Nonresonant 104 Terahertz Field Enhancement with 5-nm Slits

Transmission of Terahertz (THz) electromagnetic wave through a substrate is encumbered because of scattering, multiple reflections, absorption, and Fabry–Perot effects when the wave interacts with the substrate. We present the experimental realization of nonresonant electromagnetic field enhancement by a factor of almost 104 in substrate-free 5-nm gold nanoslits. Our nanoslits yielded greater than 90% normalized electric field transmission in the low-frequency THz region; the slit width was 5 nm, and the gap coverage ratio was 10−4 of the entire membrane, 0.42 mm2. This large field enhancement was attributed to gap plasmons generated by the THz wave, which squeezes the charge cross-section, thus enabling very highly dense oscillating charges and strong THz field transmission from the nanoslits.

maintaining the uniform air gap throughout the length, as shown in the half-section schematic and top view presented in Fig. 1a. Nanoslits with gold film on the SiN x membrane were supported by the robust Si frame.
We first fabricated the nanoslits on the SiN x -coated Si substrate. Then, bulk Si was etched out through the back-side window, as presented in the schematic cross-sectional diagram in Fig. 1b. The fabrication details will be described in the methods section. Figure 1c shows a scanning electron microscopy (SEM) image of the top view of the nanoslits. The inset of Fig. 1c depicts the gap formation in the metal film, which was measured to be 5 ± 1 nm. In the optical image (Fig. 1d), light scattered through the 5-nm gap was clearly observed. The slit was not visible when the polarization was turned to 90°. The optical transmission of white light through the nanogap indicated the clear formation of the nanogap, and the diffracted light of the longer wavelength was transmitted, whereas the transmission was null when the light was polarized along the slit direction. Figure 2 presents a schematic diagram of the THz-TDS measurement setup. For this experiment, a mode-locked Ti: sapphire femtosecond laser source (central wavelength: 780 nm, pulse width: 130 s, and frequency: 80 MHz) was split to generate and detect THz radiation. One of the beams impinged on the biased GaAs semiconductor crystal and emitted broadband THz from the metallic antenna patterned on the crystal. Then, THz was collected by a Si hemisphere and plane polarized before it was focused on the sample. The p-polarized THz pulses were normally focused on the nanogap slit. The transmitted waves were collected using parabolic mirrors (NA = 0.32) and detected via electro-optic sampling using a (110)-oriented ZnTe crystal. The THz time domain spectra were mathematically transformed into frequency domain spectra (FDS) via Fourier transformation. A Wollaston prism split the x-and y-polarized beam by using a balanced photodiode detector for the electric field amplitude measurement. The TDS was obtained for both the transverse magnetic field (TM) and transverse electric field (TE) modes. Later, the TE mode was subtracted from the TM mode to obtain the THz field amplitude through the nanoslit. The measurement was performed in both TM and TE modes; later, the enhancement of the normalized field amplitude was calculated by subtracting the transmission signal in the TE mode from that in the TM mode. The TM and TE modes were measured by focusing the plane-polarized THz beam on the nanoslit sample at 0° and 90° by simply rotating the sample by 90°. Figure 3a shows TDS data obtained from the gold nanoslits and the free space transmission from the aperture area, 0.65 × 0.65 mm 2 . The peak transmission amplitude through an array of 5-nm slits, which occupied only 0.01% of the membrane area, was as high as 50%. In contrast, the direct THz transmission in the TE mode was less than 0.1% (not shown), thus indicating very strong field enhancement inside the slits. The transmitted THz time trace data demonstrated that the periods of fundamental oscillation passed through the nanoslits shifts 150 fs earlier than through the free space aperture. The shift indicated significant changes in the effective refractive indices. A typical reference and nanoslit sample used to measure TDS is presented on the right side of Fig. 3a (upper and lower optical micrographs). The lower left panel shows a schematic of a sample with 4 × 4 nanoslit membrane arrays in a 10 × 10 mm 2 Si substrate.
We obtained FDS, as shown in Fig. 3b, after generating the spectra by Fourier transformation of the TDS. Figure 3b shows the field amplitude versus the frequency of the THz transmission from the nanoslits (solid curve), which exhibits a similar trend as the free space (dotted curve), thus indicating non-resonance transmission. The red dashed curve indicates the average field amplitude of the transmission of 10 samples. Furthermore, the field amplitudes were normalized to the free space transmission and are presented in Fig. 3c. The graph shows that the normalized field amplitude decreased with increasing frequency without any resonance. The experimental data were directly fit to 1/f, which is represented by the red curve in the graph, where f is the frequency. The non-resonance behaviour was attributed to the very high length-to-width ratio (1.3 × 10 5 ) of our nanoslits, which caused them to behave as infinite nanoslits.
To calculate the field enhancement factor, we used diffraction theory 27 because our nanoslits were made of optically opaque gold, which has a dielectric constant that is ~106 times that of air in the THz range. We measured the far-field THz-TDS from free space and from the nanoslit sample with equal-sized apertures. The transmitted electric field from free space and from the nanoslit sample were E far freespace and E far slit ; then, the normalized amplitude, t(ν ), was defined as the ratio of these two measured amplitudes: ν = E E t( ) / far slit far freespace . Division t(ν ) by the aperture coverage, β , yields the field enhancement factor, F(ν ), in the nanogap region: F(ν ) = t(ν )β , where β = A slit / A freespace = w/p (for slit width, w, and period, p).
We observed a straight 1/f-dependent field enhancement factor, as shown in Fig. 3c, where f is the frequency. We used the fitting formula λ /π h, where λ is the wavelength, and h is the nanogap depth. The curve was fit to the data at h = 52 nm, which represents the effective thickness of the gold nanogap. The field enhancement was approximately twofold larger than the value given by λ /π h when we used the actual film thickness in the calculation. This observation indicated that the effective thickness of the metal film was almost half that of the actual thickness, in agreement with an asymmetric shape with only half of the metal thickness forming the 5-nm gap. This result agreed with findings previously reported by S. Han et al. 17 The plot demonstrates that the field enhancement decreases with increasing frequency, almost monotonously, with a 1/f dependency. Higher field enhancement was observed at the lower frequency, which was almost ten thousand at approximately 0.1 THz.

