaps on metallic gratings,” J. Appl. Phys.. 79, (9 ), 7383  (1996). 0021-8979 CrossRef
Watts  R. A., Preist  T., Sambles  J. R., “Sharp surface-plasmon resonances on deep diffraction gratings,” Phys. Rev. Lett.. 79, (20 ), 3978 –3981 (1997). 0031-9007 CrossRef
Watts  R. A., Hibbins  A. P., Sambles  J. R., “The influence of grating profile on surface plasmon polariton resonances recorded in different diffracted orders,” J. Mod. Opt.. 46, (15 ), 2157 –2186 (1999). 0950-0340 CrossRef
Kurylowicz  M., Giuliani  M., Dutcher  J. R., “Using nanoscale substrate curvature to control the dimerization of a surface-bound protein,” ACS Nano. 6, (12 ), 10571 –10580 (2012). 1936-0851 CrossRef
Aissou  K. et al., “Nanoscale block copolymer ordering induced by visible interferometric micropatterning: a route towards large scale block copolymer 2D crystals,” Adv. Mater.. , 25, (2 ), 213 –217 (2012). 0935-9648 CrossRef
Huang  Y.-Z. et al., “Rapid fabrication of nanoneedle arrays by ion sputtering,” Nanotechnology. 19, (1 ), 015303  (2008). 0957-4484 CrossRef
George  M. C. et al., “Direct fabrication of 3D periodic inorganic microstructures using conformal phase masks,” Angew. Chem., Int. Ed.. 48, (1 ), 144 –148 (2009).
Shir  D. et al., “Three dimensional silicon photonic crystals fabricated by two photon phase mask lithography,” Appl. Phys. Lett.. 94, (1 ), 011101  (2009). 0003-6951 CrossRef
Chua  J. K., Murukeshan  V. M., “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr.. 80, (1 ), 015401  (2009). 0031-8949 CrossRef
Lu  M. et al., “Single-step holographic fabrication of large-area periodically corrugated metal films,” J. Appl. Phys.. 112, (11 ), 113101  (2012). 0021-8979 CrossRef
Mosher  L. et al., “Double-exposure grayscale photolithography,” J. Microelectromech. Syst.. 18, (2 ), 308 –315 (2009). 1057-7157 CrossRef
Zebda  A. et al., “Spin coating and plasma process for 2.5D integrated photonics on multilayer polymers,” Thin Solid Films. 516, (23 ), 8668 –8674 (2008). 0040-6090 CrossRef
Mack  C. A., “Understanding focus effects in submicrometer optical lithography: a review,” Opt. Eng.. 32, (10 ), 2350 –2362 (1993). 0091-3286 CrossRef
Kim  J., Joy  D. C., Lee  S.-Y., “Controlling photoresist thickness and etch depth for fabrication of 3D structures in electron-beam grayscale lithography,” Microelectron. Eng.. 84, (12 ), 2859 –2864 (2007). 0167-9317 CrossRef
Liu  D. et al., “Fabrication of polynomial 3-D nanostructures in Si with a single-step process,” J. Micro/Nanolithogr. MEMS MOEMS. 10, (1 ), 010501  (2011). 1932-5150 CrossRef

Grahic Jump LocationImage not available.

Boyan Penkov completed a BS in engineering physics at Cornell University and a MSEE in electrical engineering at the University of Washington before serving as an engineer at an early-stage company seeking to commercialize optical metamaterials. His previous work at the intersection of nanoscience and biology has yielded six journal papers, one patent, and seven peer-reviewed conference contributions. He is currently an NDSEG fellow at the Bioelectronic Systems Lab at Columbia University, and he is pursuing a PhD in electrical engineering under the direction of Kenneth Shepard.

Grahic Jump LocationImage not available.

Garry Bordonaro has been a photolithographic process engineer at CNF since 1993. He is experienced in processes using DNQ-Novolak resists in both contact and projection photolithography, and DUV resists and processes using both contact and projection. He is also experienced with CAD design, mask making, simulations using PROLITH X4 by KLA-Tencor, and general semiconductor processing. He is a trainer and lecturer in all of these areas as well. In his spare time, he tours the world as a musician with metal rock bands.

Grahic Jump LocationImage not available.

