SUPPLEMENTARY INFORMATION

Transcription

1 Supplementary Information Electrically-driven subwavelength optical nano-circuit. Kevin C. Y. Huang 1,2, Min-Kyo Seo 1,3,#, Tomas Sarmiento 2, Yijie Huo 2, James S. Harris 2 and Mark L. Brongersma 1, 1 Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA 2 Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA 3 Department of Physics and Institute for the NanoCentury, KAIST, Daejeon , Republic of Korea # minkyo seo@kaist.ac.kr brongersma@stanford.edu The supplementary information contains text and 27 figures in support of the main body of the text. It discusses fifteen specific topics: 1. Fabrication process with a GaAs substrate. 2. Fabrication process with an oxidized AlGaAs substrate. 3. Nano-LED cross-sectional schematics. 4. Emission coupling efficiency into the gap plasmon mode. 5. Gap plasmon mode size, mode confinement and propagation length. 6. Sheet plasmon dominated electroluminescence scattering images 7. Gap plasmon to sheet plasmon in-plane scattering angle distribution 8. Nano-LED electrical and emission characteristics 9. Purcell factor inside the nano-led 10. Free space coupling with slot antennas. 11. T-splitter coupling efficiency 12. Nano-LED IV curves 13. Time-resolved electroluminescence 14. Supplementary methods 15. Supplementary discussion NATURE PHOTONICS 1

2 1 Fabrication process with GaAs substrate In this section we provide the step-by-step schematics and description for the fabrication process with a high-index GaAs substrate, which is the same as described in the main text. The advantages of this method are as follows: 1. Low series resistance due to large area substrate n-contact. 2. Narrow and long QW ridge can be achieved. No aspect ratio limitation. 3. Al 2 O 3 protects the active QW region from FIB damage. 4. Self-aligned p-contact on the QW ridge. 5. Nano-LED output facet unobstructed. 6. By using a sacrificial AlGaAs layer in the epitaxial wafer, the region below the nano-led can be undercut to provide an air substrate for better gap plasmon coupling. 2 NATURE PHOTONICS

3 SUPPLEMENTARY INFORMATION Figure S1: Step-by-step fabrication process with high-index GaAs substrate. a, The QW structure is grown by molecular beam epitaxy on an n-doped GaAs substrate and consists of a 300 nm n-doped GaAs layer, an 8 nm In 0.15 Ga 0.85 As QW surrounded by 20 nm GaAs barriers and a 60 nm p-doped GaAs layer. The doping densities for the n-gaas and p-gaas are cm 3 and cm 3 respectively. b, Photolithography is performed and the edge of the wafer is plasma etched (BCl3/Cl2) to expose the n-gaas substrate. Different layers in the substrate are represented by a single color from now on for simplicity. c, Perform photolithography, then deposit 20 nm/6 nm/12 nm/200 nm of Au/Ge/Ni/Au on the exposed n-gaas substrate. The contact is annealed in a rapid thermal anneal chamber at 450 degrees Celsius for 60 seconds. d, 200 nm SiO 2 is deposited using plasma-enhanced chemical vapor deposition with N 2 O and 2% SiH 4. Photolithography is performed, then the sample is dipped in 6:1 buffered oxide etch to form isolated SiO 2 pads. e, Photolithography is performed. 10 nm/ 200 nm of Cr/ Au is deposited on top of the SiO 2 pad using electron beam evaporation. f, Electron beam lithography is performed. The sample is dipped in 20:1 HF for 10 seconds to remove the GaAs native oxide. 2 nm/ 60 nm of Ti/Au is deposited at a 45 degree tilted angle towards the large metal pad. After lift-off, a 60 nm wide p-contact remains. g, Electron beam lithography is performed. Using the p-contact as a hard mask, the exposed wafer is plasma etched (BCl 3 /Cl 2 ) to form a 130 nm tall ridge. A 5-10 nm conformal layer of Al 2 O 3 is deposited using atomic layer deposition to insulate the substrate and provide protection for the QW ridge. h, Electron beam lithography is performed. 10 nm /150 nm of Cr/ Au is deposited at a 45 degree angle away from the metal pad to ensure the output facet of the QW ridge is not coated. The ridge produces an evaporation shadow which is used for subsequent alignment in the FIB. i, 80 nm wide slot-wgbased passive circuit elements are milled in the Au slab using the FIB. For efficient excitation of gap plasmons, the slot must be aligned to the output facet of the nano-led to within nm. j, Electron beam lithography is performed to coat the nano-led in resist but expose the milled slots. The GaAs substrate is undercut by nm through the slots using H 3 PO 4 :H 2 O 2 :H 2 0 = 3:2:20 isotropic wet etch, thus completing the suspended slot WG. NATURE PHOTONICS 3

