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Abstract
In this work, high performance subwavelength grating metalens is demonstrated with high-refractive-index silicon-rich silicon nitride material compatible with CMOS fabrication processes. Conventional metalens materials namely TiO2 and GaN require expensive and time-consuming deposition processes such as atomic layer deposition (ALD) and metal-organic chemical vapor deposition (MOCVD). In order to improve the cost efficiency of metalens and its performance, the trade-offs between refractive index, fabrication difficulty and metalens performance is studied. We propose a feasible approach that is silicon-rich nitride (SiNx) as metalens material, which balance the trade-offs between refractive index and fabrication difficulty to large extent. With the advantage of ultra-high refractive index SiNx (n = 2.74) at 685 nm incidence, we are able to shrink the pitch size to unprecedented 220 nm. A propagation-phase-based grating metalens is fabricated and characterized for proof of concept. In addition, the optical parameters (n & k) can easily be adjusted through the deposition process. Our work has also promised a new degree of freedom for future optimization of metalens.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Traditional optical lenses are made from transparent materials, typically glass through mechanical processes such as grinding. The performance of conventional bulk lens is mainly limited by the mechanical error such that a perfect convex or concave surface is unattainable. Advances in CMOS nano fabrication techniques have enabled the fabrication of high-aspect-ratio nano structures with some transparent materials. This has given rise to the development of metalens/metasurface, which is formed by groups of sub-visible-wavelength sized nano structures [1–5]. Through this approach, numerous types of bulk optical devices can be replaced by a thin layer of nano structures with similar or even better performance. Furthermore, with full control of phase [3–5], transmission [6] and polarization [7], metasurface enabled the integration of multi-functionalities including achromatic focusing [8–10], color routing [11] and polarization separation [7] into one lens. These devices are formed by a thin layer of nano structures which grant them inherent advantages such as compactness and light weight. In addition, compared with traditional planar optical devices including Fresnel lenses or Fresnel zone plate, metasurfaces provide better performance in various aspects especially efficiency. This is mainly realized by the engineering with sub-wavelength precision.
The design of metalens are achieved by arranging the sub-wavelength nano structures into a space-variant phase profile [1–11]. And this profile in 2-D and 3-D are shown by Eq. (1) and Eq. (2) respectively.
The lens is lay out at x-y plane. In the Eqs, is the incident wavelength, f is the designed focal length, x and y is space coordinate assuming the center is (0,0). and are the phase needed for this phase shifter with location specified by coordinate (x) and (x, y), and and is the phase shifted at the center of lens.
The engineering of phase shift through nano structures is the most important process for the design of metalens. In order to achieve the phase profile aforementioned through propagation phase, the lens plane is first discretized into finite number of pitches (period). Then high-refractive index materials are filled into each pitch with designed geometry, which provide variation of effective index over the lens plane. The objective of this step is to achieve the engineering of optical response within each period including transmission and phase shift.
In order to achieve 2π propagation-phase coverage (distinguishing from Pancharatnam-Berry phase), high-refractive index materials such as TiO2 [3] and GaN [8] are applied. In most cases, the highest aspect ratio of nanostructures fabricated is around 10 to ensure precise phase coverage. While the application of TiO2 and GaN as lens material involves atomic layer deposition (ALD) or metal-organic chemical vapor deposition (MOCVD). This has increased the time and cost of metalens fabrication to a large extent.
The most important approach to improve the performance of metalens is to shrink the pitch size (also known as period). In this way, researchers are trying to avoid the influence on wavefront caused by the discretization of space, so that the loss caused by scattering or unwanted resonance is minimized. While the decrease of pitch size (period) in pursuit of higher focus efficiency is limited by nano fabrication, to be specific, the minimum physical dimension of a phase shifter is limited. As a result, there exist a fabrication-limited minimum pitch size for certain material and incident wavelength combination to achieve 2π propagation-phase coverage.
In this work, we have developed silicon rich silicon nitride (SiNx) as metalens material with a more cost-efficient thin film deposition process: physical vapor deposition (PVD) and plasma enhanced vapor deposition (PECVD). We have achieved a film with much higher refractive index n = 2.74 at targeting wavelength 685 nm which enabled unprecedented small pitch size of 220 nm. A subwavelength grating metalens with 220 nm pitch size under 685 nm light is designed, fabricated and characterized in this work.
