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Abstract
Microsphere photolithography (MPL) is a promising technique for cost-effective fabrication of large-scale metasurfaces. This approach generates an array of photonic jets by the collimated illumination of self-assembled microspheres. The photonic jets can be precisely steered within the unit cell defined by each microsphere by changing the angle of incidence. This allows for the creation of complex metasurface element geometries. Computer controlled articulation of the substrate relative to a static UV source allows the direct-write of different metasurface elements. However, this is time-consuming and requires registration between each exposure for complex features. This paper investigates a single exposure method with the dynamic continuous angle of incidence control provided by a Digital Micromirror Device (DMD) in the front Fourier plane of the projection system. The grayscale values of the DMD pixels can be adjusted to provide optical proximity correction. Larger patterns can be achieved by scanning the substrate relative to the exposure beam. This approach is demonstrated with the creation of hierarchical patterns. This work greatly simplifies the MPL exposure process for complex resonators and provides potential for full light field control.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces are 2D patterns of subwavelength antennas arranged in a periodic manner. They enable the engineering of electromagnetic response to light in amplitude, phase, and polarization. For frequency selective surface (FSS) type metasurfaces, the antenna geometry, as well as the material properties, determine the working wavelength range, allowing for metasurfaces to be applied from microwave to visible frequencies [1,2]. Different antenna element geometries determine the functionality of the metasurface [3]. For example, polarization-dependent emitters [4] using dipoles or tripoles resonators or negative refractive index metasurfaces [5] and spin-to-orbit coupling [6] using V-shaped resonators, while spiral resonators are employed for the development of broadband circularly polarized infrared (IR) emitters [7].
Of course, e-beam lithography and focused ion beam milling offer high resolution and flexible metasurface fabrication. However, these approaches can be costly and time-consuming, making it less practical for large-scale manufacturing [8]. Alternative fabrication techniques, such as nano-imprint lithography (NIL) [9] and step and flash imprint lithography (SFIL) [10], are more scalable but still rely on expensive templates. In addition, their rigid nature makes it difficult to apply to conformal surfaces. Other techniques, such as interference lithography (IL) [11] and nanosphere lithography (NSL) [12], do not require a template or mask but lack control over feature geometry or provide for spatial variation. Microsphere photolithography (MPL) utilizes the narrow width and high aspect ratio from photonic nanojet (PNJ) which is generated by dielectric microspheres under UV flood illumination for sub-micron features exposure. This technique poses a balance between flexibility and costs [13–16]. The direct-write nature of this technique allows for patterning of complex geometries [17–19]. By tilting and rotating the sample stage, the photonic jet can be steered to create individual spots for different angles (θ and φ), thus enabling the construction of complex features [20–24]. However, this approach still requires serial exposure at different angles to achieve complex features, leading to complex and time-consuming exposure process [25].
Wu et al. [26] employed a static mask and performed projection lithography with microsphere arrays to eliminate the mechanical movement for complex feature geometry. However, because the image plane falls behind the microspheres, extra efforts are required to elaborately control the gap between microspheres and the substrate. Bonakdar et al. [27] placed the mask at front Fourier plane of the lens. No extra effort is required to control the gap since the image is formed right after the microsphere in this configuration. However, static masks do not provide flexibility. Digital micromirror devices (DMD) have been demonstrated for spatial modulation of the illumination in MPL [25,28]. DMDs have also been utilized for angular spectra control, for example, in Fourier ptychography microscopy [29–31].
While the traditional approach requires multiple-stage exposure and registering process with tilt/rotary stages, DMD could provide continuous modulation of angular spectra for improved feature geometry control and optical proximity correction (OPC). In this study, the combination of DMD-based angle of incidence (AOI) control and scanning exposure is used for metasurface fabrication. The system is evaluated against patternable area, maximum off-normal angle. The limitations and correlations between these two characteristics are investigated. The exposure uniformity and dose control are also discussed. To demonstrate the efficacy of the system, metasurfaces with various types of resonators are fabricated and imaged by SEM. Characterization of the samples is performed using FTIR and visible laser respectively, revealing spectral and angular-dependent responses in both frequency ranges.