Andrii B. Golovin received his MSE degree in optics and electronics from the Department of Physics, Kiev State University, Ukraine, in 1987. He received his PhD degree in physics and mathematics from the Institute of Physics, Academy of Sciences, Kiev, Ukraine, in 1994. He has conducted research in the areas of laser physics, electro-optics of liquid crystals and metamaterials, and optical engineering. He has been a research professor at the Center for Metamaterials, Research Foundation of City University of New York, since December 2011. His synergetic activities include teaching courses of physics and mathematics at City College of New York (present), Stark State College of Technology (2010 to 2011), Kent State University (2005 to 2008), and National University of Colombia (1999 to 2000). He has received Tech Brief Awards from Inventions and Contributions Board of NASA (2008, 2006), Award of Ukrainian Academy of Sciences (1997), and Award from the Ukrainian Committee on Science and Technology (1996).

Grahic Jump LocationImage not available.

Igor Bendoym is principal investigator and lead simulation engineer at Phoebus Opto-electronics. After receiving his BS degree in electrical engineering from CCNY, Mr. Bendoym joined the laboratory of Dr. David Crouse as a senior research associate. He has led several Phoebuss simulation projects, as well as many academic projects in the fields of photonic crystals, antennas, metamaterials, and other optical materials.

Grahic Jump LocationImage not available.

Don M. Tennant is serving as director of operations of the Cornell NanoScale Science and Technology Facility (CNF) after a long career at Lucent Bell Labs where he was a distinguished member of technical staff and managed the advanced lithography group. His research work has had significant impact on a wide range of disciplines, including: soft x-ray imaging, extreme ultraviolet lithography (EUVL), high-precision grating production for optical network components, and gate technologies for high performance devices and circuits. He has authored or co-authored over 200 articles in these fields, has organized major conferences, and has been awarded 11 US patents. Don currently serves on the advisory committee and is the financial trustee for the International Conference of Electron, Ion, and Photon Beams and Nanotechnology (EIPBN). He is a past chairman of the Nanoscale Science and Technology Division of the AVS and was named a fellow of the society in 2010.

Grahic Jump LocationImage not available.

David T. Crouse is an associate professor in the Department of Electrical Engineering at the City College of New York, director of the National Science Foundation Industry/University Cooperative Research Center for Metamaterials, director of the Center for Advanced Technology in Photonics Applications, and founder of Phoebus Optoelectronics LLC. He received a BS in honors physics from Purdue University in 1997 and a PhD in electrical engineering at Cornell University in 2002. His research interests include fundamental and applied research on plasmonics crystals, metamaterials and nanotechnology.

© The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

Citation

Boyan Penkov ; Garry Bordonaro ; Andrii B. Golovin ; Igor Bendoym ; Donald M. Tennant, et al.
"Periodic patterning using aerial image modulation with optical lithography", J. Micro/Nanolith. MEMS MOEMS. 12(3), 033009 (Aug 02, 2013). ; http://dx.doi.org/10.1117/1.JMM.12.3.033009


Figures

Graphic Jump LocationF1 :

Overlays of the developed results against the PROLITH simulation target for a number of designs. From left to right, the dose increases from 50 to 80mJcm2; from bottom to top, the focus offset (measured toward the optical system) increases from 1.2 to 0.3 μm. The PROLITH simulation yields the expected sinusoidal pattern with a reasonable fabrication window; perturbations around the best achievable value degrade the aerial image variation.

Graphic Jump LocationF2 :

A scanning electron microscopy (SEM) image of patterned photoresist using the controlled defocus lithography technique emphasizing the variety of producible patterns. An extreme example of aerial image modulation is visible in inset (a). Inset (b) is an edge-on sine wave pattern. Finally, we see an interim example of the possible gradation in inset (c).

Graphic Jump LocationF3 :

An edge-on (θ=10°) SEM image of a periodic pattern transferred into the substrate, and coated in 25 nm gold. The photoresist pattern, here, is taken from the sample shown in Fig. 2(c).

Graphic Jump LocationF4 :

The measured p-polarized spectral reflectance (points), with the simulated spectral reluctance (solid curve), at normal incidence. The measured reflection minimum is at 911 nm, whereas the calculated reflection minimum is at 909 nm. This resonance is due to optical excitation of propagating plasmon modes along with the asymmetric curved surface. Below 800nm, diffraction losses decrease directional reflectivity.

