Periodic patterning using aerial image modulation with optical lithography

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.


Introduction
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, 2.5dimensional (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 biosensors [3][4][5][6] and assays that can control protein 7 or block copolymer 8 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 lithography 12 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 kinetics 13 are promising, but limit materials and geometry. Grayscale 14 and multilayer techniques 15 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 wellunderstood i-line illumination (λ ¼ 365 nm) 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.

Experiments and Methods
To develop an appropriate test structure, full-field finitedifference 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 antireflection 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 inputsthe focus plane and optical dose delivered-to determine the experimental parameters.
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 ≈2 μm. 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 h100i) 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 ¼ 0.5). The tool dose was verified before each batch: values of ≈10 mJ cm −2 are typical, corresponding to exposure times of ≈0.04 s. 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 developed 17 to transfer the resultant sinusoidal geometry into the underlayer: in this case, the bulk silicon wafer. A reactive ion etch process was used, with CF 4 as the etchant and CHF 3 to increase selectivity to photoresist, in a 5∶1 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 nearfield approximation. Beyond ≈700 nm, 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-≈2.16 μm 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. Fig. 1 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 80 mJ cm −2 ; 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.

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.
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.

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.
The peaks, each indicating the incident illumination coupling into a surface mode, overlap to within Δλ ¼ 2 nm. 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 fullwidth at half-maximum of 19 nm, indicating a high-quality periodic structure.

Conclusion
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.   Fig. 2(c). Fig. 4 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 ≈800 nm, diffraction losses decrease directional reflectivity.
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 peerreviewed 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.
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. Igor Bendoym is principal investigator and lead simulation engineer at Phoebus Optoelectronics. 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.
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.