2. Development of high-refractive-index silicon rich silicon nitride (SiNx) films for metalens design
Silicon nitride is a conventional material applied in CMOS industry as passivation layer. Recent advances in optical communication have seen the application of Si3N4 as ultra-low loss waveguide [12].
For the metalens application, Si3N4 with refractive index around 2.0 in visible bandwidth requires nano structures with high thickness for the coverage of 2π phase. Limited by current nano fabrication techniques, this has result in a large pitch size [13]. In this case, the negative impact of space discretization on focus efficiency is inevitable. The common upper limit for pitch size is below the Abby’s diffraction limit (), if the lens is designed for the diffraction limited focus. In order to achieve small pitch size with 2π coverage, lens material with a higher index seems required.
Common deposition of Si3N4 thin films are basically vapor deposition processes namely PVD and PECVD. Recent studies have reported adjustment of optical parameters of SiNx (x as variable) films through both approaches [14,15], but a high refractive index SiNx film suitable for metalens application has not yet been developed.
2.1 Silicon rich silicon nitride film deposited by magnetron sputter
Conventional physical vapor deposition (PVD) of silicon nitride thin film is through magnetron sputtering of pure Si3N4 target. In order to increase the refractive index of silicon nitride, the concentration of silicon is supposed to be increased. And this result in a silicon rich silicon nitride material.
In this study, we have developed a reactive magnetron sputtering process for high-refractive-index SiNx thin films. A silicon target (Kurt J. Lesker) is applied on direct current source (DC) of PVD 75 magnetron sputtering tool (Kurt J. Lesker). The DC power is fixed at 350 W. A radio-frequency bias power is applied on the substrate at 60 W. The pressure of process chamber is fixed at 6 mT with N2 and Ar gas flow simultaneously. The gas contration N2/Ar is varied from 10% to 20%. All films are deposited with thickness around 200 nm and their optical parameters (n & k) is measured through ellipsometer (Woollam). The result of n & k is shown in Fig. 1.
Fig. 1 n & k of silicon rich silicon nitride thin films deposited with different N2/Ar concentration (shown as percentage) through PVD. (a) Refractive index n. (b) Extinction coefficient k.
As shown in Fig. 1(a), the film with 10% N2/Ar ratio can provide a refractive index n > 2.6 though all visible bandwidths. But this material has a significant absorption for light below 738 nm shown in Fig. 1(b). While the refractive index drops significantly from 2.6 to below 2.4 (at 685 nm for example) when the N2/Ar ratio is increased to 11%. This film has a refractive index comparable with TiO2 and GaN but with large absorption below 570 nm (Fig. 1b). As a result, it is only suitable for metalens targeting wavelength above 570 nm.
The refractive index experiences another large decrease for films with N2/Ar ratio higher than 11% (Fig. 1a). Considering the trade-offs between light absorption and refractive index, this group of films are not preferable candidate for metalens.
In addition, we discover that the control of optical property (of SiNx) through PVD is very rough. That our targeting range of refractive index can only be achieved between 10% and 12% gas ratio. And the high extinction ratio (k) of 10% film implies the existence of pure Si with high concentration.
2.2 Silicon rich silicon nitride film deposited by plasma enhanced chemical vapor deposition
Plasma enhanced chemical vapor deposition (PECVD) has long been a reliable approach for the deposition of Si3N4. In this study we have applied SiH4 and NH3 as reaction gas for the deposition of SiNx under 350 °C. The refractive index of film is tuned by the variation of gas concentration. The pressure is fixed at 2 torr. The optical parameters (n & k) of deposited films is shown in Fig. 2, with the gas ratio SiH4/NH3 shown as α.
Fig. 2 n & k of silicon rich silicon nitride thin films deposited with different SiH4 and NH3 concentration through PECVD. (a) refractive index n. (b) Extinction coefficient k.
As can be observed in Fig. 2(a), PECVD process shows a better control of refractive index through the variation of gas concentration. For example, at 685 nm, the refractive index is continuously tuned from 2.2 to 2.82. The cut-off wavelengths (e.g. extinction coefficient above zero) are ranged from 530 nm to 600 nm.
