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Colossal Terahertz Field Enhancement using Split-Ring Resonators with a Sub-10 nm Gap Nayeon Kim, Sungjun In, Dukhyung Lee, Jiyeah Rhie, Jeeyoon Jeong, Dai-Sik Kim, and Namkyoo Park ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.7b00627 • Publication Date (Web): 02 Nov 2017 Downloaded from http://pubs.acs.org on November 5, 2017

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Colossal Terahertz Field Enhancement using Split-Ring Resonators with a Sub-10 nm Gap Nayeon Kim1,2, Sungjun In3, Dukhyung Lee*,2, Jiyeah Rhie2, Jeeyoon Jeong2, Dai-Sik Kim2, and

Namkyoo Park3 1

ASML Korea, 25 SeokWoo-Dong 445-170, Hwasung-Si, Gyunggi-Do, Korea

2

Department of Physics and Astronomy and Center for Atom Scale Electromagnetism, Seoul National

University, Seoul 151-747, Korea

3

Photonic Systems Laboratory, School of EECS, Seoul National University, Seoul 151-744, Korea

E-mail: [email protected]

Abstract

Terahertz (THz) nanogap structures have emerged as versatile platforms for THz science and applications by virtue of their strong in-gap field enhancements and accompanying high levels of sensitivity to gap environments. However, despite their potential, reliable fabrication methods by which to create THz structures with sub-10 nm gaps remain limited. In this work, we fabricated THz split-ring resonator (SRR) arrays featuring a sub-10 nm split gap. Our fabrication method, involving photolithography, argon ion milling, and atomic layer deposition, is a high-throughput technique which is also applicable to the fabrication of other THz structures with sub-10 nm gaps. Through THz-time domain spectroscopy and a numerical simulation, we identified the fundamental magnetic resonances of the nanogap SRRs, at which the electric field enhancement factor is experimentally estimated to be around 7000. This substantial field enhancement makes SRRs with a sub-10 nm gap suitable for the study of high-field phenomena and related applications.

Keywords: terahertz, nanogap, split ring resonator, field enhancement, atomic layer deposition

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Plasmonic nanogap structures have received considerable amounts of attention due to their ability to squeeze an electric field into a small volume and implement a high field environment.1-4 In the THz regime, nanogap structures have found a broad range of applications, including in switches5 and filters6 as well as in spectroscopy,7 refractive index engineering,8 and second harmonic generation.9 One of the best known gap structures is the split-ring resonator (SRR) proposed by Pendry et al., for which the effective magnetic permeability is unattainable with naturally existing materials. Pendry suggested strong electrostatic energy concentration and accompanying enhanced nonlinear effects in the split-gap region at the fundamental magnetic resonance.10 Due to the strong field enhancement near the gap, SRRs have been used to detect single molecular monolayers11 and organic materials12,13 and to study insulator-to-metal transitions in vanadium dioxide thin films.14 Further, SRRs are excellent tools when used to study nonlinear phenomena such as second harmonic generation.9,15,16

Given that a narrower gap width implies greater field enhancement inside the gap due to the stronger capacitive coupling,17,18 the field enhancements and degrees of nonlinearity of SRRs with sub-10 nm gaps are likely to be colossal. However, despite the fact that the properties of SRRs in the THz regime have been studied and applied in many areas, THz applications which make use of a sub-10 nm gap in a SRR are nonexistent given the extreme difficulties in creating a sub-10 nm gap with high uniformity on a length scale of tens of micrometers. Although electron or focused-ion-beam lithography can provide resolutions of less than 10 nm, the accompanying small field of view make the fabrication process in both cases time-consuming and impractical. Including SRRs, THz nanogap structures are also associated with this fabrication problem. For this reason, SRRs with a sub-10 nm gap have been fabricated only for optical frequencies.19 Recently, a simple fabrication method known as atomic layer lithography was developed for nanogap ring structures to realize nanometer-scale widths and wafer-scale uniformity.20 Advanced THz studies in relation to field enhancements21-23 and nonlinear quantum tunnelling24,25 have demonstrated nanogap ring structures which highlight the advantages of a sub-10 nm gap in the THz regime.