2. Photonic jet generation
Figure 1 shows the electric field distribution of PNJ generated by diameter p = 3 µm microsphere under different AOI. The field is simulated by frequency domain FEM simulation (ANSYS Electronic Desktop). The geometric model comprises a hexagonal unit cell with microsphere on top of a 135 nm thick photoresist (PR) layer with glass substrate, periodic boundary condition (BC) to expand to an infinity HCP array. A plane wave excitation at λ = 365 nm is applied with a radiation BC at the bottom. In Fig. 1(a), the PNJ is generated directly under the microsphere at normal illumination. As the AOI increases, the location of the photonic jet shifts from the unit cell center to the edge, as seen in Fig. 1(b) and (c). This phenomenon has been utilized for complex resonator and hierarchical metasurface fabrication.
Fig. 1. Simulation on PNJ generated by p = 3 µm microsphere under (a) 0° AOI; (b) 15° AOI and (c) 30° AOI.
3. Experiment setup
Figure 2(a) shows the exposure setup for dynamic angular spectra control with DMD. A UV light source (LS-100X-5CP, Bachur & Associates) is employed and directed by a pair of mirrors (MP) directs light onto an engineered diffuser (ED1-C20-MD, Thorlabs) to expand the angular spread and reduce spatial coherency. A condenser lens (CL) focuses the light onto a DMD (DLP6500, Texas Instruments). The direction of UV illumination onto DMD has been adjusted to have an AOI of 24° so that the reflected beam leaves the DMD normally. Three lenses (L1∼L3) are arranged with coincident foci after the DMD.
Fig. 2. (a) Exposure setup for dynamic angular spectra control; (b) Zemax Studio ray tracing model for exposure setup
A square field stop (FS) with a width of 8 mm is placed at the back focal point of L1, which is conjugate to the final image plane. L1 and L2 can be considered a 4F system to magnify the DMD image, while L3 performs Fourier transform to convert spatial modulation into angular space. Alternatively, L1 can also perform the Fourier transform, and L2 and L3 form a 4f system to image the Fourier spectrum to the final image plane. An aluminum mirror (M1) between L2 and L3 directs the light vertically onto an XYZ stage used to hold the sample for scanning exposure. M1 can be removed using a flip mount. Finally, the light passes through L4 (identical to L3) to form the same image onto the camera (Amscope MU503B) to provide real-time feedback.
Figure 2(b) displays the results of ray tracing analysis performed in Zemax Studio. The DMD is modeled as a mirror tilted at 12°, and MP is not included in the model since it does not affect the ray-tracing results. The diffuser plane and FS plane both conjugate to the final image plane, which determines the field of view of the final image. The plane of the DMD and the focal plane behind L2 are conjugate aperture planes, which determine the numerical aperture of the system. The relationship between the complex field across the DMD plane, U0, and the complex field across the image plane, Ui, can be determined by wave-optics analysis [32]. Equation (1) is an operator chain that represents the entire sequence of the optical elements from DMD to the image plane:
Here, Q is the quadratic-phase exponential operator and ℛ is the free-space propagation operator. Equation (1) can be simplified to Eq. (2) using the properties of the operators:
Then, stating Eq. (2) explicitly in terms of the input and output fields,
The output field is a plane wave without time dependence propagating at the direction,
Reversely, we can relate the complex field Ui(u) back to the complex field at DMD U0(x). Similarly, we will have the relationship,
Combine Eq. (5) and (6), we have
Equation (7) proves the conservation of etendue holds between DMD plane and image plane. u0 and αi respectively determines the maximum field of view (FOV) and AOI at the image plane. Due to the conservation of etendue, large FOVs and AOIs at the image plane cannot be achieved simultaneously Fig. 3 plots the tradeoff between the FOV and maximum AOI at the image plane. The black curve represents the performance of current configuration, which is limited by Eq. (7). The green and blue lines in Fig. 3 show the performance can be potentially improved by adopting a larger DMD (or other spatial light modulating device). The right axis is the combination factor of foci and corresponds to different choices of FOV. A moderate option is chosen with FOV = ± 0.7 mm and AOI = ±26° (indicated in Fig. 3) by using focal lengths of 60 mm, 200 mm, and 32 mm for f1, f2, and f3 respectively. To facilitate the scanning exposure, the final image filed is restricted by the FS at back focal plane of L1 to be a 1 mm square at the image plane.
