Electrical Detection of Surface Plasmon Polaritons by 1G0 Gold

LETTER pubs.acs.org/NanoLett

Electrical Detection of Surface Plasmon Polaritons by 1G0 Gold Quantum Point Contacts Naomi Ittah and Yoram Selzer* School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel

bS Supporting Information ABSTRACT: Electrical detection of surface plasmons polaritons (SPPs) is essential for realization of integrated fast nanoscale plasmonic circuits. We demonstrate electrical detection of SPPs by measuring their remote gating effect on 1G0 metal quantum point contacts (MQPC) made of gold. Gating is argued to take place by a photoassisted transport mechanism with nonmonotonic behavior of its magnitude as a function of distance between the MQPCs and the position of SPPs creation.

KEYWORDS: Plasmons, photoassisted transport, ballistic conductance, point contact

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urface plasmons polaritons (SPPs) are coherent oscillations of conductive electrons in a skin layer of metal capable of producing strong local electromagnetic fields in the near-field region.1 Creation, control, manipulation, and detection of SPPs are currently a matter of intensive research motivated by their great promise for applications such as nanophotonic and nanoplasmonic integrated circuits, biological sensors, solar cells, and many more.2 Excited by light, SPPs can propagate distances up to tens of micrometers, depending on the permittivity values of the metal and dielectric and on the incident light wavelength.3-10 Detection of SPPs has been mainly achieved using photon detection techniques, relying on the ability either to probe them optically in the near field or to convert SPPs into free photons with subsequent collection in the far field.11-15 Yet it is electrical detection of SPPs that is essential for the realization of plasmonic circuits operating much faster than existing electrical interconnects, with transmission and detection of optical signals in a simple and accurate way. Several schemes for electrical detection of SPPs have recently been presented using gallium arsenide structures,16 germanium nanowires,17 and a superconductor single photon detector.18 Here we show how metal quantum point contacts (MQPCs) can be used as an easy-to-fabricate on-chip method for electrical detection of SPPs that can be operated under ambient conditions and at room temperature.19 MQPCs are junctions with a constriction of one or very few atoms in cross section connecting between two metal electrodes, r 2011 American Chemical Society

revealing statistical-averaged quantized electrical conductance values in units of G0.20 MQPCs are usually formed as suspended structures in a mechanically controlled break junction setup, which prevents their coupling to metal waveguides and probably also makes them unstable under laser irradiation due to poor heat dissipation.21 We, instead, use a fabrication method devised by us,22 in which the MQPCs are not suspended and are fully anchored onto oxide covered Si substrates. This facilitates their coupling to metal waveguides and as will be shown below makes them remarkably stable under light coupling. The detection approach is based on our recent study of the electrical transport properties of 1G0 MQPCs, made of Au, under laser irradiation.19 Transport was shown to behave according to a photoassisted transport (PAT) mechanism. Numerous theoretical studies suggest that under PAT conditions a broad range of novel effects of confined oscillating electromagnetic fields on the dc conductance of nanoscale and molecular junctions should become possible.23-33 Here we demonstrate that Au MQPCs can be remotely optically gated by a PAT mechanism. A typical MQPC/waveguide structure is fabricated by three lithography/evaporation/lift-off procedures. In the first step a Cr/Au (3/50 nm) lead is patterned using photolithography. In the second step a Cr/Au (3/30 nm) lead (used as the plasmonic waveguide) is formed by shadow evaporation, leaving a gap Received: September 26, 2010 Revised: December 15, 2010 Published: January 4, 2011 529

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Figure 1. A schematic presentation of a Au MQPC/waveguide electrical plasmon detector. Creation of SPPs is achieved by normal illumination of the grating by a laser via a microscope objective. Inset: an SEM image of the grating patterned on top of the waveguide. The white arrow indicates the position of the MQPC (see text for details).

