Harnessing Plasmon-Induced Ionic Noise in Metallic Nanopores

Mar 4, 2013 - We observed a strong increase of the ionic noise upon laser light .... Furthermore, Johnson noise is white noise, which density is equal...
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Harnessing Plasmon-Induced Ionic Noise in Metallic Nanopores Yi Li,†,‡ Chang Chen,*,†,§ Sarp Kerman,†,§ Pieter Neutens,†,§ Liesbet Lagae,†,§ Guido Groeseneken,†,‡ Tim Stakenborg,† and Pol Van Dorpe*,†,§ †

IMEC, Kapeldreef 75, Leuven, B3001, Belgium Department of Electrical Engineering, KU Leuven, Kasteelpark Arenberg 10, 3001 Leuven, Belgium § Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium ‡

ABSTRACT: The ionic properties of a metal-coated silicon nanopore were examined in a nanofluidic system. We observed a strong increase of the ionic noise upon laser light illumination. The effect appeared to be strongly mediated by the resonant excitation of surface plasmons in the nanopore as was demonstrated by means of ionic mapping of the plasmonic electromagnetic field. Evidence from both simulations and experiments ruled out plasmonic heating as the main source of the noise, and point toward photoinduced electrochemical catalysis at the semiconductor−electrolyte interface. This ionic mapping technique described is opening up new opportunities on noninvasive applications ranging from biosensing to energy conversion. KEYWORDS: Plasmonics, nanopore, ionic noise, mapping, photocatalysis

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anofluidic devices based on nanopores have emerged as novel sensors with single molecule accuracy. Transport of nano-objects through a single tiny pore or channel cause ionic current fluctuations which can be monitored using such devices. One of the particularly appealing applications is the detection and analysis of DNA. Usually DNA is detected by ionic current changes,1,2 although novel strategies have arisen that are based on measuring the tunneling current through electrodes embedded at the pore orifice3,4 or on localized optical spectroscopy such as fluorescence5,6 or surface enhanced Raman spectroscopy (SERS).7 In all three strategies, a profound understanding of the noise sources within these nanopore systems is of paramount importance. The noise properties of ion transport through nanosized pores or channels have been thoroughly investigated before.8−16 However, not all reports point in the same direction. For instance, the origin of the flicker noise measured on a single dielectric nanopore is attributed either to cooperative effect on ions motion13 in confined geometry or to the fluctuation of pore wall charges.9,11,15 Knowing the exact noise sources obviously also allows to minimize the noise in experimental conditions. For instance, the experience with PDMS coated pipettes in single channel patch clamp has been transferred to the nanopore field, where the use of passivation layers is now a widespread technique to achieve low noise characteristics.8 Similarly, the use of a SiO2 protection layer or spacer can further eliminate the ionic noise and improve the dynamic performance by means of capacitance reduction.17,18 Recently, we have been developing a strategy that combines SERS with conventional nanopore ionic fluidics (see Figure 1). This strategy makes use of the localized field enhancement in metallic nanopores or nanoslits, upon resonant surface plasmon excitation, which can lead to additional nanoscale optical © 2013 American Chemical Society

Figure 1. (a) Schematic drawing of the mapping of RMS current inside a nanoslit-cavity equipped with Bragg mirror gratings. The ionic current is measured during laser illumination in a scanning mode. (b) Cross-section SEM image of nanoslit cavity equipped with Bragg mirror antenna coated with a 100 nm Au layer.

interrogation and manipulation of mechanically confined molecules and/or nano-objects. This strong and highly localized field enhancement enables the generation of SERS from the mechanically confined analytes inside the gap. In these cavities, the incident light can resonantly generate surface plasmons (SPP), which, depending on the length of the cavity sidewalls and the wavelength of the light, lead to strong field enhancements.19 We also showed that these strong field enhancements are even further increased by adding an Received: January 25, 2013 Revised: February 26, 2013 Published: March 4, 2013 1724

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additional Bragg mirror at either side of the cavity.19 In this report, we examine the ionic currents through such a nanoslit upon light irradiation and we show that resonant excitation of surface plasmons in this nanostructure induces a strong additional noise component. We measured the ionic current in function of time (plotted in Figure 2) and monitored both the mean current and the

noise caused by capacitance.17 Upon irradiation with 1 mW 633 nm laser light, a completely different PSD was observed (shown in Figure 3b). The morphology of the PSD with a laser radiation at 633 nm was in fact only comparable to the reported PSD of ionic current oscillations through a single conical nanopore upon the formation of CaHPO4 nanoprecipitates.20 The observed unknown type of noise could be coarsely fitted with Lorentzian components S L (f ) =