Here, we demonstrate the high-throughput fabrication of a THz SRR array with a sub-10 nm gap via standard photolithography, argon ion milling and atomic layer deposition (ALD). This method is readily applicable to the fabrication of other THz structures with sub-10 nm gaps as well. We measured the THz transmission spectra of SRR arrays with sub-10 nm gaps using THz-time domain spectroscopy (TDS) and then numerically simulated the transmission spectra, charge distributions, and electric field enhancements in order to investigate the 2


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resonance behavior in the THz regime. From the experiment results, the electric field enhancement factor was estimated to be around 7000 and the numerical simulation shows that the enhancement factor can reach up to 22100 for SRRs with a 10 nm gap.

Figure 1(a) shows a schematic of the unit cell of the SRR array with the sub-10 nm gap. The lattice periodicity is 100 µm, and each SRR has a side length of 80 µm and a line width of 15 µm. We fabricated two different SRR arrays with gap widths of 5 nm and 10 nm. These dimensions make the first and second resonances of the frequency range from 0.1 THz to 1.5 THz, in which range THz-TDS operates. For each sample, 3600 SRRs are fabricated in an area of 6 mm × 6 mm on a quartz substrate.

Figure 2 illustrates the fabrication process of the SRRs. First, a rectangular ring array with a sub-10 nm gap is fabricated using atomic layer lithography, as described in the literature (ref 23, steps 1-6 in Figure 2). In this case, a Cr/Au (3 nm/50 nm) film is deposited onto a quartz substrate by e-gun evaporation. On top of the Au film, a Cr/Al (30 nm/150 nm) rectangular array is patterned by photolithography. Using the pattern as a mask, Ar ion-beam milling is conducted and the surface of the sample is coated with aluminum oxide (Al2O3) less than 10 nm thick using ALD. After depositing a second layer of Cr/Au (3 nm/40 nm), the ion milling mask is removed using a KOH solution and a chromium etchant (CR-7). In this manner, we obtain nanogaps consisting of an ALD Al2O3 layer whose thickness is controlled to a nanometer level of accuracy with excellent uniformity on the wafer scale. Because the ring array sample features mechanical stability that can withstand harsh sonication23, it is suitable for post-processing to yield a more complex structure. The sample is then rotated by 90 degrees and the previous steps are repeated, apart from the ALD step, to obtain an array of slots which are less than 10 nm wide (steps 7-10 in Figure 2). Finally, the SRR array with a sub-10 nm gap is obtained from the slot array by the patterned milling of the Au film (steps 11-13 in Figure 2): An Al2O3 ion milling mask is patterned as a square-ring array by photolithography. After the final ion milling of Au, the sample is immersed in a KOH solution for 60 minutes for the chemical etching of the Al2O3 mask. The remaining Au pattern then becomes the square SRR array. The fabrication of other complex THz structures with sub-10 nm gaps is also possible by using different milling patterns. Figure 1(b) shows scanning electron microscope (SEM) images of the fabricated 5-nm-gap SRRs. The figure on the right in Figure 1(b) clearly demonstrates that the nanogap line is well formed without a short circuit. In the cross-sectional SEM images in Figures 1(c) and (d), gap widths of 5 nm and 10 nm are confirmed.

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To study the terahertz resonances of the sample, we measured the transmission spectra using THz-TDS. The normally incident THz wave was polarized perpendicularly to the gap, as illustrated in the inserts of Figures 3(a) and (b). Details of the THz source and experimental setup are given in the Supporting Information (Figures S1 and S2). The experimental results for the SRRs with 5 nm and 10 nm gaps are displayed in Figure 3(a), depicted by the blue and red lines, respectively. For comparison, the results for a gold square-ring array with identical dimensions but with no gap are included, as represented by the black dashed line.