Fig. 3. The tradeoff between maximum AOI and FOV due to conservation of etendue; Black curve represents the achievable performance with current DMD under different choice of lenses. The circle denotes the performance with current arrangement. The green and blue curves are potentially achievable performance if a larger DMD is employed. The red curve demonstrates the relationship between choice of lens focal length and system performance.
A camera is for aligning the system by examining the intensity distribution in angular space. Figure 4 shows images captured by the camera in Fig. 2 for different DMD patterns and illustrate the transformation from the DMD to angular space. The first column in Fig. 4 shows three different digital patterns used on the DMD while the second column, marked at z = 0 mm, shows images recorded at the focal plane. Regardless of the DMD pattern, identical images of the field stop (FS) are formed on the camera. The next two columns show images captured by the different distances from the focus (camera positioned by a translation stage) positions, where the positive value indicates that the camera has been moved further back from the lens using a translation stage. When the FS image is out of focus, the illumination with different AOI separates and the camera image provides the angular intensity distribution. Alignment can be performed based on these images to achieve a uniform angular intensity distribution at the focus.
Fig. 4. The image recorded by camera at different axial position with respect to different images used on DMD; The solid box indicates that the image at focus is always the image of FS regardless of what DMD image used; The dashed box shows how the image evolves at different axial position to reveal the difference in angular spectrum at focus.
While it is possible to enhance the spatial light intensity distribution by incorporating a rotary diffuser, this was not included in the current setup. Rather, the diffuser has been demagnified more than 10× and scanned exposure effectively homogenizes the irradiance. Figure 4 shows the short depth of focus of the system. A lab jack (L490MZ, Thorlabs) is used to adjust the sample relative to the focal plane. A series of trial exposures are examined under the microscope to determine that the setup can place the sample surface within ±0.01 mm of the focal plane.
4. Experiments
The S1805 PR (Microposit) is mixed with PGMEA (Propylene glycol methyl ether acetate, Sigma-Aldrich) at a 2:3 ratio to lower the PR viscosity for a thinner PR layer. A 120 nm PR layer is achieved by spin coating. 3 µm silica microsphere (Nanomicro) is self-assembled and transferred onto the substrate maintaining HCP array. After exposure using the setup in Fig. 1, the sample is developed for 30 seconds in developer (MF319), rinsed with DI water, and air-dried. Pattern transfer is achieved using lift-off, and sample characterization is performed using FTIR (Thermo Nicolet NEXUS 670) and SEM (Magellan 400). The details of sample parathion process can be found in previous publication [33].