4 Figure S2: a, Tilted SEM image of the Al 2 O 3 -coated QW ridge. The scale bar is 1 µm. b, Top view SEM image of tilted directional deposition of 150 nm Au. An evaporation shadow is visible at the end of the QW ridge. The scale bar is 1 µm. Figure S3: a, Tilted SEM image of a slot-wg-coupled nano-led with linear groove gratings. The scale bar is 2 µm. b, Top view SEM image of a directional coupler with PMMA electron beam resist encapsulating the nano-led. The scale bar is 2 µm. Figure S4: a, Tilted SEM image of a slot WG bend before wet etching. The scale bar is 1 µm.b, Tilted SEM image of the same slot WG bend after wet etching. The scale bar is 1 µm. 4 4 NATURE PHOTONICS

5 SUPPLEMENTARY INFORMATION 2 Fabrication process with oxidized AlGaAs substrate In this section we provide the step-by-step schematics and description for an alternative fabrication process with low-index oxidized AlGaAs substrate. The advantages of this method is as follows: 1. Low index substrate without the need for undercut. 2. Support very long and narrow Au strips for directional couplers 3. Higher spontaneous emission factor into the gap plasmon mode than with GaAs substrate. 4. Excellent electrical isolation. Figure S5: Step-by-step fabrication process with high-index GaAs substrate. a,the QW structure is grown by molecular beam epitaxy on an n-doped GaAs substrate and consists of a 500 nm n-doped Al 0.95 Ga 0.05 As layer, a 50 nm n-doped GaAs layer, an 8 nm In 0.16 Ga 0.84 As QW surrounded by 20 nm GaAs barriers and a 30 nm p-doped GaAs layer. The doping densities for the n-gaas and p-gaas are cm 3 and cm 3 respectively. Photolithography and plasma etching are performed to form a 600 nm tall, µm 2 QW mesa. The sample is placed in a wet oxidation chamber at 450 degrees Celsius to oxidize the Al 0.95 Ga 0.05 As layer. b, Electron beam lithography is performed. Using the electron beam resist as a mask, 100-nm-wide, 130-nm-tall QW ridge is defined using plasma etching (BCl 3 /Cl 2 ). c, Perform electron beam litography. Conformally coat the end of the QW ridge with 5 nm Al 2 O 3 using atomic layer deposition to protect the active medium against subsequent FIB milling. d, Perform electron beam litography. Deposit 2 nm/ 200 nm of Ti/ Au using electron beam evaporation to form the p-contact. Plasma etch to expose the n-gaas layer. e, Deposit 20 nm/ 6 nm/ 12 nm/ 200 nm of Au/Ge/Ni/Au n-contact. Anneal at 450 degrees Celsius for 60 seconds. f, Use FIB to mill slots and passive circuit elements starting from the output facet of the nano-led. 5 NATURE PHOTONICS 5

6 Figure S6: SEM images of fabricated nano-led on oxidized AlGaAs mesa. a, Tilted SEM image of the 500 nm tall, 20 µm by 30 µm oxidized AlGaAs mesa with n- and p-contacts. b, Zoomed in tilted SEM image of a showing the lateral n-gaas contact and 200 nm Au coated QW ridge on oxidized AlGaAs. Note the side of the QW ridge is completely covered. Figure S7: Slot-WG-coupled nano-led with low index substrate and lateral current injection. a, Schematics of nano-led on low-index substrate. b, Top view SEM image of the slot-wg-coupled nano-led. The scale bar is 2 µm. 6 NATURE PHOTONICS

7 SUPPLEMENTARY INFORMATION 3 Nano-LED Cross-sectional Schematics Figure S8: Ideal Nano-LED cross-sectional schematics. a, Cross-sectional schematics for nano-leds fabricated on GaAs substrate with 150-nm-thick Au coating. The 20-nm-thick p-contact is self-aligned on the 130-nm-tall QW ridge, both of which are encapsulated in a 10 nm conformal Al 2 O 3 and insulated from the Au over layer. The InGaAs layer is 80 nm beneath the top of the p-gaas layer. The Au thickness between the top of the QW ridge and the adjacent top Au surface can be very thin due to the shadowing effect of the electron beam evaporation, allowing light to leak out in actual devices. b, Cross-sectional schematics for nano-leds fabricated on GaAs substrate with 200-nm-thick Au coating. c, Cross-sectional schematics for nano-leds fabricated on oxidized AlGaAs substrate with 200-nm-thick Au coating which is also the p-contact. The InGaAs layer is 80 nm beneath the top of the p-gaas layer. Despite the fact that this drawing suggests that the PIN diode would be shorted by the Au coating, the shadowing effect of the electron beam evaporation introduces a small air gap between the semiconductor sidewalls and the Au, preventing current leakage. NATURE PHOTONICS 7