There are two resonance dips at 0.25 THz and 1.1 THz for the 10-nm-gap SRRs in the THz range. Given the fact that the square-ring array has no corresponding resonance, the lowest resonance at 0.25 THz is identified as the fundamental magnetic resonance, where the current circulates on the SRR. At the fundamental resonance, the circulating current generates a magnetic flux inside the ring and opposite charges are accumulated on the facing metal surfaces of the split gap. Therefore, the nanogap SRRs can be regarded as RLC circuits. On the other hand, being equivalent to an RL circuit, a ring with no split gap has no corresponding resonance. Polarization dependence of the lowest resonance reassures that it is the fundamental magnetic resonance indeed. As shown in Figure S3 in the Supporting Information, the lowest resonance at 0.25 THz does not appear for the incident polarization parallel to the gap. This is because charges of the same sign are accumulated on the metal surfaces of the gap for the parallel polarization while the fundamental resonance needs capacitive coupling between opposite charges. As the resonance frequency for an RLC circuit is fres=1/(2π(LC)1/2), SRRs with a narrower gap have a lower fundamental resonance frequency (Supporting Information, Figures S4). However, due to lowfrequency noise, the fundamental resonance is unclear and only the second resonance at 0.96 THz manifests for the SRRs with a 5 nm gap.

A numerical simulation (COMSOL Multiphysics 5.1) was conducted to determine the physical details of the resonances. The simulated transmission spectra displayed in Figure 3(b) show good agreement with the experimental spectra in terms of the overall shape. Sharp fundamental resonances are identified for the SRRs with both the 5 nm and 10 nm gaps in the simulation. The slight resonance frequency differences and the worse quality factors in the experiment can be attributed to certain width variations, residual Al2O3, or damage to the fabricated gaps. It is important to note that the resonance frequencies depend sensitively on the gap width difference of only 5 nm, which is 16000 times shorter than the side length, at 80 µm. When the gap width is broadened from 5 nm to 10 nm, the first and second resonance frequencies become shifted by ~0.1 THz. This means that substantial portions of the resonance energies are concentrated in the split gap region due to the 4


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capacitive coupling.

Figure 3(c) displays the simulated surface charge distributions at the first and the second resonances. Because the incident polarization perpendicular to the gap dictates opposite charges to accumulate on the facing metal surfaces of the gap, the charge distributions at the resonances have an odd number of nodes26,27. Namely, one node exists for the fundamental resonance and three nodes for the second resonance, as shown in Figure 3(c). A distinctive feature of the nanogap SRRs is the closely accumulated opposite charges around the gap (log scale representations clearly show this close accumulation. see Figure S5 in the Supporting Information). This close accumulation makes the charge distribution of the nanogap SRRs at the second resonances similar to that of the square ring at its first resonance and thus results in the similar transmission dips. From the high charge densities around the gaps, we can expect colossal electric field enhancements in the gaps at the fundamental resonances. At the fundamental resonance of the 10-nm-gap SRRs, the surface charge density around the gap becomes nearly 2 × 10−7 C/m2 for an incident field of 1 V/m (see Figure S4 in the Supporting Information), which is translated into a field enhancement of 22000 by the relation E = σ ε 0 .

The in-gap electric field enhancement, obtained by a numerical simulation, is plotted as a function of the frequency in Figure 4(a). At the first resonances, the field enhancement reaches ~11300 and ~22100 for the SRRs with the 5 nm and 10 nm gaps, respectively. Both field enhancements are one order of magnitude higher than those of slit arrays with the same widths (inset of Figure 4), demonstrating the merit of the SRR structure. The higher field enhancement for the 10-nm-gap SRRs is contrary to what is expected for simple slit structures. In a slit structure, capacitive coupling between the metal films makes more charges to be delivered to the facing surfaces, so that a narrower gap width lead to a higher field enhancement.28 However, because excitation of the fundamental magnetic resonance of a SRR depends on the broken symmetry introduced by the split gap,29 SRRs with a broader nanogap can have a higher excitation efficiency and thus a higher field enhancement. Further optimization of the SRR dimension parameters will yield greater field enhancement. As shown in the crosssectional electric field distribution presented in Figure 4(b), the electric field is strongly confined inside the gap. Therefore, SRRs with sub-10 nm gaps can support high-field interaction exclusively with the gap environment.

