Letter pubs.acs.org/journal/apchd5
Colossal Terahertz Nonlinearity in Angstrom- and Nanometer-Sized Gaps Sanghoon Han,† Joon-Yeon Kim,† Taehee Kang,† Young-Mi Bahk,† Jiyeah Rhie,† Bong Joo Kang,‡ Yong Seung Kim,§ Joohyun Park,∥ Won Tae Kim,‡ Hyeongtag Jeon,∥,⊥ Fabian Rotermund,‡ and Dai-Sik Kim*,† †
Department of Physics and Astronomy and Center for Atom Scale Electromagnetism, Seoul National University, Seoul 08826, Korea Department of Physics and Department of Energy Systems Research, Ajou University, Suwon 16499, Korea § Graphene Research Institute and Department of Physics, Sejong University, Seoul 143-747, Korea ∥ Department of Nanoscale Semiconductor Engineering and ⊥Division of Materials Science and Engineering, Hanyang University, Seoul 04763, Korea ‡
ABSTRACT: We investigated optical nonlinearity induced by electron tunneling through an insulating vertical gap between metals, both at terahertz frequency and at near-infrared frequency. We adopted graphene and alumina layers as gap materials to form gap widths of 3 Å and 1.5 nm, respectively. Transmission measurements show that tunneling-induced transmittance changes from strong fields at the gaps can be observed with relatively weak incident fields at terahertz frequency due to high field enhancement, whereas nonlinearity at the near-infrared frequency is restricted by laser-induced metal damages. Even when the same level of tunneling currents occurs at both frequencies, transmittance in the terahertz regime decreases much faster than that in the near-infrared regime. An equivalent circuit model regarding the tunneling as a resistance component reveals that strong terahertz nonlinearity is due to much smaller displacement currents relative to tunneling currents, also explaining small nonlinearity of the near-infrared regime with orders of magnitude larger displacement currents. KEYWORDS: terahertz nonlinearity, quantum tunneling, angstrom gap, metal−insulator−metal, graphene, aluminum oxide
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samples. In metal−graphene−metal structures tunnelinginduced transmission reduction of 97% through van der Waals gaps was presented. 17 In metal−alumina−metal structures tunneling through relatively wide gaps up to 10 nm was demonstrated.18 These are due to funneling properties of terahertz waves in metallic gap structures with sub-skindepth thickness by which an intense electric field can be concentrated inside the gap,21−24 causing electron tunneling. Here we compare tunneling-induced transmission changes through metal−insulator−metal structures at terahertz and near-infrared frequencies. Graphene and alumina layers were selected as the insulating spacers for angstrom- and nanometersized gaps, respectively. Introducing an equivalent circuit model with calculations of tunneling currents, we demonstrate how tunneling can have a much stronger effect on the terahertz transmission than near-infrared transmission. Figure 1a shows schematics of electron tunneling in metallic gap structures. When light impinges on the structure, currents are induced (Jinduced) along the metal surfaces and also inside
n a nanometer-scale or a subnanometer-scale world, the local classical electrodynamics is no longer applicable. Instead, the nonlocal hydrodynamics1−4 or a description related to quantum tunneling5,6 is needed to explain some of the phenomena. In particular, tunneling gives rise to strong optical nonlinearity, which is a foundation of many optical devices. As the optical devices become smaller and smaller, researchers have devoted their efforts to elucidating the optical implications of the tunneling phenomenon theoretically and experimentally. Most of the works were studied at high frequencies of visible or nearinfrared range.5−9 On the other hand, tunneling at the lowfrequency regime such as terahertz waves has not been much explored. The works mostly have been studied with the aids of a dc bias voltage or near-infrared pulses,10−14 and recently a few works have studied optical tunneling at terahertz frequencies.15−18 For quantitative investigations at terahertz frequencies, a sample is required to be long enough to interact with the incident wave and, simultaneously, to have a well-defined region narrow enough for electrons to tunnel through. As fabrication techniques based on deposition method and photolithography were developed, it became possible to make a sample that has a vertically aligned gap with a few nanometer width and a millimeter scale length.19,20 Previously we reported on terahertz quantum plasmonics using nano and angstrom gap © XXXX American Chemical Society
Special Issue: Nonlinear and Ultrafast Nanophotonics Received: February 14, 2016
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Figure 1. (a) Schematics of the electron tunneling in metallic gap structures. Induced currents Jinduced by incident fields make charges accumulate along gap edges, forming capacitor-like, strong electric fields at the gap. When enough fields are applied, some parts of the charges tunnel through the gap, resulting in Jtunnel so that displacement current Jd, electric fields at the gap, and also transmittance decrease. Two kinds of samples were prepared. One is a Cu−graphene−Cu structure that has a period p = 200 μm, effective gap width w = 3 Å, thicker metal thickness t1 = 300 nm, thinner metal thickness t2 = 130 nm for terahertz (THz) measurement and 200 nm for near-infrared (NIR), and relative permittivity εgap = 3. The other is a Au−alumina− Au structure with p = 20 μm, w = 1.5 nm, t1 = 300 nm, t2 = 200 nm, and εgap = 2.89. (b) Cross-sectional transmission electron microscopy images of the graphene gap (left) and the alumina gap (right). The graphene sample with double van der Waals gaps between copper and carbon atoms is approximated by a single gap of 3 Å.