Figure 2. FDTD simulation of the experiment. The different Au features are outlined in yellow. A 781 nm light source is focused on the two grating features on the right. SPPs are launched toward the MQPC on the left, where an enhancement of the field on and around a triangleshaped protrusion is observed (the color code is logarithmic). Inset: SEM image of the experimental structure. The area shown in the simulation is marked by a red rectangle.

of ∼25-30 nm between the two Au leads. The resulting gold waveguide has a typical width of 2 μm. In the third step, a grating consisting of Au bars is fabricated on top of the waveguide. A 1G0 quantum point contact is established between the waveguide and the 50 nm thick gold lead using field induced adatom migration.22 Briefly, when an appropriate voltage (a few volts) is applied between the leads, a directed diffusion of Au adatoms is initiated toward zones of high electric field that are formed in close vicinity to protrusions extending out of the leads. There, as the density of migrating atoms increases, the probability of nucleation and cluster growth progressively increases as well. The process is monitored, by measuring the conductance across the gap, and stopped as soon as one of the growing metal mounds closes the gap. This point is characterized by a sharp transition in conductance from sub-1G0 values (tunneling) to, in many cases, 1G0 (a jump to contact process). The formed contacts are found to be very stable without any change in their conductance over a time period of many hours, even under quite intensive irradiation (maximum value ∼0.3 MW cm-2).19 SPPs launching by a periodic set of ridges needs to obey the following expression of momentum conservation34

accomplished by focusing Gaussian laser beams (three lasers with wavelengths of 532 nm (2.33 eV), 658 nm (1.88 eV), 781 nm (1.58 eV) with a 100-fold objective (NA = 0.5) to a spot with a diameter estimated to be 1.0 μm (at 1/e2 of intensity). The incident beams were linearly polarized in a direction perpendicular to the ridges (x axis in Figure 1) resulting in the excitation of two SPPs propagating in opposite directions, whose intensities based on three-dimensional finite-difference time domain (FDTD) simulations (see Figure 2), strongly depend on the position of the illumination spot relative to the structure. These results are on par with previously reported experimental measurements of similar Au structures34 showing that the efficiency of SPPs excitations with λ = 781 nm is approximately 20% and it decreases with decreasing wavelength. All measurements were performed under ambient conditions at room temperature. All together, 40 contacts were measured. Because of their very high structural stability, each contact could be measured under all three lasers, where for each wavelength five to eight positions of the laser spot on the grating were chosen within a distance range of 0-7.5 μm from the point contact itself. The response of a typical 1G0 contact to a SPP is shown in Figure 3. In this specific example, λ = 781 nm and SPP excitation is induced at a distance of 1.9 μm from the MQPC. The intensity of the laser was electronically modulated between 0 and 20 mW, at a frequency of 10 Hz. The resulting dc current measured at 30 mV, was found to rapidly follow the modulation (Figure 3a). Figure 3b shows a conductance histogram based on the modulated sequence. Irradiation appears to shift the Gaussian describing the distribution of conductance values around 1G0 (“lightoff” conductance) to a new and a higher mean value (“light-on” conductance). The observed behavior is similar to our previous results, where MQPCs were directly irradiated by a λ = 781 nm laser.19 The main difference is in the smaller change of conductance (shift of the Gaussian peak) upon irradiation due to intensity loss of the launched SPPs as a function of distance from the MQPC (see detailed discussion below). We note that since the objective used in this study (100) is different than that used

kSPP ¼ k0 sin θ þ nP where kSPP and k0 denote the wave-vector magnitudes of the excited SPP and incident light, respectively, θ is the angle of light incidence in the plane perpendicular to the ridges, n is an integer, and P = 2π/Λ is the grating momentum, where Λ is the grating period. SPP excitation at normal incidence results in a SPP wavelength of λSPP = Λ. At this wavelength, the normal laser illumination is scattered on the different ridges to generate coherent SPP waves, which interfere constructively with each other increasing the efficiency of SPP excitation. The configuration for SPP excitation exploited in this work is essentially the same as that described in previous papers.34-36 Straight 130 nm high and 330 nm wide gold ridges (of nominally rectangular profile) were fabricated using electron-beam lithography on the surface of the 30 nm gold lead. The number of ridges in the configuration under investigation is 11 with a fixed period of Λ = 750 nm (see Figures 1 and 2). Illumination is 530

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Figure 3. (a) Effect of intensity-modulated SPPs on conductance, excited by a 781 nm laser from a distance of 1.9 μm away from a 1G0 contact. (b) Conductance histogram based on the modulated sequence. Irradiation appears to shift the Gaussian describing the distribution of conductance values around 1G0 (“light-off” conductance) to a new and a higher mean value (“light-on” conductance).