Si

∑ i

1+

⎛ f ⎞2 ⎜ ⎟ ⎝ fci ⎠

(1)

where SL(f) is the power spectral density, Si is the plateau power density (at 0 Hz), and fci is the corner frequency for the i th single Lorentzian model. Two components are configured in Figure 3b. The corner frequencies are located at 400 Hz and 4 kHz, and the Lorentzian plateau at 800 and 20 pA2/Hz, respectively. Because the noise can be triggered by laser illumination, and the metal-coated nanopore structures support surface plasmon resonances, we investigated whether the increased noise was related to the excitation of surface plasmons by spatial and spectral mapping experiments. The combination of the weakly wavelength-independent nanoslit-cavity and the highly wavelength-dependent gratings19 allow us to understand the relationship between the SPPs excitation and noise generation by studying the wavelength-dependency and the polarization. As can be seen from Figure 4b−d, the RMS current noise highly depended on the location, the polarization and the wavelength of the excitation. When the laser polarization was aligned parallel to the long axis of the nanoslit, an IRMS of only around 2 nA was observed in Figure 4b. For the transverse polarization, however, the IRMS was as high as 14 nA upon excitation at the center of the structure (see Figure 4c). The observation of the polarization dependence is consistent with our previous work and strongly supports the role of surface plasmons in enhancing the noise.19,21 The limited increase in IRMS for both the gratings and the flat gold surface (see Figure 4b) confirmed that the gold layer was thick enough to block the incident laser penetration into the silicon. To shed some extra light on the origin of the effect, we also performed the spatial mapping of the noise for two different wavelengths, that is, 633 and 785 nm. These spatial maps are shown in Figure 4c,d. While the highest noise was observed for 633 nm (Figure 4c), the observed spatial distribution was

Figure 2. The ionic current profile in function of time with (a) the current signal upon 1 mW of 633 nm laser irradiation; (b) the mean current and (c) the root-mean-square of the ionic current.

RMS value of the noise with and without laser excitation (1 mW focused on the nanocavity with a wavelength of 633 nm). It is clear from Figure 2a that the amplitude of the current noise immediately increased upon laser irradiation. The sudden laser irradiation change was accompanied by an initial current spike. The mean current increased with 0.15 nA, while the root-meansquare (RMS) of the current went up from 0.64 to 12 nA (shown in Figure 2b,c). When turning off the laser, both mean current and RMS current noise fell back to their original levels after discharging. To study this effect in more detail, the ionic noise power spectral densities (PSD) before, during, and after 1 mW of 633 nm laser illumination are plotted in Figure 3. Indeed, comparing Figure 3a,c, the noise spectrum returned to its former level after the laser is turned off. The noise spectrum without laser can be well explained as the sum of flicker noise, thermal noise, shot noise, dielectric noise, and output voltage-

Figure 3. Noise power density spectra at 1, 15, and 33 s of Figure 2a. (a) Before 633 nm laser illumination. (b) Illumination at 633 nm at the steady state. (c) After switching off the laser. The dashed lines in a and c indicate the flicker or 1/fα noise, where α = 2. The orange curve in b is the sum of two Lorentzian components (sum of the two dashed lines). 1725

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causes, namely heating or photocatalysis, were examined in more details. In order to examine the light-induced heat generation further, the thermal response of our nanoslit cavity was simulated using Comsol Multiphysics 4.3a22,38 (see Materials and Methods). On the basis of these simulations, focusing a 1 mW laser with a wavelength of 633 nm laser onto our nanoslit cavity, a maximum temperature increase of 1.5 K is to be expected. Besides as noted before, plasmonic induced heating is expected as being relatively homogeneous over the entire structure23,24 and should rise linearly with the power. The latter was also observed for the simulation data for both 633 nm and 785 nm wavelength as shown in Figure 5, with the slope of a 633 nm laser almost triple as high as for a 785 nm laser with a similar power.

Figure 4. The ionic RMS current noise based mapping. (a) Top view scanning electron microscope image of the plasmonic nanostructure. The dashed rectangular at the center indicates the position of the nanoslit cavity, while the two dashed squares represent the grating couplers, optimized for 785 nm wavelength. (b) A 633 nm laser illumination with polarization perpendicular to the transverse axis, (c) a 633 nm laser illumination with polarization perpendicular to the longitudinal axis, and (d) a 785 nm laser with polarization perpendicular to the longitudinal axis. A 1 mW laser power is used. Double-sided arrows indicate the polarization direction. The scale bar is 1 μm.