The selection of refractive index is based on targeting wavelength with consideration in two aspects: 2π phase coverage and phase control with limited fabrication precision. Basically, for phase shifters, high refractive index lowered the aspect-ratio needed for 2π coverage. While it increases the requirement of fabrication precision for phase control. And this PECVD process with continuous tuning of refractive index provides unprecedented balancing of these 2 factors based on targeting wavelengths.
Considering aforementioned trade-offs, the film deposited with SiH4/NH3 ratio 4.68 with high refractive-index (n = 2.74 at 685 nm) and k = 0 above 600 nm is preferable for metalens targeting beyond 600 nm bandwidths. And we have chosen this film for later design.
2.3 Shrinking the pitch size of metalens with high index SiNx material
The major approach to increase the efficiency of metalens is to minimize the influence cause by space discretization. This method, in other words, is to shrink the pitch size (period) of each phase shifter. A schematic diagram of propagation-phase-based metalens in 2-D is shown in Fig. 3, with large pitch size (Fig. 3(a)) and small pitch size (Fig. 3(b)). And the smallest reachable pitch size is limited by feature size (e.g. smallest nano structure) of nano fabrication. The structure within each pitch (period) is defined by the fill factor and thickness. Fill factor represents the percentage of period (e.g. length in 2D and area in 3D) filled by lens material. Theoretically, the phase coverage is increased with the increase of lens material’s refractive index and the thickness of phase shifter. Based on current fabrication techniques, the dimension of phase shifters is limited to certain feature size and thickness combination (e.g. maximum-achievable aspect ratio). As a result, the pitch size for conventional TiO2 based metalens is 350 nm with the thickness of 600 nm under 660 nm light [16]. This pitch size is near the limit (e.g. near the smallest-possible pitch size) for material with n = 2.4 to cover 2 π phase shift.
Fig. 3 schematic diagram for metalens (propagation phase based) cross-section. (a) Large pitch size. (b) Small pitch size.
In this study we are able to shrink the pitch size down to 220 nm under 685 nm light with silicon-rich silicon nitride developed. The phase distribution for phase shifters under 220 nm pitch with n = 2.74 and n = 2.4 is calculated through RCWA (Photon Design Ltd.) and is shown in Fig. 4(a). Both phase shifters are 600 nm thick with feature size of 60 nm, which indicating a fabrication-limited aspect ratio 10:1. As shown in Fig. 4(a), n = 2.74 can achieve a continuous full phase coverage under the fabrication-limited features while n = 2.4 material can only cover half of it.
Fig. 4 (a) Fabrication-limited phase coverage of 220 nm-pitch phase shifters. (b) Focus efficiency of simulated metalens (NA = 0.9) in 2-D with pitch size (period) ranging from 220 nm to 360 nm. (c) Field distribution of 2D metalens designed with 220 nm pitch size. (d) Field distribution of 2D metalens designed with 360 nm pitch size.
In order to evaluate the effectiveness of minimization of space discretization on focus efficiency, a series of propagation-phase-based metalens are designed in 2D with pitch size (period) ranging from 220 nm to 360 nm. These lenses are designed with high numerical aperture NA = 0.9 under incidence of 685 nm light. The thickness of the lens is fixed at 600 nm and the feature size is set around 60 nm. FDTD simulation is performed for all lenses under appropriate condition (small enough grid size and long enough simulation time is applied). The size of lens is fixed at 40 µm due to limited computing resource. And the focus efficiency is plot in Fig. 4(b).
As shown in Fig. 4(b), the focus efficiency increases from 44.8% to 75.8% with the decrease of pitch size from 360 nm to 220 nm. The field distribution of lens designed with 220 nm period and 360 nm period are shown in Fig. 4(c) and (d) respectively. The background intensity is magnified at same level in order to observe scattered light more clearly. As can be observed, Fig. 4(c) shows a smooth concentrating profile which is in clear comparison with Fig. 4(d). The lens designed with 360 nm pitch size shows strong resonance behavior at lens plane compared with 220 nm pitched lens. And the scattered light outside the focusing profile is notable in Fig. 4(d). This decrease of focusing performance of 360 nm pitched lens (compared with 220 nm lens) is a result of coarse space discretization. In this case, scattering and undesired resonance become more significant.