and will further be discussed below as well as in the Supporting Information. Figure 5 summarizes the key findings of this paper. Conductance enhancement for two representative junctions (rows) is plotted (open rectangles) as a function of laser position, d, relative to the MQPC, along the grating-decorated waveguides using three different laser wavelengths (columns). Zero distance refers to a position of a laser directly above a MQPC. Each experimental point was calculated as explained in Figure 3. This comes as another proof for the high stability of the MQPCs used here, as they do not lose their properties after more than 20 sequences of laser intensity modulations. As a general trend, for each MQPC, the G/G0 ratio appears to be decreasing with increasing d. Since this ratio is a direct measure of the intensity of the SPPs at the MQPC, the observed behavior can simply be explained by the fact that with increasing distance propagating plasmons progressively lose their intensity by processes such as Ohmic losses in the metal, scattering from surface roughness, grain boundaries, and other imperfections37 or by coupling to far field photons by the metal grating.34,38 Thus although, for example, at the center of the patterned grating (at d = 5 μm) according to theoretical calculations34 plasmons creation should be most effective (>20%), conductance enhancement is negligible since from this distance all initiated plasmons dissipate to such an extent that by the time they reach the MQPC, they have only a negligible effect on conductance. Importantly, Figure 5 also shows that the G/G0-d curves are not monotonic and have either a maximum (top row) or leveling off (bottom row) close to d = 0. This behavior is observed in all measured MQPC. To semiquantitatively explain this result, we start by describing the intensity loss of the SPPs as a function of d according to the following expression

Figure 4. Dependence of conductance enhancement on laser polarization in either the x (rectangles) or y (circles) directions. The laser wavelength is 658 nm, and the laser spot is localized ∼4 μm away from the MQPC.

in our former study (50), the change in conductance upon direct irradiation of the MQPC is larger here. Further support that the conductance enhancement is truly a plasmonic effect comes from measurements of conductance enhancement as a function of laser polarization. Creation of SPPs is expected to be maximized when the polarization is perfectly aligned with the x direction (see Figure 4), parallel to the waveguide axis. Using a 658 nm laser located 4 μm away from a certain MQPC, Figure 4 depicts the measured conductance enhancement as a function of laser power for x-directed (rectangular) and y-directed (circles) polarizations. Each point in this graph is an average of three separate measurements of the conductance enhancement at a certain value of laser power. The error bars are the standard deviation. Clear polarization dependence is observed, although enhancement is still measured when the polarization is perpendicular to the waveguide axis. We attribute this to some inaccuracy in angle adjustment and mainly by imperfections in the lithography-patterned structure.34 Conductance enhancement shows weak nonlinear behavior as a function of power. This behavior has been discussed by us in the past (ref 19)

IðdÞ ¼ Iðd ¼ 0Þe - d=δ

ð1Þ

where I is the intensity and δ is the wavelength-dependent propagation length or attenuation factor of the SPP, which also implicitly depends on the plasmonic waveguide structure and the operating loss mechanisms.37 We then invoke PAT as the transport mechanism through the MQPCs. Capacitive coupling between the two sides of a MQPC 531

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Figure 5. Effect of laser position along the waveguide (measured from the position of the MQPC) on conductance enhancement for two different junctions (rows) using three different wavelengths (columns). Points are experimental results. The continuous curves are numerical fits based on iterations using eqs 1 (with δ as a free parameter) and 2 (with R as a free parameter); see text for details.

exchange photons of energy pω with the oscillating field (see Figure 6). Relatively simple quantitative description of this process can be found in what is known as the Tien-Gordon theory.23 According to this formulation the zero-bias dc conductance of a contact can be described by the expression X  R2 Jn τðEf þ npωÞ ð2Þ Gdc ðωÞ ¼ G0 2 n where Ef is the Fermi energy, n is the sideband index, Jn2(R/2) is the square of the nth order Bessel function evaluated at R = eVω/ pω, giving the probability that transporting electrons absorb (n > 0) or emit (n < 0) n photons of energy pω and τ(Ef þ npω) is the transmission probability at an energy level npω above or below the Fermi level (depending on the sign of n). Conductance enhancement (gating) is therefore achieved if τ(Ef þ npω) > τ(Ef). The process is illustrated schematically in Figure 6b, which plots the transmission probability across a MQPC as a function of energy.25 Consider, for example, the green arrows describing electrons at the Fermi energy absorbing (up arrow) or emitting (down arrow) energy of 2.3 eV, which is the energy of a green photon. According to this plot, absorbing electrons are transmitted across the contact with transmission probability τ ∼ 0.5, while photon emitting electrons cross with τ ∼ 2.0. Electrons that do not experience an inelastic process cross the contact with τ ∼ 1. The probability for each of these processes is calculated by the Bessel function, which in turn depends on the effective intensity of the oscillating plasmon across the contact via the value of Vω. On the basis of eq 2, G/G0 is wavelength-dependent since both R and the transmission,τ(Ef þ npω) depend on the wavelength. Accurate determination of these parameters is needed for quantitative comparison with theory. However, while the values of τ can be calculated,24,25 the magnitude of R for each contact and for each wavelength is unknown, and its precise determination is not straightforward.