5. Results and discussion
5.1 AOI control
A set of DMD digital masks displaying two circles with varying separation distances δ0 are utilized to assess the AOI control. The diameter of the DMD's openings is fixed at 0.8 mm with different δ0 values, as presented in Fig. 5(a). The position of the openings (white circle) determines the illumination AOI at the image plane, thus determining the location of the PNJ in each unit cell. The location of PNJs is determined from fabricated metasurface samples on a glass slide using 3 µm Microspheres. In each unit cell, a pair of Al disks are fabricated after liftoff based on the DMD mask, as illustrated in Fig. 5(b). Figure 5(c) displays the correlation between the normalized separation distance in the sample δ/p and the separation distance in the mask δ0/W. The inset shows 8 samples with 1 mm × 1 mm pattering area from single exposure. The scale bar is 5 mm. A quadratic curve fitting is used to describe the correlation. Due to the rectangular shape of the DMD, the AOI control capability is anisotropic. Along the width direction, a maximum separation distance of δ = 1.6 µm can be achieved with δ0/W = 1, while along the length direction, the maximum separation distance of δ = 2.3 µm can be attained with δ0/W = 1.28. However, for δ0/W > 1.28, strong spherical aberration leads to exposure failure, where large illumination angles result in a significant increase in the system's OPD (Optical path difference). Customizing the shape of lenses to minimize the OPD can enhance the performance.
Fig. 5. (a) The DMD digital mask showing two opening with a fixed diameter of 0.8 mm but a varied separation distance δ0; (b) The SEM of disk pairs fabricated in single unit cell with a separation distance δ; (c) The relationship between normalized separation distance of disk pair δ/p and normalized separation distance of DMD mask openings δ0/W. Inset shows the photo of the 1 mm × 1 mm sample from single exposure.
5.2 Dose curve and effect of opening size on DMD
Due to finite FOV, large-area patterning requires step and stitching or scanning exposure. Benefiting from the CNC (Computer numerical control) stage, scanning is easier to perform with any illumination intensity variation in the scanning direction averaged to achieve a smooth dose control. The MPL exposure dose depends simultaneously on several factors, including the scanning velocity (v), the size of the DMD pattern (A0), and the grayscale value of the opening (G), assuming a constant illumination intensity:
The exposure dose depends on the scanning velocity. It can also be controlled by modifying grayscale of corresponding pixel on DMD. The opening area A0 has a more complicated effect upon exposure. Besides directly affecting the exposure dose, a wider opening size also causes AOI broadening on microspheres. A broadened AOI spectrum will change the width of PNJ and result in different feature size. This effect is characterized by fabricating aluminum disks using a diameter of 0.8 mm (100 micromirrors) and 3 mm (400 micromirrors) opening on DMD respectively. The exposure dose for each sample was scaled with the grayscale value and pattern area (A0). The disk size was plotted against the equivalent exposure dose E = GA0/v, as shown in Fig. 6(a). Similar to the dose curve from previous work [34], a minimum exposure dose (cutoff dose) is required to produce features, and the slope is much steeper at lower exposure doses than at higher doses. The disk size distribution across the lines were also measured as a function of position scanned lines (y) were also measured to characterize the exposure dose variation. Figure 6(b) displays the disk size distribution for equivalent exposure doses of 16 s/mm, 40 s/mm, and 120 s/mm from the red curve in Fig. 6(a). The uniformity of the disk size and the minimal change in line width from low to high doses suggest a top hat intensity profile at the image field.
Fig. 6. (a) The dose curve of Al disks fabricated on glass with different opening size of DMD mask (b) The disk size distribution across the scanning line in y direction with the equivalent exposure dose Eeq = 16 s/mm, 40 s/mm, and 120 s/mm.
The grayscale value uniformly changes the overall intensity at the image plane. However, the opening size on the DMD affects not only the overall intensity but also the cone angle of illumination received by the image plane. A larger cone of light received by the microsphere results in a higher numerical aperture (NA). A higher NA produces a lower peak value and a larger full width at half maximum (FWHM) of the photonic jet, as demonstrated in Fig. 8. Figure 7(a)(b) shows simulations of the photonic jet generated inside the PR from normal illumination and a cone illumination with a ± 8° apex angle, using ANSYS HFSS. Figure 7(c) plot the relative enhancement factor in the middle plane z = −67.5 nm. The decrease in peak intensity in Fig. 7(c) corresponds to the increased cutoff exposure dose, while the increase in FWHM corresponds to the increase in slope for the 3 mm opening size in Fig. 6. A similar effect is expected when using different microsphere sizes since changing microsphere size does not affect the behavior of photonic jet under the same AOI.