Figure 5. Numerical simulation of plasmonic heating induced by laser irradiation. (a,b) The cross-section view of nanoslit thermal profiles at 633 and 785 nm, respectively. The black lines define the top-coated gold nanoslit. The scale bar is 1 μm. (c) The temperature increase versus laser power. The ambient temperature is set as 293.15.K.

Although theoretically possible, plasmonic heating is unlikely to be the predominant source of the enhanced noise as this should become clear from the noise power spectral density. Among conventional noise sources, Johnson (thermal) noise and dielectric noise are the only two sources that are temperature dependent. Johnson noise linearly depends on the temperature. The power spectral density Sthermal = 4kBT/R, where kB is the Boltzmann’s constant, T is the temperature, and R is the resistance of the nanopore. The resistance in our case was 11.6 MΩ, leading to a rise of 7.14 × 10−6 pA2/Hz at 1 mW 633 nm wavelength. Furthermore, Johnson noise is white noise, which density is equally distributed in the entire frequency domain. It also means that Johnson noise can be eliminated as the source of the observed RMS noise current increase since the intensity and morphology do not correspond to the measured PSD. Second, dielectric noises generated by means of energy dissipation, giving an expression Sdielectric = 8πkBTDCf, where D is the dissipation factor and C is the capacitance of the membrane, which is linearly dependent on both frequency and temperature, resulting a slope of 1 in the PSD. Therefore,

clearly diverse for the two wavelengths. At an excitation of 633 nm, the induced noise was exclusively observed at the location of the nanoslit, while for 785 nm (Figure 4d) the gratings exhibit a significant contribution as well. Interestingly, the observed PSD was comparable when focusing on the grating area (see Figures 3b and 4d). This likely means that the SPPs propagating into the nanoslit cavity and the cavity plasmon generate the same type noise. Also these results are consistent with the role of surface plasmons as the cavity is relatively broadband, while the gratings are only resonantly excited in a narrow spectral range around 785 nm. The strong dependency of ionic noise on the plasmonic properties of both the structure and incident light suggests that the noise is strongly related to the SPPs leakage into the silicon supporting layer at the electrolyte interface. The origin of the noise can be related to local physical and/or chemical processes occurring near the metal nanoslit. To further explain the additional noise induced by the plasmons, different potential 1726

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properties, of the structures were quite comparable. The effect of the near field EM enhancement can be excluded out both from simulation and experimental results.7 We can observe that the simulated slopes of double-sided device linearly increase in Figure 5c as well. The ionic current noise as a function of 633 nm laser power is shown in Figure 7.

dielectric noise can be canceled in the manner of the morphology. Plasmonic heating cannot directly contribute to the conventional sources. Such a low increase in temperature can indeed not explain the large noise increase observed. Therefore, all of the conventional noise sources can be excluded due to their morphology of noise spectral density. Besides light-induced heating, it is known that surface plasmons can also accelerate catalytic effects (plasmon enhanced photocatalysis), which can play a role here. For a plasmonic−photocatalyst system, the four major energytransfer mechanisms25,26 are (1) plasmonic heating, (2) hot electron transfer, (3) near-field electromagnetic enhancement, and (4) resonant photon scattering. On one hand, the excitation of surface plasmons may induce the formation of hot electrons, which have energies that are sufficient to initiate electrochemical reactions at the Au/electrolyte interface. For example, transient ions can rapidly react as an electron-scatter process and can induce a subsequently reaction on the metal surface.27 On the other hand, the Au film that supports the surface plasmons is deposited on a silicon substrate for which it is known that electron−hole pairs can be generated upon illumination with visible light. Although the silicon substrate is shielded by the 100 nm thick Au film, light can leak into the silicon substrate in two ways (shown in Figure 6). First, as the

Figure 7. Ionic RMS current properties as a function of 633 nm laser power for both devices. Top-sided gold device are labeled in green square and double-sided gold device in orange circle.