Figure 2. Schematic of THz time domain spectroscopy (TDS) measurement.
Femtosecond laser pulses were divided for THz generation and detection. Broadband THz generated by the biased GaAs emitter was plane polarized, collimated and then focused on the nanoslits, and the transmitted beam was detected with a ZnTe crystal. A Wollaston prism separated the beam into two orthogonal, linearly polarized beams for the electric field amplitude measurement using a balanced photodiode detector. The TDS was obtained for both the TM and TE modes after the TE mode was subtracted from the TM mode to obtain the THz field amplitude through the nanoslit.
In our setup, the minimum reliable frequency with which we could observe the drop in the field enhancement was 0.05 THz. We believe that the enhancement was saturated beyond this frequency. Thus, 1/f fitting was valid for the enhancement factor beyond the peak. The normalization was completed with the free space transmission through an aperture that was made with optically thick aluminium foil of the exact same size as the membrane. The experimental results of the 10 different samples are shown in the inset.
To explain the very high field enhancement through the nanoslit without the substrate, we simply assumed that the nanoslit was a nanocapacitor that enabled the storage of a large charge. When THz waves pass through the nanoslits, the sidewalls of the slits act as nanocapacitors, owing to the oscillating opposite charge carrier concentrated around them. The charge density is proportional to the incident field and inversely proportional to the gap width. For narrow gaps, the charge density creates a very strong electric field that enhances the signal by several orders of magnitude relative to the incident electric field. The charges at the edges of the metallic slit oscillate with the alternation of the incident electric field and re-radiate the electromagnetic wave, where the gap acts as an antenna. The re-radiated power depends on the charge density or the electric field at the gap. By measuring the re-radiated electromagnetic waves, we estimated the field enhancement factor at the slit. The first experimental realization of a nonresonant field enhancement factor of nearly 1,000 was previously demonstrated with a 70-nm-wide gold slit 21 . Our current measurement with 5-nm-wide nearly free-standing nanoslits is presented in Fig. 3c; the enhancement was nearly 10,000 at the lower frequency near 0.1 THz. Because both results demonstrated the same 1/f dependence, the decrease in the gap width markedly increased the enhancement factor, up to nearly 10 4 , at the frequency 0.14 THz. Although our field enhancement factor was less than half of the resonant transmission through a slot antenna array with a nearly 1-nm gap, as reported by X. Chen et al. 28 , it is the highest nonresonant enhancement factor ever reported in the scientific literature. Moreover, our nanoslit array was nearly transparent to the THz field, even though the metal thickness was half of the skin depth at that frequency, whereas the aforementioned work 28 reported only 60% transmission from the 5-nm gap. It is important to note that the skin-depth of gold at this frequency was 201 nm, which was 40 times that of our slit width and double the thickness of our gold film, thus indicating that electromagnetic waves were not only highly squeezed at the nanogap but also highly re-emitted through the nanogap. In our case, the gap width was a million times smaller than the wavelength; however, the length of the slit was of the same order as the wavelength.
In order to analyse the substrate effects in transmission and the field enhancement factor, we performed TDS measurements with nanoslits on substrate and without substrate. Our substrate was bulk silicon (Si 〈 100〉 , thickness: 300 μ m, resistivity: 10 ohm.cm), and we obtained the frequency dependent normalized field amplitude and field enhancement factor through the nanogap with and without substrate as presented in Fig. 3d. The open black squares (the amplitude was multiplied by 10 for comparability) and the open red circles represent the transmission through the nanogap with and without substrate, respectively. The normalization was done separately with . where n s and n g are refractive index of substrate and gap material, respectively. In our sample, the substrate is Si (n ≈ 3.417) and gap material is Al 2 O 3 (n ≈ 3.32). Hence, the nanoslit responses to an effectively smaller wavelength λ eff = λ 0 /n eff , where λ 0 denotes free space wavelength that reduces the transmission and correspondingly it yields a lower field enhancement 22 .