8 4 Emission coupling efficiency into gap plasmon mode Figure S9: FDTD simulation geometry schematics for a 130-nm-tall, 80-nm-wide nano-led with GaAs substrate coupled to a 150-nm-tall, 80-nm-wide Au slot WG. The physical dimensions of the GaAs-based nano-led is fixed while we vary the substrate material from GaAs, oxidized AlGaAs to air. For each configuration, we calculate the fraction of power emitted into the gap plasmon mode, fraction of power absorbed by the Au and the fraction of power emitted into the substrate. a, Top view. b, Side view through the center of the nano-led and the slot WG indicated by the blue dashed line in a. c, Cross-sectional view through the nano-led region indicated by the left cyan dashed line in a. d, Cross-sectional view through the slot WG region indicated by the right cyan dashed line in a 8 NATURE PHOTONICS

9 SUPPLEMENTARY INFORMATION Figure S10: FDTD simulated electrical field profile for a 130-nm-tall, 80-nm-wide nano-led with GaAs substrate coupled to a 150-nm-tall, 80-nm-wide Au slot WG. The plotted quantity is log(re(e 2 )). The green dashed box denotes the flux surfaces through which the power emitted downwards into the substrate, power emitted in the -y direction and the power absorbed by the metal are calculated. The yellow dashed box denotes the flux surface through which the guided gap plasmon mode power is calculated. a, Top view. b, Side view through the center of the nano-led and the slot WG. c, Cross-sectional view through the nano-led region. d, Cross-sectional view through the slot WG region. Figure S11: FDTD simulated electrical field profile for a 130-nm-tall, 80-nm-wide nano-led with different substrates substrates coupled to a 150-nm-tall, 80-nm-wide Au slot WG. The plotted quantity is log(re(e 2 )). As the refractive index of the substrate is reduced from GaAs to air, the coupling efficiency of the dipole emission increases from 10% to 50%, mostly due to the reduction of available modes present in the substrate. a, Schematic of the side view through the center of the nano-led and the slot WG. b, log(re(e 2 )) for GaAs substrate. c, log(re(e 2 )) for oxidized AlGaAs substrate. d, log(re(e 2 )) for air substrate. Due to strong interference effects in to the active region for the nano-led with air substrate, the emission in the +y direction into the air slot WG can be greater than the emission in the -y direction for optimal placements of the dipole emitter. NATURE PHOTONICS 9

10 Figure S12: FDTD simulated excitation efficiency for a x-oriented dipole placed inside a 130-nm-tall, 80-nmwide nano-led with varying substrates coupled to a 150-nm-tall, 80-nm-wide Au slot WG as a function of emitter y-position. a, Fraction of power coupled to the Au slot WG. The air substrate configuration exhibits the highest efficiency ( 50%) while GaAs shows the lowest ( 10%). As the emitter is moved away from the output facet of the nano-led, the coupling efficiency oscillates as a result of the varying Purcell factor in the cavity while the average coupled power drops due to increased absorption. b, Fraction of power directed downwards is dramatically suppressed using a low index substrate (air) compared to a high index GaAs. c, Fraction of power absorbed by the metal is approximately constant over all y-positions. The metal losses are higher with a low index substrate because most of the emitted power is confined in the slot region. d, Fraction of power emitted towards the -y direction approximately complements a for all types of substrates. Since the -y direction is assumed to be semi-infinite without the transition to the air slot WG, the dependence on the substrate index is weaker. 10 NATURE PHOTONICS

11 SUPPLEMENTARY INFORMATION 5 Gap plasmon mode size, mode confinement and propagation length Figure S13: FDTD simulated 80-nm-wide Au slot gap plasmon mode excited by an x-oriented dipole placed in the center of the slot 4 µm away as a function of Au thickness at 970 nm excitation wavelength. Scale bar is 500 nm. a, E 2 mode profile for 100-nm-thick Au slot. b, E 2 mode profile for 240-nm-thick Au slot. c, E 2 mode profile for 400-nm-thick Au slot. As the Au thickness is increased, the excited field intensity in the slot decreases due to increased mode area and weakened emitter/ gap plasmon mode coupling strength. d, Gap plasmon propagation length as a function of Au thickness. e, Gap plasmon mode confinement factor as a function of Au thickness. f, Gap plasmon effective mode area as a function of Au thickness (blue crosses). The red line is a linear fit to the simulated data points. The mode area exhibits a linear relationship with respect to the Au thickness, an indication that the total energy increases in proportion to the rectangular slot area and that the energy outside the slot region is approximately constant. NATURE PHOTONICS 11

