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1 DOI: 1.138/NNANO Epitaxial graphene quantum dots for high-performance terahertz bolometers Abdel El Fatimy *, Rachael L. Myers-Ward, Anthony K. Boyd, Kevin M. Daniels, D. Kurt Gaskill, and Paola Barbara *. * Supplementary Notes: Estimate of incident power: We used a Microtech backward-wave oscillator source with tunable frequency in the range 1 18 GHz. From the factory calibration curve, the output power at.15 THz is 25 mw. The THz radiation was focused within a 5.25 mm diameter circle using a Winston cone, giving an average power density of 1,155 W m -2. The distance between the end of the Winston cone and the surface of the SiC substrate where we patterned the dots was about 5 mm. We worked on samples with two different types of designs: with and without antennas, as shown in the images in the insets of Fig S1. We patterned the antennas on some of the devices for future NATURE NANOTECHNOLOGY 1

2 DOI: 1.138/NNANO work at higher THz frequencies to study the effect of the antenna on the absorbed radiation. (This is beyond the scope of the current work. Here we characterize the devices using absorbed power to evaluate their upper limit of performance and we can measure the absorbed power directly from the current-voltage characteristics with radiation ON-OFF, as described in the main text.). For the devices with antennas, we used a log periodic antenna as source and drain electrodes 1,2 designed to be broadband in the range from.7 THz to 4 THz. The measurements presented in this work are all at.15 THz, outside the antenna range, therefore it is not surprising that there is no notable increase of a b 7 4 I DC (na) 35 ON OFF I DC (na) 2 ON OFF 35 7 (mv) 35 7 (mv) Figure S1. THz response of graphene dots with and without antennas. a and b, Current-voltage characteristic for 2-nm dots with (red) and without (black).15 THz radiation at 3K. The absorbed power is 2 pw for the device in a and 5 pw for the device in b. Insets: Optical images of the dots (the scale bars are 5 m). For the device in b the electrodes are patterned as log periodic antennas. measured absorbed power for devices with antennas. Fig. S1 shows a comparison of the.15 THz response from 2-nm dots without and with antenna. We conclude that these electrodes do not play a major role in affecting the absorbed power at.15 THz. We therefore estimate the power incident on the device by using just the power incident on the graphene area between the electrodes (the dot pattern), roughly 2 m 2 for most devices, yielding 23 nw (37 nw for a couple of devices with 32 m 2 graphene area see Table S1). A detailed list for 19 2 NATURE NANOTECHNOLOGY

3 DOI: 1.138/NNANO SUPPLEMENTARY INFORMATION samples is shown in Table S1. For most devices the absorbed power ranges from 3 pw to 3 pw, two to three orders of magnitude smaller than the estimated incident power. For the 5 devices outside this range, the 3 with lower absorbed power are smaller, higher resistance dots and the 2 with higher power are dots with larger graphene area and diagonal steps. The absorbed power also varies depending on the position of the devices, indicating that the power from the Winston cone is non-uniform. Variations may also be due to variations in the output power of the source corresponding to slightly different operating parameters (cathode current and heater current) during different measurements runs. Future measurement will focus on increasing the coupling between the THz radiation and the devices by using antennas designed to increase the detection area and improve the impedance mismatch, for example by including shunt capacitors to reduce the device impedance at THz frequency. Samples 8 x 8 mm 2 Graphene area (µm 2 ) Dot diameter (nm) Orientation to SiC steps Absorbed power (pw) 3DN3 2 1 perpendicular 2 16DI1 2 3 perpendicular.4 3 perpendicular 8 5 perpendicular 7 15 perpendicular parallel perpendicular perpendicular perpendicular 67.5 NATURE NANOTECHNOLOGY 3