Nanoslit fabrication methods.
We fabricated the gold nanoslits on the large area SiN x membrane by using atomic layer lithography and standard microfabrication techniques on a 4" Si wafer. A schematic flow chart of the fabrication process is presented in Fig. 4. We first fabricated the ALD nanogap in the metal on the Si substrate and then used atomic layer lithography and plugged and lifted off the excess metal by etching the sacrificial layer 26 . Then, the back-side bulk Si was etched out, thus resulting in nanoslits on the SiO 2 /Si 3 N 4 membrane. Finally, Al 2 O 3 and the SiO 2 layer were etched out, thereby releasing the air gap gold nanoslits.
The process began with the thermal oxidation of a 4 inch Si wafer (〈 100〉 , p-type, 10 ohm.cm resistivity) to make 1-μ m SiO 2 as a passivation layer, and this was followed by low pressure chemical vapour deposition (LPCVD) to grow 1-μ m low-stress silicon nitride. After the first metal layer (Au: 100 nm) was deposited, patterning on the metal film was completed by photolithography (Fig. 4i), and this was followed by sacrificial layer/etch mask deposition (Fig. 4ii), lift-off (Fig. 4iii), and ion milling (Fig. 4iv). An Al 2 O 3 layer was deposited (Fig. 4v) by ALD at 250 °C on the sidewall of the Au film. In ALD, Tri-methylaluminium and water vapour were sequentially pulsed through the chamber, with N 2 purging after each injection, until 19 cycles yielded 5-nm-thick Al 2 O 3 . Subsequently, the second metal layer (Au 95 nm) was deposited on top of the first (Fig. 4vi), and the excess 2 nd layer was lifted off (Fig. 4vii) by etching the sacrificial layer. The lift-off of the second layer removed excess metal and opened up the ALD layer in between the first and second layers. 300-nm-thick aluminium was used as both an etch mask for ion milling and a sacrificial layer to lift off the excess 2 nd layer on top of it. The Al etchant (1 M KOH, or any strong alkaline solution at room temperature) entered through the intentionally uncovered Au area, etched the Al, and lifted off the excess 2 nd layer Au film. The etchant also slightly etched Al 2 O 3 , and ultra-sonication and cleaning in acetone, methanol and deionized (DI) water were performed to remove residues at the nanogap. Further surface polishing of the nanogap was carried out with an almost vertical (85°) Ar ion milling process.
The back-side bulk silicon was selectively etched out (Fig. 4ix) through the pre-defined window by a tetramethylamoniumhydroxide (TMAH 20 wt%) solution at 90 °C, after the deposition of the protective SiO 2 layer (Fig. 4viii) on the top of the nanogap surface. The SiO 2 protected the nanogap and supported the etching of Si by preventing the metal-coated Si substrate from forming as an etch shield. The protective layer was later etched out by dipping it in HF solution, which also removed the bottom SiO 2 layer (Fig. 4x). Dipping the sample in HF also etched the alumina between the metal, thereby exposing the air gap in the metal. To release the fully free-standing nanogap metal membrane for material transportation through the slits, the remaining thin Si 3 N 4 membrane was also etched out with reactive ion etching (RIE). In most cases, after etching the nitride membrane, the gold membrane became unstable and collapsed. The nanogaps either collapsed or, where the bridge-like structure survived, widened. Thus, we kept the robust nitride membrane to support the metallic nanoslits and increase the stability of the nanogap for the THz experiments.

Conclusion
A large nonresonant electromagnetic field enhancement was experimentally realized with practically infinite gold nanoslits. The field enhancement was almost 10 4 in the lower THz frequency regime without any resonance peak, and then it monotonously decreased, following the 1/f curve. The large field enhancement in the nanogap region can be explained by the nanocapacitor model, and is formed as a result of the excitation of SPPs when the THz field is incident on the metal surface. The non-resonance effect was attributed to the practically infinite (length-to-width ratio ~10 5 ) and substrate-free nature of the nanoslits. The substrate-free nanoslits were fabricated using plug-and-lift-off and standard Si microfabrication techniques in which the gap width and uniformity were determined by atomic layer lithography. The yield of such an ultra-thin nanoslit membrane depends on the strength of the metal microribbon, with negligible deformities due to temperature and pressure. The developed substrate-free nanoslits may be useful in studies of gap plasmonics, quantum tunnelling, nonlinear optics, and nanophotonics, for which high field enhancement is important.