12 6 Sheet plasmon V.S. gap plasmon electroluminescence scattering images Figure S14: EL images of straight slot-wg-coupled nano-leds with linear grooves on the top Au surface. The nano-led EL scattering images taken for the two polarizations overlaid on top of the SEM image of the source as shown in Figure 2b. a, Collected EL image for y-polarized detection. The polarized light scattering from the linear grooves is consistent with the scattering behavior of sheet plasmons emitted from the nano-led region propagating on the top metal surface. Such leakage of the nano-led emission into the sheet plasmon mode is not desirable and in this device occurs as a result of imperfect alignment of the slot WG to the nano-led. The scale bar is 2 µm. b, Collected EL with x-polarized detection. The polarization of light scattering from the end of the WG is consistent with gap plasmons propagating inside the slot. The scale bar is 2 µm. Figure S15: Sheet plasmon excitation in T-splitter coupled nano-led. Large misalignment between the slot WG and the nano-led causes strong sheet plasmon excitation. a, EL image for x-polarized detection. No scattering from the top port is observed indicating the lack of gap plasmon excitation. The scale bar is 2 µm. b, Electroluminescence image for y-polarized detection. The entire left branch produces significant scattering indicating strong excitation of sheet plasmons. The scale bar is 2 µm NATURE PHOTONICS

13 SUPPLEMENTARY INFORMATION 7 Gap plasmon to sheet plasmon in-plane scattering angle distribution Figure S16: EL scattering images with polarization sensitive detection for a 5-µm-long straight-slot-coupled nano-led. 40-nm-deep concentric grooves surround the end of the slot WG to analyze the sheet plasmon scattering direction and polarization. The scale bar is 2 µm. a, EL image for y-polarized detection. Light scattering observed in the forward azimuthal direction with a polarization consistent with sheet plasmons traveling upward from the source to the grating structure on the top Au surface. b, EL image for x-polarized detection. Light scattering is observed at all azimuthal angles except in the forward direction. The polarization is consistent with sheet plasmons emitted from the end of the slot WG. c, EL scattering intensity as a function of azimuthal angle for x-polarization (blue) and y-polarization (red) detection. NATURE PHOTONICS 13

14 Figure S17: In-plane azimuthal angle dependence of gap plasmon excitation of sheet plasmon at the end of the slot WG. a, Measured x-polarized sheet plasmon excitation radiation pattern after subtraction of the background sheet plasmon emitted directly from the nano-led region. b, Simulated x-polarized sheet plasmon excitation radiation pattern from the end of the slot WG. 14 NATURE PHOTONICS

15 SUPPLEMENTARY INFORMATION 8 Nano-LED electrical and emission characteristics Figure S18: Electroluminescence spectrum from a 20 µm by 10 µm planar LED at different driving current densities at room temperature. The peak emission wavelength is 963 nm and the full-width at half-maximum is 35 nm. NATURE PHOTONICS 15

16 Figure S19: Electroluminescence spectrum for 130-nm-tall, 80-nm-wide nano-leds at different pulsed driving voltages. a, Emission spectrum for the 150-nm-Au-coated, 4-µm-long nano-led driven at different pulsed voltages. The dots are the raw measurement data. The solid lines are the smoothed spectrums using a low-pass filter. The spectrum is the same as that of the bare QW due to significant light leakage from the side of the QW ridge. b, Emission spectrum for 200-nm-Au-coated, 2.5-µm-long nano-led. The spectrum exhibits Fabry-Pérot resonances along the length of the QW ridge (black arrows). The free spectral range is approximately 20 nm. At high driving voltage, emission from the GaAs barrier is visible (orange arrow). Figure S20: SEM image of nano-led and LED mesa. a, Tilted SEM image of a 2.5-µm-long, 200-nm-thick Au coated nano-led. The scale bar is 1.5 µm. b, Tilted SEM image of a 10-µm-wide, 20-µm-long, 500 nm tall LED mesa. The scale bar is 10 µm. A thin layer of Al 2 O 3 serves as an electrical insulator between the contacts and the substrate. 16 NATURE PHOTONICS

17 SUPPLEMENTARY INFORMATION Figure S21: Fabry-Pérot resonances of 200-nm-Au-coated nano-led and LED mesa. a, WG mode dispersion relation for propagating modes in GaAs (red) and the gap plasmon mode (blue) calculated in FDTD ignoring Au metal loss. The gap plasmon mode index is 5.24 at a wavelength of 950 nm. b, Measured EL emission spectrum of 2.5-µmlong, 200-nm-thick Au coated nano-led (blue) and theoretically predicted Fabry-Pérot resonance wavelengths (red dashed) taking into account the GaAs dispersion, gap plasmon modal dispersion and the gap plasmon reflection phase ( π/2). The experimental free spectral range is 20 nm and the theoretically predicted value is 21 nm. c, Measured EL emission spectrum for 10-µm-wide, 20-µm-long, 500-nm-tall LED mesa. The measured free spectral range is 6.5 nm, which is much shorter than the gap plasmon resonances shown in b. NATURE PHOTONICS 17