Figure 6. Schematic presentation of the gating mechanism at a MQPC. (A) A SPP produces an oscillating potential drop across the gap (marked by the positive/negative signs). Arrows indicate electrons that participate in the transport process through a bridging constriction. (B) The change of conductance upon interaction with the oscillating potential depends on the transmission profile at the point contact as a function of energy relative to the Fermi level. Examples for two wavelengths are shown 532 nm (green arrows) and 781 nm (red arrows).

transforms a propagating SPP into a time-varying potential across the contact (Figure 6) defined as Vω cos ωt, where Vω is the oscillating amplitude and ω is the frequency of the laser.23-25 Vω is determined by the laser light intensity, the environment, the geometry of the contact, the polarization of light, and the frequency itself.39-44 As has been experimentally shown by us19 and theoretically by others,45 a (shortening) 1G0 contact, connecting between the two sides of the gap, is not a high enough conductor to nullify the developed oscillating potential across it. Therefore, the oscillating potential across the gap gates the contact by inducing inelastic events in which transporting electrons through the 1G0 channel 532

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Nano Letters Therefore, as in our previous study19 we used theoretical transmission values to calculate each curve, taking into account the wavelength, an R value that gives the best fit to the G/G0 value at d = 0. These R values are reported in Figure 5. By the definition of R (=eVω/pω) a direct correlation between the intensity of the plasmon I(d = 0) and Vω is thus established: I(d = 0) = cVω2, where c is a proportionality constant suitable for all d values. Iteratively, we then use δ as a free parameter in eq 1 to describe the attenuation of the SPP as a function of distance. For each δ value, a curve of I as a function of d is calculated, which is then translated to R and used in eq 2 to calculate G/G0 as a function of d. Iterations proceed until a good fit is established as depicted in Figure 5. The experimentally observed nonmonotonic behavior of the G/G0-d curves is thus argued to be a direct outcome of the Bessel functions in eq 2, which describe the PAT mechanism at the contacts upon SPPs creation. The curve-fitting iterative procedure results in errors associated with R and δ. Good fitting is achieved within a variation of (0.02 in R and (0.2 in δ. The R (=eVω/pω) values reported in Figure 5 (at d = 0) imply high effective Vω values across the contacts. For example, with λ = 532 nm and R = 1.66, the effective Vω is 3.8 V. Assuming this potential is dropped across a gap of 1 nm, it corresponds to an electric field that is higher by a factor of ∼1000 than the field of the laser (∼3 mV/nm). This apparent field enhancement is higher by an order of magnitude than reported values obtained using metal features with similar geometry.40-44 However, there are recent new results, based on Raman measurements and also electrical measurements of optical rectification, reporting that enhancement of 1000 is possible for extremely small gaps.46,47 Indeed, in the case of MQPC very small gaps are expected, and hence these recent results directly support the R values reported in this study. Further discussion on this important issue can be found in the Supporting Information. We also note that the propagation lengths extracted using our procedure are somewhat shorter than previously reported values.37,38 This can be explained by the fact that in contrast to previous studies where SPPs propagated through smooth metal waveguides (assuming negligible roughness), here the entire waveguides (between initiation point and the MQPC) are covered by gratings, which continuously couple the SPPs to free space photons, substantially attenuating in this way the propagation of plasmons. Indeed to support this argument FDTD simulations show that the expected propagation length in our structure is δ ∼ 0.5 μm. With average experimental δ value of ∼1.3 μm, and considering the complexity of the detection process and imperfections in the waveguide structure, we consider the agreement between the two numbers reasonable. The quite intensive attenuation also explains the weak nonlinear behavior of the conductance enhancement as a function of (parallel) laser power plotted in Figure 4. In a previous paper we have shown that conductance enhancement under conditions of intensive irradiation, and high R values, behaves nonlinearly with incident laser power.19 In fact, this was argued to be a direct result of the governing PAT mechanism and the fact that this process can be described by eq 2 which is nonlinear with R. However, when a MQPC is excited from a distance of 4 μm, the propagating plasmons and the resulting effective oscillating field across the contact are attenuated to such an extent that PAT takes place in a regime where nonlinearity, although it still exists, is much less pronounced. In conclusion, we demonstrate electrical detection of SPPs by their gating effect on the conductance of MQPCs. Gating appears

