Optical rectification and field enhancement in a plasmonic nanogap

Journal name:
Nature Nanotechnology
Year published:
Published online


Metal nanostructures act as powerful optical antennas1, 2 because collective modes of the electron fluid in the metal are excited when light strikes the surface of the nanostructure. These excitations, known as plasmons, can have evanescent electromagnetic fields that are orders of magnitude larger than the incident electromagnetic field. The largest field enhancements often occur in nanogaps between plasmonically active nanostructures3, 4, but it is extremely challenging to measure the fields in such gaps directly. These enhanced fields have applications in surface-enhanced spectroscopies5, 6, 7, nonlinear optics1, 8, 9, 10 and nanophotonics11, 12, 13, 14, 15. Here we show that nonlinear tunnelling conduction between gold electrodes separated by a subnanometre gap leads to optical rectification, producing a d.c. photocurrent when the gap is illuminated. Comparing this photocurrent with low-frequency conduction measurements, we determine the optical frequency voltage across the tunnelling region of the nanogap, and also the enhancement of the electric field in the tunnelling region, as a function of gap size. The measured field enhancements exceed 1,000, consistent with estimates from surface-enhanced Raman measurements16, 17, 18. Our results highlight the need for more realistic theoretical approaches that are able to model the electromagnetic response of metal nanostructures on scales ranging from the free-space wavelength, λ, down to ~λ/1,000, and for experiments with new materials, different wavelengths and different incident polarizations.

At a glance


  1. Measurement approach and layout.
    Figure 1: Measurement approach and layout.

    a, Schematic diagram of electrical characterization measurement. b, Colourized scanning electron microscope (SEM) image of a typical nanogap device. The actual tunnelling gap is not resolvable by SEM. c, Larger SEM view of electrodes and nanogap. d,e, False-colour maps of the silicon Raman line (d) and the photocurrent (e) for the device shown in c. In d blue indicates a weak silicon signal, thus indicating the location of the gold electrodes. In e, the colour bar runs from red (20 nA) to blue (0 nA). The photocurrent is clearly localized to the nanogap, to within optical resolution.

  2. Demonstration of optical rectification.
    Figure 2: Demonstration of optical rectification.

    ac, Photocurrent (red, Iphoto) and (1/4)Vac22I/V2 (black) as a function of Vdc for three different samples. The shared shapes of these curves, including changes of sign, demonstrate that the photocurrent arises from the rectification process. Note the differing current scales for the three devices. The different conductances and nonlinearities presumably result from microscopic details of the electrode surfaces and geometry. Insets: conductance in units of μA V−1 for each device. The gap distances derived from tunnelling measurements are 1.4, 0.44 and 0.92 Å. Inferred Vopt values are 30, 25 and 33 mV, with uncertainties of 10%. Inferred electromagnetic fields and field enhancements are 2.1 × 108 V m−1 and 718 for a, 5.7 × 108 V m−1 and 1,940 for b, and 3.6 × 108 V m−1 and 1,230 for c.

  3. Further evidence for optical rectification.
    Figure 3: Further evidence for optical rectification.

    Rectified photocurrent, Iphoto, as a function of incident laser power. Error bars indicate one standard deviation of the Iphoto measurements at each laser power. Linear power dependence (see text) was found by a weighted least-squares fit (red line).

  4. Theoretical basis for validity of rectification.
    Figure 4: Theoretical basis for validity of rectification.

    a, Geometry considered in the theoretical analysis of the distance dependence of linear conductance. We start with a single-atom contact grown along the left fence111right fence direction. b, Stretched geometry with a distance d between the gold tips. c, Calculated linear conductance as a function of d (circles). The solid line shows the fit to the exponential function G = G0exp[−β(d − d0)]. The fit parameters are indicated in the graph. d Zero-bias transmission as a function of the energy for the different geometries of c, with d increasing from top to bottom. Note the logarithmic vertical axis, and that the transmission remains a smooth function of energy over a broad range around the Fermi level.

  5. Field (right axis) at the tunnelling region as a function of gap distance (top axis) for five devices (shown in different colours) measured a number of times at 80 K.
    Figure 5: Field (right axis) at the tunnelling region as a function of gap distance (top axis) for five devices (shown in different colours) measured a number of times at 80 K.

    The gap distance (and therefore the enhanced field) changes as the gap geometry evolves over the course of repeated measurements. The field and gap distance are derived from measurements of the conductance (bottom axis shows ln(G0/G)) and optical frequency voltage (left axis shows Vopt normalized by ln(G0/G)), based on the assumption that d − d0 is the relevant scale over which Vopt falls, and β = 1.85 Å−1. Error bars result from the statistical uncertainty in Vopt and ln G.


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  1. Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, Texas 77005, USA

    • Daniel R. Ward &
    • Douglas Natelson
  2. Institut für Theoretische Festkörperphysik, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany

    • Falco Hüser &
    • Fabian Pauly
  3. Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, 28049 Madrid, Spain

    • Juan Carlos Cuevas
  4. Department of Electrical and Computer Engineering, Rice University, 6100 Main Street, Houston, Texas 77005, USA

    • Douglas Natelson


D.R.W. fabricated the devices, performed all measurements and analysed the data. D.N. supervised and provided continuous guidance for the experiments and the analysis. F.P., F.H. and J.C.C. carried out the theoretical modelling and DFT calculations. The bulk of the paper was written by D.R.W. and D.N. All authors discussed the results and contributed to manuscript revision.

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