Figure 2. Experimental transmission setups. (a) Terahertz timedomain spectroscopy system based on a 1 kHz regenerative amplifier. HWP: half-wave plate, BS: beam splitter, LN: prism-cut lithium niobate (LiNbO3) crystal for THz generation. (b) NIR transmission setup. CCD: charge coupled-device detector, APD: avalanche photodiode for detection.
spectroscopy (THz-TDS) with high power terahertz pulses, which were generated via pulse-front-tilted optical rectification in a prism-cut LiNbO3 crystal using a 1 kHz Ti:sapphire regenerative amplification system.27 The maximum incident field was 200 kV/cm at the focal position of the samples, and field intensity was controlled using a pair of wire grid polarizers. Transmitted fields were collected with parabolic mirrors and then detected by electro-optic sampling28 using GaP or ZnTe crystals. The near-infrared measurement setup is described in Figure 2b. We performed transmission measurement using a femtosecond Ti:sapphire laser in which the center frequency, repetition rate, and pulse width are 830 nm, 80 MHz, and 150 fs, respectively. The laser beam was focused to samples with ∼1 μm diameter spot size via an objective lens. A wave plate together with a polarizer was used to alter the intensity of the incident field. Transmitted fields were guided to an avalanche photodiode for detection. In both setups polarizations of the incident waves were perpendicular to the long axis of the metallic gaps.29 Figure 3 shows transmitted peak power versus incident power for both terahertz and near-infrared frequencies at the focal region. The peak power densities are estimated from the peak position of the temporal pulse profile with measured average power, repetition rate, beam spot size, and pulse width. The temporal pulse profile can be obtained by the square of measured time traces of electric fields for terahertz frequency, and is approximated with a Gaussian function for near-infrared frequency. Shown in Figure 3a, terahertz nonlinearities are obvious for both structures. As the incident power increases, the transmitted power deviates further away from the linear regime (dashed line) with no tunneling. On the contrary, few nonlinearities are seen in the near-infrared regime for both the nanogap and the angstrom gap samples (Figure 3b). It is noted that before damage occurs at the maximum power, the response
the metal if the metal thickness is thinner than skin depth. By these currents charges move to gap edges and are accumulated to form enhanced electric fields inside the gap. The gap between metals acts like a capacitor, and displacement currents Jd are developed by oscillation of the induced charges.21 Starting with an incident power low enough to generate no tunneling current, Jd equals Jinduced. As the power increases, electric fields inside the gap become higher and a portion of the induced charges passes through the gap (Jtunnel). Consequently, accumulated charges Q, Jd, and the fields inside the gap are reduced. Because Jinduced is determined by the incident field intensity and the transmitted electric field through the structure in far-field region is proportional to the gap electric field via the Kirchhoff integral formalism,25,26 tunneling reduces transmittance, which is defined as the ratio of the transmitted power to the incident power. Conversely, we could observe the tunneling between the gaps via measuring a decreasing transmittance with an increasing incident power. We prepared two kinds of samples using deposition and exfoliation techniques.19,20 One is a Cu−graphene−Cu slit array structure for effectively 3 Å sized gaps, and the other is a rectangular ring-shaped array of Au−alumina−Au structures for 1.5 nm sized gaps. Cross-sectional transmission electron microscopy images of the gaps are shown in Figure 1b. Both types of samples17,18 were used in this study. To examine tunneling from measurements of the optical transmission at terahertz and near-infrared frequencies, two experimental setups were used. For terahertz measurement, as presented in Figure 2a, we performed terahertz time-domain B
