Supplementary material for High responsivity mid-infrared graphene detectors with antenna-enhanced photo-carrier generation and collection Yu Yao 1, Raji Shankar 1, Patrick Rauter 1, Yi Song 2, Jing Kong 2, Marko Loncar 1 and Federico Capasso 1,* 1 School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, 02138, USA 2 Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, 02139, USA *Corresponding author: Federico Capasso, capasso@seas.harvard.edu (1-617-384-7611) Pierce 205A, 29 Oxford Street, Cambridge, MA 02138 Contents I: The responsivity of graphene photoconductors... 2 II: Graphene growth and transfer... 3 III: Enhancement of absorption with antenna structures... 4 IV: Detector RC constant calculation... 5 Reference... 6 1
I: The responsivity of graphene photoconductors When light is incident on the graphene detector, the photogenerated electrons and holes move in response to the applied voltage, which results in photocurrent I Ph. Assume one pair of excess carriers are generated at x=x 0, as shown in Fig. S1, the probabilities for the electron and holes to reach the electrodes are exp /, exp /, respectively. Where is the photo-carrier recombination lifetime, is the carrier drift velocity (it is the same for electrons and holes in graphene). By adding up the contributions from all absorbed photons, we obtain the photocurrent, (SI-1) Assuming monochromatic light of frequency and uniform illumination on graphene channel, the photo-carrier generation rate per unit distance W(x 0 ) is given by where is the incident power, α is the fraction of incident light absorbed in the (SI-2) graphene layer and M is the hot carrier multiplication factor 1,2, which scales linearly with photon energy 3. Eq. (SI-1) then leads to, 2 1 2 where / is the transit time of photocarriers across the gap g. 1 (SI-3) The photoconductive gain is defined as // /. From Eq. SI-3, the gain is given by 2 1 (SI-4) According to the equivalent circuit model, as also shown in Fig S1, the photocurrent output I L is given by /. Therefore, the responsivity is 2 1 (SI-5) 2
Figure S1. (a) The graphene photoconductor in a bias circuit and (b) its equivalent circuit model. R G is the resistance of the graphene channel between the electrodes, R S is the contact resistance between graphene and the electrodes, R L is the load resistance. II: Graphene growth and transfer The graphene was grown on copper foil in a home-built system using Low-Pressure Chemical Vapor Deposition (LPCVD). 4 First, the copper foil was placed in a quartz tube and annealed at 1000 o C for 30min while flowing H 2 at a rate of 10 sccm. Graphene was then grown for 30 min by increasing the H 2 flow rate to 70 sccm and setting the CH 4 flow rate to 4 sccm. The chamber pressure during the growth phase was 1.90 Torr. The growth conditions outlined above produce high-quality graphene with very few bilayer regions. Finally, the graphene was transferred onto SiO 2 using PMMA as a transfer membrane. 5 PMMA was spin-coated onto one side of the graphene/copper/graphene and baked for 10min at 80 o C. The graphene on the back-side was removed with an O 2 plasma etch. The stack was then placed in FeCl 3 -based copper etchant for 15min, allowing all of the copper to dissolve. The remaining graphene/pmma film was rinsed in DI water, transferred onto the substrate and blow-dried using a N 2 gun. Fig. S2 shows a typical Raman spectrum of the graphene sheet after it is transferred onto SiO 2. 3
Figure S2. Raman spectrum of CVD graphene transferred on SiO2 substrates. The main peaks are labeled. III: Enhancement of absorption with antenna structures For single layer graphene, if the charge carrier concentration in the graphene sheet is ~0, the calculated light absorption is constant, ~2%, from visible to mid-infrared wavelength range based on the graphene permittivity calculated at room temperature T=300 K, using the random-phase approximation (RPA) in the local limit 6,7. By placing plasmonic antennas on graphene, the light absorption close to the antenna resonance wavelength can be greatly enhanced, due to the highly enhanced electric field in the graphene layer. According to FDTD simulations, the light absorption in the graphene layer of an antennaassisted graphene detector is about 10% at the resonance wavelength (4.44 µm), as shown in Fig. S3, which is 5 times of that in a reference device without antennas. 4
Figure S3. Calculated light absorption in graphene as a function of vacuum wavelength for samples with and without antennas. The graphene permittivity is calculated at temperature T=300 K. Mobility µ=1,000 cm 2 /Vs. IV: Detector RC constant calculation Based on the high-frequency equivalent circuit model of the antenna-assisted graphene detector, we can calculate the detector RC constant. Since this detector is composed of an array of nano-photodetectors (M N), the resistance and capacitance of the detector array is R DS =(R G +R S ) M/N, C DS =C Gap N/M, respectively. The capacitance C Gap 1e-5 pf (estimated for the antenna gap size 60 nm) is much smaller than the parasitic capacitance of the detector contact pads (C P =60 pf) and load capacitance (C L ) in our measurement setup; therefore, the RC constant of the detector can be estimated by τ RC =R L R DS (C L +C P /2+ C DS )/(R L +R DS ). At the gate voltage V G =V CNP =5V, the resistance between electrodes D and S is measured to be R DS =1.0 k Ω. The capacitance between the contact pad (120 µm by 200 µm) and the substrate is obtained by CV measurement C P 60 pf. In the pulse measurement setup, the detector is connected with a pre-amplifier using a SMA to BNC cable (impedance=50 Ω, capacitance 100 pf/m, length 0.5 m) to measure the photovoltage response, R L =500 Ω, C L 50 pf. Therefore, the estimated response time is τ RC =(R L //R DS )(C L +C P /2+C DS ) 30 ns. In comparison, the RC constant of 5
the reference detector without antennas are estimated to be τ RC_R =(R L //R DS_R )(C L +C P /2+ C DS ) 40 ns, which is longer than that of the antenna-assisted detector because the source-drain resistance R DS_R =5.5 k Ω, as shown in Fig. 1 (d). If one uses insulating substrates to reduce the parasitic capacitance and minimizes the load capacitance, the ultimate limit of the detector RC constant of the detector is determined by the capacitance C DS of the graphene-antenna structure, i.e., τ D = (R L //R DS )C DS 0.01 ps. Figure S4. Schematic of the antenna-assisted graphene detector and its high-frequency equivalent circuit model. The bottom left shows the circuit model of a single nanodetector formed by one pair of antennas and the graphene in the gap between them. Reference 1 Brida, D. et al. Ultrafast collinear scattering and carrier multiplication in graphene. Nat Commun 4 (2013). 2 Winzer, T., Knorr, A. & Malic, E. Carrier Multiplication in Graphene. Nano Lett 10, 4839-4843 (2010). 3 Tielrooij, K. J. et al. Photoexcitation cascade and multiple hot-carrier generation in graphene. Nat Phys 9, 248-252 (2013). 6
4 Li, X. S. et al. Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science 324, 1312-1314, doi:doi 10.1126/science.1171245 (2009). 5 Reina, A. et al. Large Area, Few-Layer Graphene Films on Arbitrary Substrates by Chemical Vapor Deposition. Nano Lett 9, 30-35, doi:doi 10.1021/Nl801827v (2009). 6 Falkovsky, L. A. & Pershoguba, S. S. Optical far-infrared properties of a graphene monolayer and multilayer. Phys Rev B 76, 153410, doi:artn 153410 Doi 10.1103/Physrevb.76.153410 (2007). 7 Falkovsky, L. A. & Varlamov, A. A. Space-time dispersion of graphene conductivity. Eur Phys J B 56, 281-284, doi:doi 10.1140/epjb/e2007-00142-3 (2007). 7