18 9 Purcell factor inside the nano-led Figure S22: Simulated Purcell factor and EL spectrum for 2.5 µm long nano-leds with different widths. a, Spatially averaged Purcell factor for x-polarized dipoles placed at the x = 0 position inside the nano-led cavity modeled with 3D FDTD simulations. The Purcell factor drops dramatically from 80-nm-wide nano-led to 300- nm-wide nano-led. The amplitudes of the resonances are also much lower for wider QW widths as expected due to weaker emission coupling to the gap plasmon mode. b, Measured EL spectrum from 2-µm-wide, 2.5-µm-long LED coated in 200 nm Au. c, Simulated EL spectrum by multiplying the Purcell factor shown in a by the emission spectrum of a large area LED shown in b. The simulated spectrum for the 80-nm-wide nano-led is the same as the results shown in Fig. 2c. As the QW width increases, the resonance positions shift and decrease in amplitude, which demonstrates that a good agreement between the simulated and experimental results shown in Fig. 2 is only possible if the behavior of the measured nano-led cavity is accurately modeled by the simulation. 18 NATURE PHOTONICS

19 SUPPLEMENTARY INFORMATION Figure S23: FDTD simulated spontaneous emission enhancement factor as a function of slot width for an x- oriented dipole placed at the center of an infinitely long Au-coated nano-led ridge. The GaAs LED ridge is 130 nm tall, coated with 150 nm Au. The substrate is either GaAs or air. a, Spontaneous emission enhancement as a function of slot width for a nano-led with a 5 nm conformal Al 2 O 3 coating. There is no significant difference between GaAs (blue) and air (red) substrate. The enhancement increases with decreasing width. Overall enhancement is quite low even for 30 nm width slots. b, Spontaneous emission enhancement as a function of slot width for a nano- LED without any Al 2 O 3 coating. There is no significant difference between GaAs (blue) and air (red) substrate. The enhancement increases with decreasing width and reaches a much higher factor of 14 compared to a at a slot width of 30 nm. NATURE PHOTONICS 19

20 10 Free space coupling with slot antennas Figure S24: FDTD simulated outcoupling efficiency for gap plasmons scattering from the end of a 150-nm-tall, 80-nm-wide Au slot WG with side slot antennas of varying length. The center-to-center separation between slot antennas and the slot WG is 160 nm. a, Schematics of the simulation showing the input gap plasmon and flux surfaces through which the power coupled to free space and sheet plasmon are calculated. The red arrows indicate the sheet plasmon power integration surfaces. The blue arrow indicate the upwards-propagating free space radiation integration surface. b, Fraction of power coupled to free space and sheet plasmons (summed over both +y and -y half-space) as a function of the side slot antenna length L. At short L, the scattering efficiencies approach that of the unaccompanied slot termination, where 70% of the input power is reflected and only 15% is outcoupled. At L=320 nm, a slot antenna resonance is established, outcoupling up to 70% of the input gap plasmon power while dramatically decreasing the reflection through impedance matching with free space. c, Top view of the simulated instantaneous electric field profile in the slot WG and the slot antennas for L=320 nm. Strong electric field with a single antinode is observed inside the side slots where the phase is opposite to that of the field inside the slot WG. 20 NATURE PHOTONICS

21 SUPPLEMENTARY INFORMATION 11 T-splitter coupling efficiency Figure S25: FDTD simulated coupling efficiency for gap plasmons interacting with a T-splitter junction. a, Schematics of the simulation showing the input gap plasmon and flux surfaces through which the power leakage at the junction (blue surface), power scattered by the left port (purple surface) and power scattered by the forward port (green surface) are computed. b, Fraction of input power scattered upwards to free space by the junction (blue), left port (purple) and forward port (green) as a function of the Au slot thickness at a fixed slot width of 80 nm. For thin Au thicknesses, the leakage is significant due to the low aspect ratio of the slot and poor confinement factor of the mode. In this regime, the propagating mode is not quasi-static thus the splitting ratio at the junction is not 50/50. As the Au thickness increases, leakage is reduced monotonically and the difference between the left/ forward scattered gap plasmon power decreases. NATURE PHOTONICS 21

22 12 Nano-LED IV Curves Figure S26: LED IV characteristics. a, IV curves for a 20 µm by 10 µm planar LED (blue) and a 130-nm-tall, 80-nm-wide, 4-µm-long nano-led (red). The nano-led IV curve shows higher turn-on voltage ( 2 V) and earlier reverse break down. The modeled IV curve with the ideal diode equation without leakage is shown in black dashed line for the large area LED and green dashed line for the nano-led. b, Average current density vs. applied pulsed voltage amplitude. The voltage pulse width is 10 ns and the repetition rate is 1 MHz. For pulsed excitation, the turn-on voltage is approximately 4.5 V. 22 NATURE PHOTONICS