4 DOI: 1.138/NNANO perpendicular perpendicular DI parallel 17 4 parallel parallel parallel parallel parallel 19 27ER diagonal 5 2 diagonal 2 Table S1. List of devices and the measured absorbed power. The absorbed power is measured from the.15 THz response of 19 devices with different dot diameter and different orientation with respect to the SiC steps. Estimate of device speed: The speed of the device is determined by the thermal time constant, = Ce /GTH, where the electronic heat capacity Ce = (2π 3/2 kb 2 n 1/2 Te)/(3 vf), n is the carrier density and vf is the Fermi velocity 3. We do not know the doping of graphene after the nanopatterning process, however, for a typical carrier density n = 1 12 cm -2, we estimate Ce < J/(K m 2 ) for Te < 9 K, leading to a response time smaller than 2.5 ns (the area of our patterned graphene is about 2 m 2 ). We note that this estimate is for the intrinsic response time of the device. The specific measurement circuit used to detect the response will significantly increase the response time from this value and needs to be carefully designed to maximize the device speed. 4 NATURE NANOTECHNOLOGY

5 DOI: 1.138/NNANO SUPPLEMENTARY INFORMATION Performance as a function of dot diameter and orientation: We measured several devices with different diameter and current flow orientation with respect to the SiC steps. The best performance is for dot diameter smaller than 2 nm and device orientation with current flow perpendicular to the SiC steps. The results are shown in Fig. S2. a Responsivity (V/W) Diameter (nm) b Electrical NEP (W/Hz.5 ) 1E-13 1E-14 1E-15 1E Diameter (nm) Figure S2. Bolometric performance vs. dot diameter and orientation. Measured responsivity at.15 THz (a) and NEP (b) as a function of dot diameter at 2.5K. Devices with current flowing perpendicular, parallel and diagonal to the SiC steps are in black, red and blue symbols, respectively. Fig. S3 shows transmission optical images of two devices revealing the terraces and showing different device orientation with respect to the terraces. The graphene connecting the two electrodes is not visible and we schematically outlined the graphene pattern with red lines. NATURE NANOTECHNOLOGY 5

6 DOI: 1.138/NNANO a b Figure S3. SiC terraces and device orientation. Transmission optical images of two devices with orientation perpendicular (a) and parallel (b) to the SiC terraces. The vertical parallel lines are the steps of the terraces. The inner radius of the smallest circular branch of the antenna is about 5 microns and the spacing of the steps is about one micron. Discussion on Joule heating and THz heating: We previously pointed out that the change in the current voltage characteristics (IV curves) of the quantum dots due to THz radiation is very similar to the change caused by heating. Fig. S4 shows the IV curves of a 15-nm dot measured at 2.5 K with THz radiation OFF (black) and ON (red). I DC (pa) K - ON 2.5 K - OFF 6 K - OFF 15 nm Figure S4. THz heating. IV curves of a 15- nm dot with.15 THz radiation ON (red) and OFF (black) measured at 2.5 K. The red curve matches the IV curve of the same dot measured at higher temperature, with THz radiation OFF (mv) 6 NATURE NANOTECHNOLOGY

7 DOI: 1.138/NNANO SUPPLEMENTARY INFORMATION In the same graph we plot the IV curve of the same dot measured at 6K with THz radiation off (green curve). We find that the green curve matches the red curve quite well (the temperature of the red curve is only slightly higher), further supporting the bolometric detection mechanism. In our quantum dot bolometer analysis, we assumed that when the THz radiation is OFF, the nonlinearity of the IV curves is mainly due to Joule heating. Here we will justify this assumption by further analyzing the IV curves of one of our dots with radiation ON and OFF at different base temperatures, without changing the THz power. Fig. S5 a shows the IV curves of the 3-nm dot with THz radiation ON (black) and OFF (red) at 2.5 K, that we presented in Fig. 2a of the manuscript. Here we provide more details on the measurements absorbed power. As described earlier, we measure the differential conductance at zero bias of the curve with THz radiation ON. This a I DC (pa) b I DC (pa) di di DC /d (ns) DC /d (ns) ± mv (mv) ± I DC = mv (mv) 6K 2.5 K ±.4 pw Figure S5. Joule heating. IV curves of a 3- nm dot with.15 THz radiation ON (red) and OFF (black) measured at 2.5 K (a) and 6K (b). The insets in each graph show the differential conductance as a function of bias for each curve and the bias point where the zero bias differential conductance of the curve with radiation ON matches the differential conductance of the curve with radiation OFF. Those bias points correspond to similar values of Joule power at different temperature, confirming that the nonlinearity of the OFF curves with radiation off is mainly due to Joule heating. I DC =.56 ±.6pW 35 7 (mv) NATURE NANOTECHNOLOGY 7