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ratio between the maximum transmitted field amplitude with and without the sample: Egap = E0τ/β where E0 is the incident electric field on the sample and β the coverage ratio of the gap area to the illuminated area.25,26 For the graphene gap sample presented in Figure 4a, the near-infrared field directly through the metal layer is comparable to that through the gap with unknown phase differences,30 making it necessary to use an average value for the plot (blue-filled squares).31 Egap reaches ∼1.5 V/nm, showing unchanged transmittance in spite of the high incident fluence nearing the damage threshold. In stark contrast, Egap in the terahertz regime can reach up to >10 V/nm owing to high electric field enhancement at the narrow gap,19,32 causing a serious decrease of the transmittance accompanied by larger tunneling currents (red-filled circles). In the case of alumina gaps shown in Figure 4b, Egap is formed up to ∼5 V/ nm at both frequencies, but nonlinear features are only exhibited at the terahertz frequency. Again, the near-infrared regime suffers from much smaller nonlinearity despite expected tunneling currents equaling that of the terahertz regime. For a theoretical modeling we introduce equivalent circuits depicted in Figure 4c and calculate tunneling conductivities. For a graphene gap at terahertz frequencies, where the angstrom gap length can be considered infinite, the equivalent circuit is RC in nature. At near-infrared frequencies, all samples are considered RC due to a relatively small wavelength and beam spot size compared to the gap lengths. The alumina gap at the terahertz frequency, with clear resonance from the 100 μm perimeter of the rectangular ring in the array sample, is regarded as an RLC circuit. In the RC circuits capacitance C is determined by structural dimensions and resistance R is calculated from tunneling conductivity, which depends on Egap: C = ϵ0ϵgaptl/w, R = w/(σttl), where w, l, t, ϵ0, ϵgap, and σt are gap width, gap length, effective metal thickness, vacuum permittivity, relative permittivity of the gap material, and tunneling conductivity, respectively. For the RLC circuit, additional inductance L, which can be calculated from the measured resonance frequency fres = 1/(2π LC ), is added to the RC circuit in parallel. To determine R values, we calculate tunneling conductivities based on potential barrier concepts assuming a square quantum barrier with image potential.33 Once each component of the circuits is determined, transmittances can be calculated from proportionalities between incident fields and induced currents, and between Egap and E0τ: T/T0 = |Z/Z0|2 where Z and Z0 are overall impedances at a specific incident power and at the lowest incident power (Z = [−iωC + 1/R]−1 for the RC circuit and Z = [−iωC + 1/R − 1/ (iωL)]−1 for the RLC circuit). Calculated transmittances are plotted as solid lines in Figure 4a and b. Barrier height Vb = 3 eV, w = 3 Å, l = 2 mm, t = 130 nm, and ϵgap = 3 were used for the graphene gaps,17,34,35 and Vb = 3.7 eV, w = 1.5 nm, l = 40 μm, t = 200 nm, and ϵgap = 2.89 for the alumina gaps.18,36 In the calculation for terahertz transmittance of the alumina gaps a frequency of f = 0.305 THz, which is near f res = 0.3 THz, was set. In the graphene gap, the center frequency of the TDS systems (f = 0.4 THz) was used for the terahertz regime and f = 360 THz for the near-infrared. For the graphene gaps, calculations predict the correct trend of much larger nonlinearity for the terahertz frequency, right from the beginning of the incidence power (Figure 4a). For the alumina gap, owing to its much larger gap width relative to the graphene gap, both terahertz and near-infrared calculation results stay linear until Egap ≈ 3.5 V/nm, after which the
Figure 3. Transmitted peak powers for different incident peak powers at the focal region in (a) THz and (b) NIR measurements. Data for an alumina gap of 1.5 nm width and graphene gap of 0.3 nm width are plotted as blue-filled squares and red-filled circles, respectively. Solid lines are β-spline connections for visualization. Each dashed line means linear regime with no additional tunneling. Tunneling-induced transmission reduction is observed at only THz frequencies.