3. Lens fabrication and characterization
A grating based metalens with NA = 0.65 is designed by rotating the 2-D phase profile along its central axis with diameter of 40 µm. This lens is then fabricated with CMOS compatible nano fabrication techniques. The SEM picture at center area (5 × 5 µm) is shown in Fig. 5. The width of narrowest ring measured is around 60 nm.
The silicon rich silicon nitride (SiNx, n = 2.74) layer with thickness of 600 nm is deposited on the substrate of glass wafer as lens material. Then a 300 nm thick SiO2 layer is deposited on top of SiNx layer as a hard mask. Before E-beam lithography, a photoresist layer (ZEP520A) of 200 nm is spin coated on top of SiO2 layer. The 2-D lens pattern is written by E-beam and the pattern is created on the photoresist after development. The lens structure is then transferred into SiO2 hard mask layer by reactive ion etching (R.I.E.) and the residual photoresist is stripped by O2 plasma stripper. The pattern is finally transferred into silicon rich silicon nitride layer by another reactive ion etching process. The selectivity of SiNx/SiO2 is around 2.0 with the application of 20% of SF6 concentration during reactive ion etching.
The reason for our utilization of SiO2 layer as hard mask is because there is no E-beam photoresist available (at 200 nm thickness) to provide enough selectivity versus SiNx to achieve direct R.I.E. with 600 nm depth. While the thickness of E-beam resist is limited by the feature size around 60 nm. As a result, a two-step R.I.E. process with hard mask is necessary for the fabrication of this metalens.
The lens is then characterized through a laser based optical system consist of diode laser, quarter waveplate, linear polarizer, 3-axis motion mount, 50x objective, tube lens and camera. The schematic diagram of the characterization system is shown in Fig. 6(a)
Fig. 6 (a) Schematic diagraph for characterization system. (b) Characterized field distribution at the plane of focus. (c) Focus profile of the SiNx based metalens.
The characterized field distribution on the plane of focus is shown in Fig. 6(b) and the focus profile is plot in Fig. 6(c). The measured focus efficiency is around 42% with diffraction limited FWHM of 702 nm. The airy disk can be observed in Fig. 6(b). An airy disk can be observed from the image which is indicating good focus behavior. While 3-D FDTD simulation of this lens indicating a much higher focus efficiency of 79%. This difference of focus efficiency between simulation and characterization is mainly caused by the limitation of characterization system in two aspects: 1. The 50x objective applied (Olympus, LMPLFLN 50x) has NA of 0.5 which is considerably lower than our lens’s NA = 0.65. As a result, it is not able to catch the peak intensity of diffraction limited focus. 2. The resolution for motion system (Thorlabs, MT3A) is 0.5 µm, which is similar to the size of diffraction limited focus (532 nm). In this case, the capture of exact focal plane become extremely challenging.
4. Discussion
Emerging metalens is designed based on the discretization of space into finite number of pitches (periods) and the application of high-refractive index materials. While traditional metalens material such as TiO2 or GaN involves expensive and time-consuming deposition process. In addition, further shrinking of pitch size in pursuit of better performance is restricted by nano fabrication limitation and material’s refractive index.
In this study, we have developed a more cost-effective CMOS compatible silicon rich silicon nitride material for metalens fabrication with considerably higher refractive index. The pitch size of propagation-phase-based metalens can be shrinked to unprecedented 220 nm for the incidence of 685 nm light. A subwavelength grating metalens is designed and characterized for the prove of concept. The feature size and aspect ratio of the 220 nm pithed metalens demonstrated are similar to conventional TiO2 350 nm pitched metalens. This is enabled by the development of ultra-high refractive index SiNx thin film (n = 2.74) at 685 nm incidence.
The major drawback of this silicon rich silicon nitride material is the absorption under certain visible wavelength. As a result, it is not preferable for the design of achromatic metalens. On the other hand, this special dispersion relationship provides the integration of metalens with long-pass filter. In addition, with the continuous tunability of refractive index through PECVD, silicon rich silicon nitride films provide a new degree of freedom for the modification of phase through artificial phase shifters.
Funding
National Science Foundation (NSF-ECCS-1428069 and NSF-ECCS-1644731); University of Michigan (UM-041227).
Acknowledgments
The author would like to thank Vishva Ray for the help on E-beam lithography.
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