8 DOI: 1.138/NNANO conductance is higher than the zero-bias differential conductance with radiation OFF (black curve), because the THz radiation is heating the device, as shown in Fig. S4. When the THz radiation is OFF, only Joule power is heating the device, causing an increase of differential conductance when the bias voltage is increased. If we assume that the non-linearity of the IV curve with radiation off is solely due to Joule heating, then we will need a value of Joule power as large as the THz power to cause an increase of differential conductance in the black curve that matches the increase produced by the THz radiation in the zero-bias differential conductance of the red curve. The inset in Fig. S5a shows the differential conductance of the black and red curve as a function of bias voltage. The zero-bias differential conductance of the red curve matches the differential conductance of the black curve at the voltage bias VDC = 22.3 mv, corresponding to a Joule power of about.4 pw. Fig. S5b shows the same analysis with the device temperature raised to 6K, without changing the THz power. If the non-linearity of the black curve is mainly due to Joule heating, we expect that the zero-bias differential resistance of the red curve, corresponding to the device heated with THz radiation, should match the differential resistance of the black curve, with THz radiation OFF, at a bias point with Joule power that is approximately the same as the value measured at 2.5 K. The match of differential conductance occurs at a similar value,.56 pw. The two values differ by less than two standard deviations and the variation can be explained with variation of output power of the THz source with time, since the two measurements were taken a few hours apart (we measured dots of different size and orientation at one fixed temperature before heating the sample and test the devices at a higher temperature). Heat flow diagram Fig. S6 shows a basic schematic for the thermal circuit of our device. The graphene is made of three parts: two triangular shapes on each side of the dot, labeled 1 and 2 and the dot, labeled 3. In the thermal diagram we separated the graphene lattice, schematically shown as a grey box, and the electrons, shown in blue for each part of the graphene area. We estimate that the thermal resistance 8 NATURE NANOTECHNOLOGY

9 DOI: 1.138/NNANO SUPPLEMENTARY INFORMATION between the graphene lattice and the SiC substrate (not shown in the diagram) is very small compared to the other thermal resistances that represent cooling channels for the electron gas considered below 4 and that, when thermal power is provided to the device, the graphene lattice and the metal electrodes are at the same bath temperature T, whereas the electrons equilibrate at a temperature Te > T. The electrons in the parts 1 and 2 of the device have two main cooling paths to the bath temperature: diffusion to the metal electrodes (R T diff) and phonon collisions (R T e-p). The dot (part 3 of the device) is thermally connected to parts 1 and 2 (R T 13 and R T 23) as well as to the lattice (R T e-p) Metal R T diff R T 13 R T 23 Electrode R T diff Metal Electrode RT e-p R T e-p Graphene lattice R T e-p Figure S6. Thermal model. Diagram showing heat conduction paths for electrons (blue shapes) in the different parts of the graphene (the two triangular parts on each side of the dot, 1 and 2, and the dot, 3). We assume that the graphene lattice (grey box) and the metal electrodes are at the bath temperature T. We use the Wiedemann-Franz law to estimate R T 13, R T 23 and R T diff. The sum R T 13 + R T 23 is related to the large electrical resistance that we measure in our devices, since the constrictions on each side of the dot dominate the electrical resistance. For the smallest (3 nm) dots this resistance is as high as several hundreds of M at a temperature of a few K. We cannot measure the electrical contact resistance related to R T diff separately, but we can estimate that is smaller than the room temperature NATURE NANOTECHNOLOGY 9