In Figure 7, it is clear that coating the backside strongly inhibits the noise generation (with the slope of −3 pA/mW). IRMS after backside passivation stays more or less constant with optical power at 138 pA. The current noise of topside coated device goes saturated at 52.96 nA. As the simulations show that the local field enhancement and the plasmon induced heating do not change significantly upon coating of the backside, we can attribute the additional noise to the plasmon-induced catalysis at the silicon/electrolyte interface. The intrinsic property of silicon matches the requirement of two electrochemical reactions, hydrogen production29 and oxygen decomposition30 in an aqueous environment. Conclusion. The noise properties of a plasmonic nanoslit cavity are investigated with laser illumination. While focusing the laser onto the cavity, a new type of ionic noise is observed. It is found to be strongly dependent on the optical properties of both the structure and incident light, such as the location of the laser spot and the wavelength and polarization of the excitation laser. Plasmonic induced heating is simulated but is demonstrated not to be the origin of the noise. The noise power spectral density is analyzed as Lorentzian components, indicating the possibility of plasmonic induced electrochemical interactions. Finally, by coating both front and back side of the nanoslit cavity with metal, the pathway of the noise has been verified to be the plasmon induced silicon catalysis but not directly through gold surface. For practical purposes, a denoising approach is developed for performing ionic measurements on semiconductor nanocavities equipped with plasmonic materials. By avoiding semiconductor-electrolyte interfaces, realized by backside metal coating in this case, the RMS current noise is completely eliminated. The power spectral densities are also found to be lack of those Lorentzian components with laser illumination. The demonstrated plasmonic effect further supports several emergent applications at subwavelength such as mapping technique based on ionic signal31 and monitoring localized chemical reactions32 and especially for plasmon-enhanced catalysis.33 Since plasmon-induced catalysis mediated by

Figure 6. Two possible contributions of plasmonic induced ionic noises: (I) direct plasmon induced photocatalysis on the metal surface (purple dashed curve); (II) two-step plasmon induced semiconductor photocatalysis (green curves). The SPPs leakage generates electron hole pairs into the silicon (a), allowing for the electrochemical reactions at the interface (b).

silicon substrate has a much higher index than the water on top of the metal film, the plasmons can leak directly to modes in the silicon substrate. Second, at the bottom of the nanoslit, near the hot spot, the top of the metal film is in direct contact with the silicon, giving a direct leakage path. The excited electron− hole pairs in the silicon can generate electrochemical reactions at the silicon/electrolyte surface. Although this pathway has more barriers to overcome, the result from noise measurement of polysilicon emitter bipolar transistors supports that a Lorentzian feature exists from 8 Hz to 10 kHz.28 In order to prove which of these two pathways of plasmon induced photocatalysis is responsible for the RMS current noise increase under laser illumination, a 10 nm/20 nm layer of titanium/gold was deposited on the backside of the nanocavity. This removed a direct interaction between silicon and the electrolyte solution, while the optical properties, hence SPPs 1727

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Lorentzian function, as the simplest case of current fluctuation or steplike transitions, represented the statistical process of only two states. The parameter of a single Lorentzian model was the corner frequency fci, which was related to the relaxation time constant τon,i and τoff,i.