Fig. 7. (a) The enhancement factor E2/E02 distribution of photonic generated by 3 µm microsphere under plane wave illumination at normal incidence; (b) The photonic jet generated by 3 µm microsphere under a cone illumination with ±8° apex angle; (c) The enhancement factor E2/E02 at the middle plane z = −67.5 nm in PR along x direction.
Fig. 8. Proximity correction achieved by adjusting DMD grayscale value (a)-(c) Series of Al tripole resonators exposed with different distributions. (d) Dipole resonators, (e) split ring resonators, and (f) spirals.
5.3 Optical proximity correction
The DMD digital mask directly controls the geometry exposed. The grayscale values on the DMD pattern can be adjusted for optical proximity correction (OPC). Figure 8(a-c) illustrates this process with aluminum tripole resonator. Figure 8(a) shows that a uniform grayscale distribution produces a triangular geometry due to overexposure near the center of the pattern. Reducing the grayscale value at the center of the pattern produces separated features due to underexposure (Fig. 8(b)). Tripole resonators are successfully patterned after several more iterations of the grayscale distribution. Figure 8(d-e) shows this procedure applied to several other types of metasurface resonators.
5.4 Split ring resonator and FTIR
Raster scans were used to fabricate larger samples. A glass substrate is used to fabricate aluminum SRR resonators with an area larger than 1 cm × 1 cm. The scanning velocity is set at 0.2 mm/s, and the total exposure duration for this sample is about 8 minutes. Figure 9 shows the polarization-dependent reflectance of the sample using FTIR. Reflectance is measured from both TE (red) and TM (blue) polarizations at 30° AOI. The insets display the photo of the sample and SEM image of the SRR resonators. The experimental results (solid line) from FTIR agree well with the simulation results from HFSS (dashed line). Discrepancies arise from differences in the optical properties used to model the substrate (fused silica [35]) versus the soda-lime microscope slides used in the experiments.
Fig. 9. The comparison of FTIR measured (solid line) and HFSS simulation (dashed line) reflectance spectra of SRR under TE- and TM- polarization. Insets: SRR fabricated over 1 cm × 1 cm area on glass and the SEM image of SRR
5.5 Hierarchical metasurface with diffractive effects
Complex hierarchical patterns can be achieved by coordinating the DMD with the stages. This is analogous to selecting a different style of pen (the DMD) to write with (the x-y stages) Fig. 10 shows different numbers of aluminum disks arranged within the unit cell defined by each microsphere. The first column shows the SEM images of different disk arrangements. Figure 10(a) shows the SEM image of single disk array with nominal periodicity p = 3 µm which equals the diameter of microspheres. Figure 10(b) shows four small disks arranged in a diamond shape inside each unit cell. The disks are separated by half the microsphere diameter, so that the periodicity of the disks is half that for a single resonator centered in each unit cell. The other type of resonator comprises three small disks lined up in each unit cell, as displayed in Fig. 10(c). The separation distance between two lined-up disks is 1 µm, with a 2.6 µm separation distance between each line. The frequency domain of the disk pattern is investigated by (Fast Fourier Transform) FFT images (second column) of first column and diffraction patterns (third column) recorded on the screen behind the sample. A 10W Optical Parametric Amplifier (LightConversion) was pumped using a 20W Pharos femtosecond laser (LightConversion) to produce 465 nm, 520 nm and 630 nm beam. The beam was restricted to using an iris to reduce spot size and illuminated onto the sample at normal incidence to produce diffraction pattern. Other diffraction patterns that display selective diffraction orders can be achieved by controlling the arrangement of the disks and the process parameters. However, creating a monocrystalline of self-assembled microspheres for this application is challenging for large areas.
