High-efficiency metalenses for zone-plate-array lithography

In addition to its key role in fabricating masks for projection lithography, maskless lithography is important for nanostructures research where the delay and cost of mask fabrication is undesirable, and also in applications where the limited exposure field of projection lithography (33 × 26 mm) is undesirable. With scanning-electron-beam lithography (SEBL), the exposure field size is not limited, the depth-of-focus is large and sub-100 nm resolution is readily achieved. For these reasons, SEBL is widely used in nanostructures research. One can envisage circumventing the problem of slow writing speed by employing several electron beams in parallel, but a plethora of issues, such as stray electric and magnetic fields, the difficulty of thermal control in a vacuum and the need for a path to ground must be taken into account.¹ Spatial-phase locking (SPLEBL) has been proposed to circumvent the stability and precision issues with electron beams,² but to date it has not been implemented outside the research laboratory.

In zone-plate-array lithography (ZPAL), a large array of diffractive-optical microlenses is used to focus a set of parallel-input beams into focal spots on a scanning substrate.³ A spatial-light modulator individually modulates each beam on, off, or to an intermediate gray-level. Each pixel of the modulator directs a beam of light to a specific microlens. By precisely coordinating the scanning of the substrate with the modulated light, complex patterns of arbitrary geometry can be written. Under the current design, up to 1000 simultaneous, independent parallel beams can be used. The relative positions of all beams are spatially fixed, allowing for accurate calibration of beam locations. Conceptually, this is similar to an ink-jet printer where each aperture of an array dispenses a small, controllable droplet of ink as the substrate is scanned. LumArray’s prototype ZP-150 is depicted schematically in Fig. 1.

ZPAL’s key features include (1) patterning via fixed focal spots and a moving stage; (2) simultaneous utilization of multiple focal spots to increase speed; (3) focal-spot intensity control via a spatial-light modulator; (4) diffractive-optical microlenses for focusing as well as alignment; (5) stage control via an encoder grid rather than a laser interferometer; (6) correction in software for errors in focal-spot positions or intensities.

Feature (1) is important for long-range spatial-phase coherence (LRSPC) since stage position can be measured to the sub-1 nm level and the patterned field can be as large as stage travel permits. Focal-spot writing avoids optical-interference effects, i.e., focal-spot intensities are added, not fields. Feature (2) assumes that any complex pattern can be decomposed into instructions for each of the multiple focal spots. For this, the spatial-light modulator, (3), is required, as it is also for linewidth control and proximity-effect correction. Diffractive optics, (4), makes a wide choice of wavelengths available, down to the x-ray range, as well as focal-spot engineering, discussed below. The encoder grid, (5), ensures that positional accuracy is not influenced by atmospheric pressure or composition. Our current encoder grid limits written fields to 150 mm, although the stage can accommodate substrates up to 200 mm. Finally, systematic position or intensity errors that can be measured can generally be corrected in software, feature (6).

In the recent literature, diffractive-optical microlenses are commonly referred to as metalenses.⁴ Metalenses offer many compelling advantages, especially in a massively parallel array. Fresnel zone plates, one of the most basic metalenses, consist of a set of concentric circular rings, called zones, whose periodicity decreases with increasing radius such that first-order diffraction from all zones converge to a common focus on the optical axis, thus acting as a lens. With on-axis, monochromatic illumination, metalenses achieve diffraction-limited focusing with a single structured planar surface. Diffractive elements can function at any wavelength, from radio waves to x rays, or even for focusing particle beams.⁵ Changing the numerical aperture or design wavelength can be as simple as changing the linewidth or thickness of the diffractive structure. Across an array of metalenses, critical parameters such as consistent focal length and spot size are easily controlled. Diffractive metalenses can be made cheaply, reproducibly, and in large quantities using planar fabrication processes (i.e., lithography plus pattern transfer).

