Optical wireless link between a nanoscale antenna and a transducing rectenna

Initiated as a cable-replacement solution, short-range wireless power transfer has rapidly become ubiquitous in the development of modern high-data throughput networking in centimeter to meter accessibility range. Wireless technology is now penetrating a higher level of system integration for chip-to-chip and on-chip radiofrequency interconnects. However, standard CMOS integrated millimeter-wave antennas have typical size commensurable with the operating wavelength, and are thus an unrealistic solution for downsizing transmitters and receivers to the micrometer and nanometer scale. Herein, we demonstrate a light-in and electrical signal-out, on-chip wireless near-infrared link between a 220 nm optical antenna and a sub-nanometer rectifying antenna converting the transmitted optical energy into direct electrical current. The co-integration of subwavelength optical functional devices with electronic transduction offers a disruptive solution to interface photons and electrons at the nanoscale for on-chip wireless optical interconnects.

2a is an energy diagram illustrating electron tunneling through a MIM junction polarized by a bias V dc .
Here, φ1 , φ2 are the energy barrier heights of the metal on the left side and the right side of the MIM interface and E F is the Fermi energy. Following the interpretation provided by Brinkman et al, the simplified expression for the tunneling current (I) through such a junction is given by, 3 Supplementary Equation 1 Where, ) 025 . 1 exp ( 10 16 .
In our experiment, we expect a very minimal asymmetry in the barrier height over the gap since the material on both sides is similar. However, a residual asymmetry is generally observed 4,5 , which probably results from a geometry-dependent modification of the barrier height 6 . In general, for bulk Au-SiO 2 interface the height of the Schottky barrier is around 4.5 eV as SiO 2 has an electron affinity of 0.75 eV. 7 However, in case of atomic scale gaps, formation of image charges at the metal-insulator interfaces may result in significant lowering of the height of the barrier [8][9][10] . We include all these aspects into our calculation to estimate the set of parameters g, φ and Δφ by fitting the experimentally recorded I-V characteristics curve with Supplementary Equation 1 upon fixing the cross-section area A to a constant value. It is experimentally difficult to infer A as electron microscopy provides a general configuration of the junction but failed to indicate where tunneling is really occurring. Imaging a pristine gap on a non-conductive glass substrate with a high resolution SEM microscope proves to be extremely challenging. This precludes operating the SEM under optimal acceleration voltages because charging effects will inevitably disturb the image. In the SEM micrograph presented in the manuscript, the image was obtained by sputtering the device with a thin layer of Au to enable the evacuation of the charges. The procedure is thus destructive.
Supplementary Figure 2| Estimation of the electromigrated junction gap width. a Energy diagram illustrating the electron tunneling through an atomic scale MIM junction under an applied bias V dc . b I-V characteristics of the electromigrated junction used in our experiment. The black data points represent the experimentally measured I-V characteristics of the junction. The blue plot is the Simmons' formula fit of the experimental data with fitting parameters A = 100 nm 2 , φ = 2.06 eV, Δφ = -0.31 eV and g = 4.56 Å. c Evolution of all the fitting parameters (φ, Δφ and g) as a function of cross section area A. The points highlighted by yellow color indicate the set of parameters obtained from the fit represented in Supplementary Figure 2b.
Supplementary Figure 2b shows the fitting (red line) of the experimentally recorded I-V plot (black data points) assuming a cross-section of 100 nm 2 (an active area which is 10 nm thick by 10 nm wide) which results in an estimation of the gap width g = 4.56 Å with φ = 2.06 eV and Δφ = -0.31eV. In Supplementary Figure 2c, we plot the evolution of all the parameters as a function of various crosssectional areas. From these calculations, we conclude that the tunneling gap has an effective width remaining below 5 Å.
A study by Frimmer et al. suggested that the Ti adhesion layer evaporated between the glass substrate and the Au may form a TiO 2 barrier at the electromigrated gap. Based upon the representation of the IV characteristics in the form of a Fowler-Nordheim plot and an analysis of the transition voltage, the authors proposed a modified energy barrier and concluded that the tunneling transport occurs through TiO 2 11 . However, interpretation of transition voltage spectroscopy as a measure of the barrier height is highly debated in the literature. In fact, recent studies suggest that transition voltage observed in Fowler-Nordheim plots do not stand for a change in the electron transport mechanism from direct tunneling to field emission. Instead, the minimum of the Fowler-Nordheim plot mainly signifies a transition towards a higher nonlinearity order in the I-V curve 12,13 . From the tunneling current expression in Supplementary Equation 1 an analytical expression for transition voltage V T can be determined: where m is the mass of electron, e is the charge of electron and g is the gap width in Angstrom. The makes clear that such response is not occurring here. This is expected considering the excitation condition and the geometry of the device. In the present scenario, the 785 nm wavelength laser is polarized along the orientation of the electrodes and is thus enable to resonantly excite the plasmon response of the 100 nm wide constriction.
From this set of data, we conclude that when the junction is illuminated symmetrically with a centered laser beam, optical rectification is predominant and the recorded photocurrent is devoid of any laserinduced thermal contributions.
Illumination of the transmitter antennas. To complement the above experiment we monitor the conductance ∂I/∂V at f chop when adjacent nanoantennas are illuminated. Laser-induced thermal variation of the conductance should modulate the recorded photocurrent 14 . We simultaneously map the I phot signal and ∂I/∂V, both at f chop by scanning the laser through the area comprising the optical antennas as presented in Supplementary Figure 5a and b, respectively. The incident polarization of the laser is kept along the vertical axis for the entire experiment (maximized antenna transmission towards the rectenna). It is evident from these maps that we could not measure a change even down to 10 -5 level in the conductance map which can be correlated to the recorded I phot signal. Therefore, we can infer from this experiment that the recorded photocurrent is produced through the optical rectification of the transmitted radiation and not due to any laser-induced modulation of the junction conductance. transmitter instead of a 220 nm unit results in a lower electromagnetic field at the junction (Fig. 4b). Here