is both linear and repeatable/hysteresis free, for both samples. In other words, few nonlinear responses are seen until the sample gets damaged. It is worth noting that the graphene gap and the alumina gap samples endure up to different incident powers when compared with each damage threshold of the metals. The graphene sample started to melt at the incident peak power density of ∼10 kW/μm2, at which a bare Cu film also got damaged. On the other hand, an incident peak power density of >6.5 kW/μm2, which destroyed the alumina gap sample, did not alter the bare gold film. This indicates that tunneling was not observed at the near-infrared frequency even when a breakdown between Au−alumina−Au gaps occurred whereby significant tunneling was expected to be in existence when compared with nonlinear responses in the terahertz regime. If the same amplitude of electric field is applied in the gap, the same amount of instantaneous tunneling current will flow at both terahertz and near-infrared frequencies. Clearly, the high-frequency optical pulse suffers from detection problems regarding tunneling-induced nonlinearity, given the same tunneling currents for terahertz and near-infrared regimes. To estimate how tunneling affects terahertz transmission and near-infrared transmission differently, the measured transmission data should be recalibrated for the electric field inside the gaps. Calculated transmittances T as a function of the gap electric field are plotted in Figure 4a and b. Transmittance values were normalized by that of the lowest power data for each plot. Electric fields inside the gaps, Egap, were estimated from the normalized transmitted amplitude, τ, defined as the C
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Figure 4. Normalized transmittance T/T0 as a function of electric field at the gap Egap for (a) the graphene gaps and (b) the alumina gaps. Experimental data are plotted as symbols, and theoretical calculations as solid lines. In (a) Egap induced by NIR the incident field is restricted by laserinduced damage of the metals. However, the THz field can exert an Egap up to >10 V/nm due to high field enhancement. In (b) the THz transmittance shows a sensitive response to the tunneling, while the NIR transmittance is little changed even with a 5 V/nm Egap. (c) Equivalent circuits of the gap structures. The graphene gaps at THz and NIR and the alumina gap at NIR are regarded as RC circuits, and the alumina gap at THz as an RLC circuit. Capacitance C is calculated from structural dimensions, and inductance L from the measured resonance frequency. Resistance R is determined by tunneling conductivity. (d) Conductivities of displacement currents σd and tunneling currents σt for the graphene gaps when Egap = 1.5 V/nm is applied. σd is proportional to frequency, while σt keeps the same value. THz transmission is sensitive to the tunneling because σt is much larger than σd.
terahertz regime shows much stronger nonlinearity (Figure 4b). These theoretical results are in good agreement with experiments. The earlier onset of experimental terahertz nonlinearity is most likely due to the gap width variations inherent in our sample preparation. We now look into the relative magnitudes of tunneling currents and displacement currents, to elucidate the difference between terahertz and near-infrared regimes, to gain fundamental physical insights. We plotted conductivities of displacement currents and tunneling currents in Figure 4d, which were calculated from the theoretical model for the graphene gaps with Egap = 1.5 V/nm, the maximum electric field inside the gap in the case of experimental near-infrared driving. Under a fixed Egap, tunneling current densities and also tunneling conductivities σt keep the same value, respectively, in all frequency ranges if we neglect the tunneling time on the order of a few femtoseconds.37,38 However, conductivities of displacement currents σd are proportional to the frequencies (σd = −iωϵ0ϵgap). As a result, σt has a much larger value than σd at the terahertz frequency, so that terahertz transmission is sensitive to variations of the tunneling, while near-infrared transmission is scarcely affected by the tunneling because σt is always much smaller than σd. This analysis is consistent with an existing theory for plasmonic nanostructures in which nonlocal effects are under considerations anticipating lower contributions of quantum tunneling at higher frequency.1
In conclusion, we have demonstrated tunneling-induced nonlinearities of metal−insulator−metal structures in terahertz and near-infrared ranges. To do this, two kinds of samples were prepared. One is a Cu−graphene−Cu slit that has an effectively 3 Å wide gap, and the other is a rectangular ring shaped Au− alumina−Au slot that has about a 1.5 nm gap width. Transmission measurements showed an obvious dependence of transmittance on the incident power at terahertz frequencies. On the other hand, transmittance of a near-infrared wave was little affected by the power until sample damage occurs. We also showed from the equivalent circuit model with a tunnelinginduced resistance that terahertz transmission is much more sensitive to the tunneling than near-infrared transmission even when the same field intensity is applied at the gaps. This is because much fewer displacement currents are required for achieving the same field intensity and tunneling in the case of the terahertz regime. Unlike in harmonic generations in transparent nonlinear crystals, where high frequencies dominate, in our case the lower the frequencies, the larger the nonlinearities can be.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: (D.-S. Kim)
[email protected]. Notes
The authors declare no competing financial interest. D
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ACKNOWLEDGMENTS This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP: NRF-2015R1A3A2031768, NRF-2011-0017494, WCI 2011-001) (MOE: BK21 Plus Program-21A20131111123).
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