semiconductor can provide more energy dissipation than on metals, electrochemical reactions catalyzed by light has huge potential to be optimized for the applications of the solar energy and water splitting.25,34 Materials and Methods. Fabrication of Plasmonic Metallic Nanocavity. The nanoslit-cavity chips were fabricated by standard micromachining procedures.19,35 Briefly, electron beam lithography and silicon anisotropic wet etching (KOH etching) were used to form the nanoslit-cavity on a freestanding Si membrane in a silicon-on-insulator chip. A similar process, but based on UV lithography, was used to etch the backside silicon layer for generating a freestanding membrane. The nanocavity was then opened using a dip in 2% HF, followed by sputtering 10 nm Ti and 100 nm gold. The cavity has a depth of 700 nm and a vertex of 70.5°. Here, a typical nanoslit has a dimension of 30 nm width (Figure 1b) and 1 μm length. For characterization, the nanocavity devices were observed using a scanning electron microscope (Philips, XL30 FESEM) at a 5 kV accelerated voltage. A chip with such nanoslit was mounted into a PMMA optical flow cell to separate the electrolyte into two individual reservoirs for the electrical measurements (Figure 1a). Mixture solution of 1 M KNO3, 10 mM Tris-acetate, and 1 mM EDTA at pH 8.0 was used during all measurements. Freshly prepared Ag/AgCl electrodes were placed far away from the lens. Using a resistive feedback amplifier (β = 0.1, Axopatch 200B, Molecular Devices), ionic currents were recorded at 100 kHz bandwidth. Electrical Noise Measurements. For the electrical measurements, a chip with a nanocavity was mounted into a custommade (PMMA) optical flow cell to separate the electrolyte into two individual reservoirs. A buffer solution (1 M KNO3, 10 mM Tris-acetate, and 1 mM EDTA; pH 8.0) was used during all measurements. Freshly prepared Ag/AgCl electrodes were placed at 1 cm away from the lens. Using a resistive feedback amplifier (β = 0.1, Axopatch 200B), ionic current traces were recorded at 100 kHz bandwidth with 250 kHz sampling rate. The optical properties of the nanocavity equipped with groove-gratings has been studied and optimized for 785 nm excitation in our previous works.19,36 For optical measurements of Figure 4a, a 60× water immersion lens (Olympus, NA 0.9) was dipped into the top reservoir. An incident laser (633 nm or 785 nm at 1 mW) was focused on the nanocavity with its polarization initially perpendicular to the longitudinal axis of the structure. The diameter of the laser spot was estimated as ∼1 μm. A piezostage was used to scan a region of 20 μm by 10 μm surrounding the nanostructure in steps of 500 nm. The laser beam moved uniformly along the horizontal direction. The duration time for each point was 1 s for current signal recording with an additional 10 kHz 8-pole low-pass Bessel filtering. RMS current noises were calculated with 0.1 s traces. Filled contour figures of RMS current noises are shown in Figure 4b−d. The data were processed using custom Matlab (MathWorks) scripts. Two-sided power spectral densities (PSD) of 1 s traces were estimated over the frequency range [0,125 000) Hz by periodogram algorithm.37 The mean value and root-meansquare (RMS) of current noise was calculated with 1 s traces for Figures 2 and 6. RMS current noise as a synonym for standard deviation of ionic current was directly evaluated by the standard function in the Matlab as well. Lorentzian Fitting of the Burst Noise. Analysis of the ionic current noise produced by laser illumination gave the spectrum that was fitted by two Lorentzian components. A single

fci =

1 1 ⎛ 1 1 ⎞ ⎜⎜ ⎟⎟ = + τoff, i ⎠ 2πτi 2π ⎝ τon, i

Here the noise power density generated by burst signals was treated as the sum of single Lorentzian-shaped model with fast and slow frequencies. Comsol Simulation for Plasmonic Heating. We used the procedure described by Donner et al.38 First, the heat source density of the given structure was computed in the RF module of Comsol22 using perfectly matching layers. Subsequently the heat transfer and laminar flow modules were used to solve the steady case of the temperature. The temperature dependent parameters of gold, silicon, and water were taken from the Comsol material library.



AUTHOR INFORMATION

Corresponding Author

*E-mail: (C.C) [email protected]; (P.V.D.) pol.vandorpe@ imec.be. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS C.C., P.N., and P.V.D. gratefully acknowledge financial support from the FWO (Flanders).



REFERENCES

(1) Bayley, H.; Cremer, P. S. Nature 2001, 413, 226−30. (2) Dekker, C. Nat. Nanotechnol. 2007, 2, 209−15. (3) Ivanov, A. P.; Instuli, E.; McGilvery, C.; Baldwin, G.; McComb, D. W.; Albrecht, T.; Edel, J. B. Nano Lett. 2011, 11, 279−285. (4) Tsutsui, M.; Taniguchi, M.; Yokota, K.; Kawai, T. Nat. Nanotechnol. 2010, 5, 286−90. (5) McNally, B.; Singer, A.; Yu, Z.; Sun, Y.; Weng, Z.; Meller, A. Nano Lett. 2010, 10, 2237−2244. (6) Chansin, G.; Mulero, R.; Hong, J.; Kim, M. J.; DeMello, A.; Edel, J. B. Nano Lett. 2007, 7, 2901−6. (7) Chen, C. Plasmonic nanopores for direct molecular identification. Ph.D. Thesis, KU Leuven, 2011. (8) Tabard-Cossa, V.; Trivedi, D.; Wiggin, M.; Jetha, N. N.; Marziali, A. Nanotechnology 2007, 18, 305505. (9) Smeets, R. M. M.; Dekker, N. H.; Dekker, C. Nanotechnology 2009, 20, 095501. (10) Zwolak, M.; Lagerqvist, J.; Di Ventra, M. Phys. Rev. Lett. 2009, 103, 1−4. (11) Powell, M. R.; Vlassiouk, I.; Martens, C.; Siwy, Z. S. Phys. Rev. Lett. 2009, 103, 9−12. (12) Bezrukov, S.; Kasianowicz, J. Phys. Rev. Lett. 1993, 70, 2352− 2355. (13) Tasserit, C.; Koutsioubas, A.; Lairez, D.; Zalczer, G.; Clochard, M. C. Phys. Rev. Lett. 2010, 105, 1−4. (14) Siwy, Z.; Fuliński, a. Phys. Rev. Lett. 2002, 89, 1−4. (15) Hoogerheide, D. P.; Garaj, S.; Golovchenko, J. a. Phys. Rev. Lett. 2009, 102. (16) Smeets, R. M. M.; Keyser, U. F.; Dekker, N. H.; Dekker, C. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 417−21. (17) Rosenstein, J. K.; Wanunu, M.; Merchant, C. A.; Drndić, M.; Shepard, K. L. Nat. Methods 2012, 9, 487−492. 1728