Tables

References

Watanabe  M., Mizukami  K., “Well-ordered wrinkling patterns on chemically oxidized poly(dimethylsiloxane) surfaces,” Macromolecules. 45, (17 ), 7128 –7134 (2012). 0024-9297 CrossRef
Fuchs  Y. et al., “Holographic molecularly imprinted polymers for label-free chemical sensing,” Adv. Mater.. 25, (4 ), 566 –570 (2012). 0935-9648 CrossRef
Fischer  B., Fischer  T. M., Knoll  W., “Dispersion of surface plasmons in rectangular, sinusoidal, and incoherent silver gratings,” J. Appl. Phys.. 75, (3 ), 1577 –1581 (1994). 0021-8979 CrossRef
Kitson  S. C. et al., “Surface profile dependence of surface plasmon band gaps on metallic gratings,” J. Appl. Phys.. 79, (9 ), 7383  (1996). 0021-8979 CrossRef
Watts  R. A., Preist  T., Sambles  J. R., “Sharp surface-plasmon resonances on deep diffraction gratings,” Phys. Rev. Lett.. 79, (20 ), 3978 –3981 (1997). 0031-9007 CrossRef
Watts  R. A., Hibbins  A. P., Sambles  J. R., “The influence of grating profile on surface plasmon polariton resonances recorded in different diffracted orders,” J. Mod. Opt.. 46, (15 ), 2157 –2186 (1999). 0950-0340 CrossRef
Kurylowicz  M., Giuliani  M., Dutcher  J. R., “Using nanoscale substrate curvature to control the dimerization of a surface-bound protein,” ACS Nano. 6, (12 ), 10571 –10580 (2012). 1936-0851 CrossRef
Aissou  K. et al., “Nanoscale block copolymer ordering induced by visible interferometric micropatterning: a route towards large scale block copolymer 2D crystals,” Adv. Mater.. , 25, (2 ), 213 –217 (2012). 0935-9648 CrossRef
Huang  Y.-Z. et al., “Rapid fabrication of nanoneedle arrays by ion sputtering,” Nanotechnology. 19, (1 ), 015303  (2008). 0957-4484 CrossRef
George  M. C. et al., “Direct fabrication of 3D periodic inorganic microstructures using conformal phase masks,” Angew. Chem., Int. Ed.. 48, (1 ), 144 –148 (2009).
Shir  D. et al., “Three dimensional silicon photonic crystals fabricated by two photon phase mask lithography,” Appl. Phys. Lett.. 94, (1 ), 011101  (2009). 0003-6951 CrossRef
Chua  J. K., Murukeshan  V. M., “Patterning of two-dimensional nanoscale features using grating-based multiple beams interference lithography,” Phys. Scr.. 80, (1 ), 015401  (2009). 0031-8949 CrossRef
Lu  M. et al., “Single-step holographic fabrication of large-area periodically corrugated metal films,” J. Appl. Phys.. 112, (11 ), 113101  (2012). 0021-8979 CrossRef
Mosher  L. et al., “Double-exposure grayscale photolithography,” J. Microelectromech. Syst.. 18, (2 ), 308 –315 (2009). 1057-7157 CrossRef
Zebda  A. et al., “Spin coating and plasma process for 2.5D integrated photonics on multilayer polymers,” Thin Solid Films. 516, (23 ), 8668 –8674 (2008). 0040-6090 CrossRef
Mack  C. A., “Understanding focus effects in submicrometer optical lithography: a review,” Opt. Eng.. 32, (10 ), 2350 –2362 (1993). 0091-3286 CrossRef
Kim  J., Joy  D. C., Lee  S.-Y., “Controlling photoresist thickness and etch depth for fabrication of 3D structures in electron-beam grayscale lithography,” Microelectron. Eng.. 84, (12 ), 2859 –2864 (2007). 0167-9317 CrossRef
Liu  D. et al., “Fabrication of polynomial 3-D nanostructures in Si with a single-step process,” J. Micro/Nanolithogr. MEMS MOEMS. 10, (1 ), 010501  (2011). 1932-5150 CrossRef

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