23 SUPPLEMENTARY INFORMATION 13 Nano-LED Time-Resolved Electroluminescence Figure S27: Time-resolved EL for a 130-nm-tall, 80-nm-wide, 4-µm-long nano-led driven with 6 V, 2 MHz, 10 ns voltage pulses (average current of 5 na). Red dots are the raw time-resolved intensity data. The blue line is the data processed with a low-pass filter, the fall time of the EL is 3 ns and is limited by the 7 ns fall time of the driving voltage (black dashed line). NATURE PHOTONICS 23

24 14 Supplementary Methods Full-field 3D FDTD simulations are performed using a combination of in-house codes as well as the publicly available software MEEP developed by MIT to calculate the emission properties from the sources (Supplementary Fig. S10-S13, S21-S22). The spatial grid resolution is 5 nm and the boundary condition used is an absorbing perfectly match layer. For electric field intensity distribution plots, the gap plasmons are excited in the slot WG using a single continuously oscillating electric dipole source placed at the center of the slot oriented normal to the sidewalls. After the simulation has reached steady state (typically 50 optical periods), the complex electric field at each spatial location is extracted and converted to intensity. The electric dipole coupling efficiency to gap plasmons, substrate propagating waves and metal absorption are simulated using the approximate 3D geometry of the experimentally fabricated Au-coated nano-led devices. The Au permittivity dispersion is modeled using a Lorentz-Drude dispersion while the GaAs index is fixed at n=3.5. The coupling efficiency into each radiation channel is obtained by computing the power flowing through each surface surrounding the nano-led active region (Supplementary Fig. S9, S10) and normalizing by the total emitted power from the electric dipole. The spontaneous emission enhancement factor (Supplementary Fig. S22-S23) is calculated by normalizing the total emitted power from the dipole inside the structure of interest by the radiated power from the same dipole placed in a homogeneous GaAs medium. The gap plasmon mode profile, propagation length, confinement factor and mode area (Supplementary Fig. S13) are calculated by exciting the gap plasmon mode using an x-oriented electric dipole placed at the center of the slot WG and observing the field profile at various distances away from the source point. By plotting the electric field intensity as a function of distance and fitting the decay to a single exponential, we obtained the gap plasmon propagation length (Supplementary Fig. S13d). The mode confinement factor (Supplementary Fig. S13e) is calculated by normalizing the gap plasmon guided power inside the rectangular slot area by the total gap plasmon guided power within a 800 nm by 800 nm square region centered around the slot. The effective mode area (Supplementary Fig. S13f) is given by 34 A m ( r e,ω)= 1 2ɛɛ 0 E( r e,ω) 2 [ɛ 0 d(ɛω) dω E( r, ω ) 2 + µ 0 H( r, ω ) 2 ]d A (1) where the integrand is the electric and magnetic field energy density of the mode and the denominator is the electric field energy density at the location of the emitter. In this case, r e is taken to be the center of the slot. To show that oscillations observed in the EL spectrum of 200 nm Au-coated nano-led fabricated on oxidized AlGaAs substrate (Fig. 2a,c) can be attributed to Fabry-Pérot resonances of a single gap plasmon mode inside the nano-led ridge, we calculate the resonance wavelengths of the gap plasmon inside the WG cavity using the phase matching condition: 2n mode (λ)l + φ r (λ) =mλ (2) where n mode (λ) is the gap plasmon mode index as a function of wavelength, L =2.5 µm is the physical cavity length, and φ r (λ) π/2 is the gap plasmon reflection phase as a function of wavelength S 1 and m is an integer denoting the resonance order. As a first-order approximation for n mode (λ), we sum the material dispersion of GaAs at 950 nm dn/dλ = nm 1 with the gap plasmon modal dispersion (dn/dλ = nm 1 ) calculated with a fixed GaAs index of 3.5 (Supplementary Fig. S21a). The gap plasmon mode index is 5.24 at 950 nm wavelength. Therefore n mode (λ) (λ 950) (3) 24 NATURE PHOTONICS

25 SUPPLEMENTARY INFORMATION Combining Eq. 2 and Eq. 3 solving for λ, we obtain the resonance wavelengths shown in Supplementary Fig. S21b (red dashed lines). NATURE PHOTONICS 25