Since the earliest research, binary pi-phase zone plates, fabricated in the spin-on glass, hydrogen silsesquioxane (HSQ)⁶ have been exclusively employed. Under the paraxial approximation, the maximum focal efficiency is ∼34%,⁷ while actual performance, especially at high numerical aperture, falls short of this. The background (greater than 66%) is spread over an area much larger than individual microlenses. For small-area patterns, this background effect is generally negligible. However, because background exposure is cumulative, the aerial-image contrast of dense patterns exposed over large areas is degraded. The deleterious effect of a high background can be compensated via proximity-effect correction (PEC), as is well known in e-beam lithography, but PEC cannot solve all problems. Accordingly, metalenses with higher focal efficiency and lower background are important for the ZPAL platform to address large-area, high-density patterning.

Much of the metalens literature uses so-called “inverse design” in which one calls for a certain result at the focus and a computer chooses the diffractive-optical structure that will produce it.⁸ In this way, metalenses that operate over a broad spectral range, or that have a depth-of-focus much larger than the classical result,⁹ or that produce a focal spot at one wavelength and a donut pattern at another,¹⁰ can be designed.

In a classical Fresnel lens, the 2π to 0 variation in optical path is achieved via a prismatic dielectric. Effective-index modulation,¹¹ in which the dielectric thickness is uniform and subwavelength holes or pillars are inserted to vary the phase delay, is a more efficient approach, especially for the high diffraction angles of the outer zones. Effective-index modulation is also well suited to modern nanofabrication techniques.

In order to compare the performance of newly designed metalenses with the pi-phase zone plates previously employed, the same lens diameter (135 μm), focal length (100 μm), and wavelength (405 nm) are used. This corresponds to 51 zones and a numerical aperture (NA) of 0.56. Figure 2 shows e-beam patterning of the central zones and outer zones for two, closely related, effective-index approaches. To form the final metalens, these patterns are transferred into an organic dielectric of 1.9 index on top of a 1.6 mm-thick fused-silica substrate via reactive ion etching. The patterned dielectric is 450 nm thick (i.e., the 2π thickness). A pillar or hole of 45 nm diameter thus has an aspect ratio of 10 to 1, which we consider a practical limit.

Each zone is divided into subwavelength “cells.” For example, in Fig. 2(a), zone 2 is divided into 22 cells and in Fig. 2(b), zone 51 is divided into 4. For the first 3 central zones, the diffraction angle is small enough that the phase of transmitted light can be calculated from the direct optical path. The size and positioning of subwavelength holes or pillars is chosen to yield a spherical wave converging to a focal spot at the focal plane. Beyond zone 3, the remaining zones are very nearly periodic, so a different approach is used.

To gain more insight and provide a path for rapid optimization, we employ a simplification known as the “locally periodic approximation.” Each zone of the metalens is modeled as a linear diffraction grating whose periodicity is equal to the width of the zone. The performance of the metalens itself is estimated by averaging the diffraction efficiency of the constituent zone-equivalent gratings. Recall that a refractive lens that’s nominally 100% efficient will put only 82% of the transmitted light within the first zeros of the airy-distribution function. Given this, we apply a scaling factor of 0.8 to the zone-averaged grating efficiencies to provide an estimate of the overall focal efficiency of a metalens.

Our approach eliminates the need to incorporate rigorous lens simulation methods into the optimization phase, thus speeding the process. The estimated efficiency produced by this method is in good agreement with the more rigorous calculation of efficiency using finite-difference time-domain (FDTD) methods. Both the diffraction efficiency and the transmission phase of a linear grating can be accurately simulated using rigorous coupled wave analysis (RCWA). For this, we used the commercially available G-Solver package.¹² 

An example of such an optimization is shown in Fig. 3 for the outmost of the 51 zones. It is noteworthy that the genetic algorithm achieved higher diffraction efficiency by filling cell 1 with dielectric and making most of cell 4 empty, thereby favoring a full 2π to 0 transition at the boundaries.

Figure 4 compares the grating-averaging approach, described above, to a binary pi-phase zone plate and a four-level Fresnel effective-index metalens. Figure 5 compares the FDTD simulation of the point-spread function of the four-level Fresnel metalens and a grating-optimized metalens.