In addition to the simulation study, we experimentally estimated the enhancement factor for the fabricated 10nm-gap SRRs at the fundamental resonance because of the considerable difference in the transmission dip between the experiment and the simulation. The in-gap field enhancement cannot be obtained directly from far 5


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field measurements, so that we estimated the enhancement factor by two methods with different assumptions. The first method is to find out the incident electric field strength when the in-gap electric field reaches the breakdown field strength. The second method is to attribute the difference in transmitted amplitude between the SRR array with a 10 nm gap and the square ring array to the in-gap field and apply diffraction theory. Details of the two methods are given in the Supporting Information (Figures S6 and S7). The two methods give consistent results, from which we can regard the field enhancement factor as ~7000.

In summary, we fabricated THz SRR arrays with sub-10 nm gap widths using a combination of photolithography, argon ion milling, and ALD. Our fabrication method is a high-throughput process which covers the entire substrate. The gap width is determined by the ALD Al2O3 thickness, with precision levels therefore on the nanometer scale. Using the proposed method, other gap antenna structures, such as bowtie antennas or plasmonic oligomers, can also be readily fabricated with sub-10 nm gaps. The THz resonance behavior of the nanogap SRRs and the gap width dependence were investigated using THz-TDS and numerical simulations. The experimental results and those of the simulation are in accordance with regard to the transmission spectra and provide evidence that the fundamental magnetic resonances are supported by the sub10 nm gaps. The numerical simulation indicates that the SRRs have colossal in-gap electric field enhancements of 11300 and 22100 with the 5 nm and 10 nm split gaps, respectively, at the fundamental resonances and the experimental estimation gives an enhancement factor around 7000 for the 10-nm-gap SRRs.

The SRR arrays with sub-10 nm gaps demonstrated here are promising platforms for high-field experiments. With the SRR structures, high electric fields can be applied to materials in the sub-10 nm gaps at the designed frequencies, even with a low-power THz source. Quantum dots,30 two-dimensional materials,24 or phase-change materials31,32 placed in the nanogaps are expected to show novel phenomena driven by the high THz fields, enriching the functionalities of SRR-based metamaterials.

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Supporting Information

Experimental setup for the THz transmission measurement; Transmission amplitudes in time domain and frequency domain before normalization; Transmission spectra for the incident polarization parallel to the gap; Equivalent RLC circuit model; Surface charge distributions at the resonances visualized on a log color scale; Methods for field enhancement estimation from the experimental data.

Author Information

The authors declare no competing financial interests.

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP: NRF-2015R1A3A2031768, NRF-2014M3A6B3063708, NRF-2008-00580) (MOE: BK21 Plus Program-21A20131111123).

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Figure Legends

Figure 1 (a) Schematics of an array of SRRs with sub-10 nm gaps and a unit cell. (b) SEM images of nanogap SRRs. Left: a SRR array. Middle: a single SRR. Right: the 5 nm gap of a SRR. The horizontal lines on the side arms are due to ion milling debris, not the nanogaps. (c) Cross-sectional image of the 5-nm-gap SRR. (d) Crosssectional image of the 10-nm-gap SRR.

Figure 2 Schematics of the high-throughput fabrication process used to create the SRR array with a sub-10 nm gap.

Figure 3 Experimental and simulated results from a 5-nm-gap SRR array, a 10-nm-gap SRR array, and a squarering array with no gap. (a) Measured transmission spectra. (b) Simulated transmission spectra. (c) Surface charge distribution (in C/m2 with an incident field of 1 V/m2) for the first resonances (0.15, 0.25, and 1.05 THz for 5 nm, 10 nm, and no gap cases, respectively) and the second resonances (correspondingly for the 1.1, and 1.2 THz for 5 nm, and 10 nm cases).

Figure 4 (a) Electric field enhancement averaged over the gap volume versus the frequency. (b) Cross-sectional electric field distribution at half of the height of the 10-nm-gap SRR for the first resonance.

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