Fig. 10. First column: the SEM images of (a) Single Al disk pattern with nominal periodicity p = 3 µm (b) Four Al disks per unit cell with periodicity p = 1.5 µm (c) Three Al disks per unit cell with anisotropic periodicity of 1 µm and 2.6 µm; Second column: the FFT of SEM image from (a) (b), and (c); Third column: corresponding diffraction pattern generated by λ = 630 nm laser from an optical parametric amplifier pumped by a 1030 nm femtosecond laser beam.
The modification of the diffraction pattern discussed above is heavily reliant on the alignment of the microsphere array orientation and the direction of the disk patterning. However, in Fig. 11, an example is presented where the microsphere array orientation does not have any significant influence. Figure 11(a) shows a sample patterned with inverse PR dipoles displaying the letters “LPML,” for Laser Precision Manufacturing Laboratory. The SEM image of dipoles, arranged in the −45°, 0°, 45°, and 90° directions, are shown in the insets of each letter. Figure 11(b)-(e) shows the diffraction patterns under λ = 520 nm illumination with a vertical polarization from each letter, which are modified based on the dipole's orientation. The insets in Fig. 11(b) also shows the diffraction pattern under λ = 630 and 465 illuminations, which indicates wavelength independence. Compared to the direction parallel to the dipole, there are more diffraction orders in the direction perpendicular to the dipole because the dipole changes the 2D array into a 1D grating. The dipole direction interrupts the consistent periodicity from the microsphere array, “turning off” the diffraction order in that particular direction. Consequently, the dipole array exhibits angular dependence in reflection. As shown in Fig. 11(f)-(i), when viewed from different azimuthal angles, the letter comprises dipoles perpendicular to the viewer has been lit up.
Fig. 11. (a) Inverse dipoles patterned with PR on glass showing “LPML” with SEM images of each letter (scale bar: 3 µm); (b) Diffraction pattern from first letter “L” (−45°) at λ = 520 nm illumination with insets showing patterns at λ = 630 nm and 465 nm, with arrow indicating incident E-field polarization; (c)–(e) Diffraction patterns from the other of the letters; (f)–(i) Reflection with angular selection observed from individual letters when the viewing direction perpendicular to the dipole orientation
6. Conclusion
This paper demonstrated and explored the use of dynamic angular field control and scanning exposure to enhance the flexibility of MPL. The DMD was employed at the Fourier plane of projection lens for dynamic angular field control. This method allows for continuously variable AOI control, avoiding the need for a complicated registering process required with multi-exposure for discrete angles from our previous work. Both simulation and experimental results demonstrate that the system achieves a uniform intensity profile over a 1 mm × 1 mm area with AOI tunable within ±26° in all directions. With the addition of scanning exposure from CNC translation stages, hierarchical patterning of metasurfaces with multiple meta-atom geometries over a large area has been achieved. Potentially, CNC stages can be replaced by a galvo scanner for better control. This study shows the design principle for dynamic angular spectra control using a DMD Fourier plane. The maximum FOV and AOI are correlated and subject to the conservation of etendue. The factors that contribute to the scanning exposure dose curve also has been discussed. Among them, the opening on the DMD affects the illumination intensity and the properties of PNJ simultaneously, causing change in dose curve slope. The ability of local angular spectra control also enables OPC for complicated metasurface elements geometries. Geometric parameters (e.g. linewidth, diameter) of individual elements that are determined by exposure dose can be spatially varied by controlling scanning velocity. Continuous spatial variation can be achieved along the scanning direction; however, the resolution of spatial variation is subject to the FOV = 1 mm in the perpendicular direction. The periodicity is determined by the microsphere diameter, but by controlling AOI from the DMD, we demonstrated doubling or tripling the periodicity with simple disk pattern within monocrystalline microsphere array. Additionally, a hierarchical sample with differently arranged multi-disk resonators patterned in different letters effectively modified the diffraction pattern in certain direction and resulting in anisotropic reflectivity of the sample.
Funding
National Science Foundation (CMMI 1947391); Army Research Office (W911NF-32-1-0055).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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