While numerical simulation of diffraction efficiency is useful for evaluating metalens designs, physical measurement is required to verify performance. A modified Leitz Ergolux microscope is used as the test bench. The metalens is illuminated at normal incidence using a collimated 405 nm laser. Two images are recorded using a CMOS digital camera (Point GreyReseach, Inc. model FL2G-50S5M-C). The images are postprocessed using the image j image-analysis package.¹³ The microscope objective must have good transmission at 405 nm and an NA higher than that of the metalens under test. A 0.9NA, UV-optimized objective lens was used (Leica 501-773140). The first image is taken in close proximity to the metalens so that its integration yields the total transmitted light. The second image is taken at the focal plane of the metalens. Integration over a small radius provides an estimate of the total light in the first-order focus. The local intensity of the focal spot is ∼10⁵ higher than that of the incident light. Since this factor is greater than the dynamic range of the camera, the exposure time is reduced by a factor of 100 when imaging the focal spot, and the incident laser power is reduced by a factor of 10, yielding a scale factor of 1000 between the measured values of the two images. Appropriately scaled, the metalens efficiency is the ratio of the light within the focal spot to the total light transmitted through the lens. This measurement does not account for losses within the microscope optics and therefore is not absolutely accurate. However, since the test configuration is consistent for all measurements, it provides a reasonable comparison of the efficiency of different metalenses. We found good agreement between measured efficiency values and the values predicted by numerical simulation.

The ZPAL platform was designed for long-range spatial-phase coherence (LRSPC). Although electronic application do not currently require LRSPC, some photonic application do, one such being diffraction gratings for monochrometers and spectrometers at synchrotron and free-electron-laser facilities. Although applications requiring LRSPC are currently limited, one can anticipate that the availability of such a technology will lead to new applications not currently envisaged. The history of technology is replete with such examples.

Figure 6 illustrates the use of ZPAL to pattern a grating that exhibits long-range spatial-phase coherence. The peak-to-peak line-placement error is <20 nm across a 100 mm length; the RMS error is 6.4 nm at a particular Y value.

Several investigators have reported metalenses with extended depth-of-focus via inverse design.⁹ If this can be achieved without significantly increasing focal-spot diameter, it would significantly aid patterning with the ZPAL platform.

It is well known that the focal spot size produced by a metalens is approximately equal to half the width of the outmost zone. Hence, metalens resolution is directly proportional to the resolution of the process used in its fabrication. The ZPAL platform was originally envisaged for use at the Carbon K x-ray wavelength of 4.5 nm.¹⁴ Photon sieve metalenses operating at the EUV wavelength of 13 nm have been reported.¹⁵ The absence of a spatial light modulator operating at wavelengths shorter than deep UV limits consideration of such short wavelengths for maskless ZPAL lithography.

Another approach to higher resolution ZPAL is absorption modulation optical lithography (AMOL) which would employs only wavelengths in the visible range.¹⁶ It has been described in detail elsewhere but to date has not been implemented in a practical system.

LumArray’s zone-plate array lithography (ZPAL) technology has been developed as a versatile option for high-resolution and high-accuracy optical pattern generation. However, as a metalens, the zone-plate itself has been a limiting factor in many applications. Low focal efficiency of the binary pi-phase zone-plate means that a majority of the photons incident on the photoresist are distributed as a diffuse background thereby degrading image contrast. The most direct way to improve image contrast is to improve focal efficiency of the metalens array by swapping the zone-plate for a more advanced metalens. We show that the effective-index technique with a straightforward Fresnel design can be used to increase focal efficiency to ∼69%, a 2X improvement over the original binary-pi-phase zone plate. Test metalenses fabricated using electron-beam lithography and reactive-ion etching were found to have focal efficiency consistent with predictions based on numerical modeling. A method for optimizing the focal efficiency of a metalens is developed using optimization of equivalent diffraction gratings.

Zachary Babbitz provided valuable help with RCWA in the initial stage of this work. The research described in this paper was supported in part through Purchase Order No. 2310703 from Sandia National Laboratory.

Authors H.I.S., M.W., F.Z., and T.S. are employees of LumArray, Inc. Author M.M. has no conflict of interest.

Henry I. Smith: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Visualization (equal); Writing – original draft (equal). Mark Mondol: Methodology (equal); Resources (equal); Software (equal). Feng Zhang: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Timothy Savas: Investigation (equal); Methodology (equal); Resources (equal); Validation (equal). Michael Walsh: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.