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to take place via a PAT mechanism. Work is under progress to realize by the above experimental capabilities and observed effect, rapid electroplasmonic switches.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional information covering potential distribution across a MQPC, effect of laser spot size, and conductance enhancement at low R values. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Support for this research was given by the ISF (both standard and F.I.R.S.T. tracks), the James Franck program, and the Wolfson charitable fund. N.I. acknowledges support by a converging technologies fellowship via the ISF. ’ REFERENCES (1) Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Nature 2003, 424, 824. (2) Zia, R.; Schuller, J. A.; Chandran, A.; Brongersma, M. L. Mater. Today 2006, 9, 20. (3) Weeber, J. C.; Krenn, J. R.; Dereux, A.; Lamprecht, B.; Lacroute, Y.; Goudonnet, J. P. Phys. Rev. B 2001, 64, No. 045411. (4) Dowson, P.; De Fornel, F.; Goudonnet, J. P. Phys. Rev. Lett. 1994, 72, 2927. (5) Weeber, J. C.; Lacroute, Y.; Dereux, A. Phys. Rev. B 2003, 68, No. 115401. (6) Steinberger, B.; Hohenau, A.; Ditlbacher, H.; Stepanov, A. L.; Drezet, A.; Aussenegg, F. R.; Leitner, A.; Krenn, J. R. Appl. Phys. Lett. 2006, 88, No. 094104. (7) Dallapiccola, R.; Dubois, C.; Gopinath, A.; Stellacci, F.; Dal Negro, L. Appl. Phys. Lett. 2009, 94, No. 243118. (8) Ju, J. J.; Park, S.; Kim, M.; Kim, J. T.; Park, S. K.; Park, Y. J. Appl. Phys. Lett. 2007, 91, No. 171117. (9) Peale, R. E.; Lopatiuk, O.; Cleary, J.; Santos, S.; Henderson, J.; Clark, D.; Chernyak, L.; Winningham, T. A.; Del Barco, E.; Heinrich, H.; Buchwald, W. R. J. Opt. Soc. Am. B 2008, 25, 1708. (10) Cilwa, K. E.; Rodriguez, K. R.; Heer, J. M.; Malone, M. A.; Corwin, L. D.; Coe, J. V. J. Chem. Phys. 2009, 131, No. 061101. (11) MacDonald, K. F.; Sa0 mson, Z. L.; Stockman, M. I.; Zheludev, N. I. Nat. Photonics 2009, 3, 55. (12) Van Wijngaarden, J. T.; Verhagen, E.; Polman, A. Appl. Phys. Lett. 2006, 88, No. 221111. (13) Bashevoy, M. V.; Jonsson, F.; Krasavin, A. V.; Zheludev, N. I. Nano Lett. 2006, 6, 1113. (14) Bashevoy, M. V.; Jonsson, F.; MacDonald, K. F.; Chen, Y.; Zheludev, N. I. Opt. Express 2007, 15, 11313. (15) Kuttge, M.; Vesseur, E. J. R.; Verhoeven, J.; Lezec, H. J.; Atwater, H. A.; Polman, A. Appl. Phys. Lett. 2008, 93, No. 113110. (16) Neutens, P.; Dorpe, P. V.; Vlaminck, L. D.; Lagae, L.; Borghs, G. Nat. Photonics 2009, 3, 283. (17) Falk, A. L.; Koppens, F.H. L.; Yu, C. L.; Kang, K.; Snapp, N.L .; Akimov, A. V.; Jo, M. H.; Lukin, M. D.; Park., H. Nat. Phys. 2009, 5, 475. (18) Heeres, R. W.; Dorenbos, S. N.; Koene, B.; Solomon, G. S.; Kouwenhoven, L. P.; Zwiller., V. Nano Lett. 2010, 10, 661. (19) Ittah, N.; Noy, G.; Yutsis, I.; Selzer, Y. Nano Lett. 2009, 9, 1615. (20) Agraït, N.; Levi Yeyati, A.; van Ruitenbeek, J. M. Phys. Rep. 2003, 377, 81. (21) Guhr, D. C.; Rettinger, D.; Boneberg, J.; Erbe, A.; Leiderer, P.; Scheer, E. Phys. Rev. Lett. 2007, 99, No. 86801. 533

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