26 15 Supplementary Discussions Using a simple Fabry-Pérot model, one can extract the plasmon coupling efficiency directly from the oscillation amplitude of the experimental EL spectrum. The analysis is as follows: Fig. 2c shows that our emission baseline intensity at 950 nm is 0.7, with an oscillation amplitude of 0.1. Assuming the round-trip propagation loss is high, such that the plasmon only sees the mirror once (single interference) to the first order, the peak amplitude can be expressed approximately as: (E 0 + E p + E p rp) 2 = where E 0 is the amplitude of the emission other than the plasmon mode, E p is the plasmon amplitude, r is the reflection, p is the round trip propagation loss. Assume r =1for the most conservative estimate, p = 0.36 (propagation length equal to round trip length), (E 0 + E p ) 2 =0.7, we obtain E p =0.157 which leads to a lower bound plasmon coupling efficiency of E 2 p/(e 0 + E p ) 2 =3.5% Note that by assuming r =1, we drastically underestimate the plasmon coupling efficiency. A more reasonable estimate 27 of r for 80-nm-wide MSM waveguide is 0.5, in which case the plasmon coupling efficiency inside the active region becomes 14%, which is in line with our pure simulation estimates. Our experimentally-determined total system wall plug power efficiency for the electrically-driven nanocircuit shown in Fig. 2b is (detected scattered optical power from the end of the 5-µm-long WG divided by the input electrical power) as described in the main text. There are many parameters which contribute to the total efficiency, here are our best estimates of each of these efficiency factors. The ratio between the emission energy potential and our driving voltage potential is 0.57, the current injection efficiency is 0.04 (see the next paragraph) and the coupling efficiency of the source to gap plasmons in the slot WG of 5%, the transmission of the gap plasmon over the 5-µm-long slot WG of 40%, upwards scattering of the gap plasmon from the end of the slot WG of 5% and a QW ridge internal quantum efficiency of 80%. With these numbers, we expected the wall plug efficiency to be approximately The large discrepancy between the experimentally measured value and our estimate breakdown is expected because of insufficient Au overlayer thickness to cover the sides of the QW ridge as well as large uncertainties in several factors which are difficult to quantify. These include the carrier escape rate from the QW, surface recombination rate at the QW sidewalls, operating junction temperature and electric field effects on the internal quantum efficiency, all of which are parasitic effects which we have conservatively assumed to be nonexistent to obtain a lower bound of the out-coupling efficiency. A substantial leakage current is quite common for LEDs with a large perimeter of sidewall etching. Here, the diode current in the absence of leakage used in the above calculation for the nano-led total wall plug efficiency and in Supplementary Fig. S26a is estimated as follows: Starting with the measured IV curve of the large area LED (20 µm by 10 µm) shown in Fig. S26a, we fitted the diode equation: J = J s e (V f V bi RsJ) k b T q (4) V f is the forward voltage across the diode, V bi is the built-in voltage of the junction (1.2 V, slightly below the emission bandgap), k b is the Boltzmanns constant and T is the temperature. J s and R s are the fitting parameters, where R s is the series resistance in Ωcm 2. They are determined to be J s = A/cm 2 and R s = 0.03 Ωcm 2. Now assuming the bulk diode characteristics stays the same (J s and V bi unchanged) as we shrink the LED down to our nano-led dimensions, we can predict the diode current by scaling up the series resistance, as it is inversely proportional to the device area. The large area LED has 600 times the area of the nana-led (80 nm by 4 µm), therefore, the R s for the nano-led is approximately 18 Ωcm 2. Using these parameters, the diode current is 3.5 A/cm 2 at the operating voltage of 2.25 V, which is 23 times less than the total measured current of 80 A/cm 2, therefore the current injection efficiency is approximately 0.04 for the nano-led. Note that this is only an approximate model to the first order, which does not properly take into 26 NATURE PHOTONICS