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Letter

(18) Waggoner, P. S.; Kuan, A. T.; Polonsky, S.; Peng, H.; Rossnagel, S. M. J. Vac. Sci. Technol., B 2011, 29, 032206. (19) Chen, C.; Hutchison, J. A.; Van Dorpe, P.; Kox, R.; De Vlaminck, I.; Uji-I, H.; Hofkens, J.; Lagae, L.; Maes, G.; Borghs, G. Small 2009, 5, 2876−82. (20) Powell, M. R.; Sullivan, M.; Vlassiouk, I.; Constantin, D.; Sudre, O.; Martens, C. C.; Eisenberg, R. S.; Siwy, Z. S. Nat. Nanotechnol. 2008, 3, 51−7. (21) Chen, C.; Clemente, F.; Kox, R.; Lagae, L.; Maes, G.; Borghs, G.; Van Dorpe, P. Appl. Phys. Lett. 2010, 96, 061108. (22) Lodewijks, K.; Van Roy, W.; Borghs, G.; Lagae, L.; Van Dorpe, P. Nano Lett. 2012, 1−5. (23) Baffou, G.; Quidant, R.; Girard, C. Appl. Phys. Lett. 2009, 94, 153109. (24) Baffou, G.; Girard, C.; Quidant, R. Phys. Rev. Lett. 2010, 104, 1− 4. (25) Linic, S.; Christopher, P.; Ingram, D. B. Nat. Mater. 2011, 10, 911−21. (26) Warren, S. C.; Thimsen, E. Energy Environ. Sci. 2012, 5, 5133. (27) Navalon, S.; De Miguel, M.; Martin, R.; Alvaro, M.; Garcia, H. J. Am. Chem. Soc. 2011, 133, 2218−26. (28) Deen, M. J.; Rumyantsev, S. L.; Schroter, M. J. Appl. Phys. 1999, 85, 1192. (29) Hou, W.; Cronin, S. B. Adv. Funct. Mater. 2012, DOI: 10.1002/ adfm.201202148. (30) Pourbaix, M. Atlas of electrochemical equilibria in aqueous solutions; National Association of Corrosion Engineers: Houston, TX, 1974; Vol. 39, p 541. (31) Keyser, U. F.; Krapf, D.; Koeleman, B. N.; Smeets, R. M. M.; Dekker, N. H.; Dekker, C. Nano Lett. 2005, 5, 2253−2256. (32) Venta, K.; Wanunu, M.; Drndić, M. Nano Lett. 2013, 13 (2), 423−429. (33) Mukherjee, S.; Libisch, F.; Large, N.; Neumann, O.; Brown, L. V; Cheng, J.; Lassiter, B.; Carter, E. A.; Nordlander, P.; Halas, N. J. Nano Lett. 2013, 13, 240−247. (34) Zhdanov, V. P.; Kasemo, B. Chem. Phys. Lett. 2012, 524, 16−19. (35) Chen, C.; Juan, M.; Li, Y.; Maes, G.; Borghs, G.; Van Dorpe, P.; Quidant, R. Nano Lett. 2012, 12, 125−132. (36) Chen, C.; Verellen, N.; Lodewijks, K.; Lagae, L.; Maes, G.; Borghs, G.; Van Dorpe, P. J. Appl. Phys. 2010, 108, 034319. (37) Oppenheim, A. V., and Schafer, R. W. Discrete-Time Signal Processing, Prentice-Hall: New York, 1989. (38) Donner, J. S.; Baffou, G.; McCloskey, D.; Quidant, R. ACS Nano 2011, 5, 5457−62.

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