10 DOI: 1.138/NNANO resistance of the largest dot, 5 k. From this we estimate that the thermal conductance due to diffusion to the electrodes is higher than W K -1 by using the Wiedemann-Franz law (we assume that the variation of the electrical contact resistance with temperature is small). We estimate the thermal conductance due to collisions with phonons using the result for monolayer graphene from ref. 5 : G T e-p = 1/R T e-p = 4ππ2 DD 2 EE FF KK BB 4 AATT 3 15ρρħ 5 vv FF 3 vv ss 3 = 4ΣAATT 3. Here we considered the case where Te and T are smaller than the Bloch-Grüneisen temperature of monolayer graphene 5, TBG (we do not know the doping of our graphene, but we estimate TBG ~ 7 K for a reasonable value of charge density, n=1 12 cm -2 ). In the formula, we used a deformation potential D = 18 ev (from ref. 6 ), the Fermi energy EF = 1 mev, a graphene area A = 2 µm 2, the graphene mass density = kg m -2, the Fermi velocity vf = 1 6 m s -1 and the sound velocity vs = m s -1, yielding G T e-p = W K -1 at T = 1 K and an electron-phonon coupling constant = 5 mw m -2 K -4. The thermal conductance extracted from our electrical measurements in Fig. 1d is GTH ~ W K -1 at 6 K, yielding =.4 mw m -2 K -4, lower than the estimated value but similar to other values previously reported 7. Although these are just rough estimates (we do not know the doping level of graphene and we cannot measure the contact resistance separately) and it is also likely that the defects due to nanopatterning contribute to deviations from these estimates (in previous work, 7 lattice disorder has been suggested as a possible cause for the reduction of electronphonon coupling by more than one order of magnitude), the value of thermal conductance extracted from the measurements compares well to the estimated value and values reported in other studies 8. References 1 Mendis, R. et al. Spectral characterization of broadband THz antennas by photoconductive mixing: Toward optimal antenna design. Ieee Antennas and Wireless Propagation Letters 4, 85-88, doi:1.119/lawp (25). 1 NATURE NANOTECHNOLOGY

11 DOI: 1.138/NNANO SUPPLEMENTARY INFORMATION 2 Rinzan, M., Jenkins, G., Drew, H. D., Shafranjuk, S. & Barbara, P. Carbon Nanotube Quantum Dots As Highly Sensitive Terahertz-Cooled Spectrometers. Nano Letters 12, , doi:1.121/nl3975h (212). 3 Fong, K. C. & Schwab, K. C. Ultrasensitive and Wide-Bandwidth Thermal Measurements of Graphene at Low Temperatures. Physical Review X 2, doi:1.113/physrevx (212). 4 Wang, Z., Bi, K., Guan, H. & Wang, J. Thermal Transport between Graphene Sheets and SiC Substrate by Molecular-Dynamical Calculation. Journal of Materials 214, 5, doi:doi:1.1155/214/47988 (214). 5 Viljas, J. K. & Heikkila, T. T. Electron-phonon heat transfer in monolayer and bilayer graphene. Physical Review B 81, doi:1.113/physrevb (21). 6 Chen, J. H., Jang, C., Xiao, S. D., Ishigami, M. & Fuhrer, M. S. Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nature Nanotechnology 3, 26-29, doi:1.138/nnano (28). 7 Betz, A. C. et al. Hot Electron Cooling by Acoustic Phonons in Graphene. Physical Review Letters 19, doi:1.113/physrevlett (212). 8 McKitterick, C. B., Prober, D. E., Vora, H. & Du, X. Ultrasensitive graphene far-infrared power detectors. Journal of Physics-Condensed Matter 27, doi:1.188/ /27/16/16423 (215). NATURE NANOTECHNOLOGY 11