27 SUPPLEMENTARY INFORMATION account the actual shunt leakage mechanism. For this reason, our estimated R s of 18 Ωcm 2 is artificially high and is not representative of actual device resistance. In order to correctly obtain the leakage current, one must model the the behavior of a non-linear element placed in parallel to the diode. The typical 5 V driving voltage pulses are approximately 10 ns in duration (Supplementary Fig. S27). Since we did not specifically design the electrical transmission line to be impedance matched to the wire bond pad or the nano-led at the pulse frequency, actual voltage across the junction will be much less than 5 V. By taking an IV curve of the device at DC, we see that the nano-led turn-on voltage is much less than 5 V (Supplementary Figure S26a) even though the turn-on is softer with higher series resistance compared to the large area LED. Our emission detectability threshold average current is around 1.5 A/cm 2 and can be achieved at around 1.4 V DC input voltage, which is only 0.13 V above the bandgap energy of the QW. From an electrical device point of view, our metal-semiconductor contacts are far from optimal and there is of course much room for improvement but forward voltage optimization is not the main objective of this paper. For a forward biased PN junction, the dominant capacitance results from the stored minority carriers outside the depletion region which build up during the turn-on transient. If the p-contact is Schottky, it can contribute extra stored charges. Assuming that the stored charges is approximately the built-up minorities carriers in the PN junction, the turn off-transient time toff will be the time it takes for the PN junction to remove these minority carriers, approximately given by t off = τln(1 + I F /I R ) where τ is the minority carrier lifetime in the PN junction, which, for the case of our structure, will be close to the carrier lifetime in the quantum well as the 3 µm carrier diffusion length S 2 is much greater than the thickness of the device, I F is the forward current during the on cycle (V F /R S ), and I R is the reverse current during the off cycle (V R /R S ). We see that the turn-off transient, which in general is the speed limiting factor, is independent of the R S because it appears both in I F and I R. The consequence of higher R S is larger energy dissipation because higher V F and V R is required to achieve the same current. Note that this is different from charging or discharging a passive capacitor because the carrier behavior in a PN junction is governed by diffusion and recombination, not just drift alone. In summary, provided that we can apply fast voltage pulses (necessary driving electronics and impedance matched transmission lines), the modulation speed of the LED emission will be limited by the minority carrier lifetime in the active region. To characterize the operation of the slot WG coupled nano-led, we capture the image of the EL in a microscope setup with polarization-sensitive detection to obtain a spatial map of the free space scattering. Supplementary Fig. S14 are EL images of the device shown in Fig. 2b in the two orthogonal detection polarizations either parallel to the slot (Supplementary Fig. S14a) or normal to the slot (Supplementary Fig. S14b). We use polarization-sensitive detection to distinguish the scattering from the two possible guided pathways on the metal surface, namely one-dimensionally (1-D) confined SPPs on the top metal/air interface (sheet plasmons, with longitudinal electric fields that are polarized parallel to direction of propagation S 3 ) and 2D-confined MDM gap plasmon in the slot (polarized normal to the direction of propagation). As making a distinction between these channels is of great importance in the proof that light can be efficiently coupled to slot WGs, we first illustrate what happens in the undesirable situation where a nano-led couples to both gap plasmons in a slot and sheet plasmons on the top Au pad surface. Comparing Supplementary Fig. S14a and b taken from such a source, the scattering from the linear grooves is purely y-polarized as expected from decoupled sheet plasmons while the scattering from the slot WG termination is x-polarized which is consistent with gap plasmon propagation. Rigorous EM simulations show that when the gap plasmons reach the termination, 15% is scattered to free space radiation (+z and z half space), 15 % is coupled to sheet plasmons while 70 % is reflected back inside the slot (Supplementary Fig. S24). It is not immediately clear at first glance whether the observed sheet plasmons (Supplementary Fig. S14a) are generated directly by the nano-led or converted when the gap plasmon encounters the end of the slot WG. If we consider NATURE PHOTONICS 27

28 the anti-symmetric distribution of the z-component of the electric field on either side of the slot for the gap plasmon mode, scattering into sheet plasmons should result in minimum field intensity in the forward direction (+y-direction). However, the scattering image in Supplementary Fig. S14a shows a maximum in the +y-direction thus we conclude that most of the observed sheet plasmon is emitted in all directions on the xy-plane directly from the nano-led. The excitation of sheet plasmons are undesirable but can be minimized by accurate alignment of the slot WG to the output facet of the nano-led as shown in Fig. 3 and Fig. 4. Since the gap plasmon mode is highly dispersive, it is reasonable to ask the question whether the relatively broad bandwidth of the LED combined with the WG dispersion will limit the ultimate transmission bandwidth of the interconnect. Our calculated gap plasmon mode dispersion which is in good agreement with our experimental Fabry-Pérot resonance (Supplementary Figure S21b) is refractive index units per nm at 950 nm wavelength (modal index of 5.24). This translates to 6.3 ps/nm-m. Using a very conservative wavelength spread in our nano-led of 80 nm (actual FWHM is close to 40 nm), the bandwidth-distance (BL) product for the subwavelength slot waveguide is 493 Mbps-m. Even though this is far less than conventional optical fibers used for long haul communication, for on-chip interconnects, the slot WG is only intended to be used over a distance of several µm. At a distance of L = 100 µm, the 3db bandwidth is 3.45 THz (f 3db =0.7B), which shows that the WG propagation loss, rather than its dispersion will be the limiting factor for the optical nano-circuit modulation speed. 28 NATURE PHOTONICS

29 SUPPLEMENTARY INFORMATION References S1. Chandran, A., Barnard, E. S., White, J. S. & Brongersma, M. L. Metal-dielectric-metal surface plasmon-polariton resonators. Phys. Rev. B 85, (2012). S2. Fiore, A. et al. Carrier diffusion in low-dimensional semiconductors: A comparison of quantum wells, disordered quantum wells, and quantum dots. Phys. Rev. B 70, (2004). S3. Raether, H. Surface-plasmons on smooth and rough surfaces and on gratings. Spring Tracts in Modern Physics 111, (1988). NATURE PHOTONICS 29