Generation of photovoltage in graphene on a femtosecond timescale through efficient carrier heating

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1 DOI: 1.138/NNANO Generation of photovoltage in graphene on a femtosecond timescale through efficient carrier heating K. J. Tielrooij, L. Piatkowski, M. Massicotte, A. Woessner, Q. Ma, Y. Lee, K. S. Myhro, C. N. Lau, P. Jarillo-Herrero, N. F. van Hulst, and F. H. L. Koppens NATURE NANOTECHNOLOGY Macmillan Publishers Limited. All rights reserved

2 DOI: 1.138/NNANO I. MATERIAL DETAILS The dual-gated device contains an exfoliated graphene flake, contacted by two chromium-gold contacts, on top of 3 nm of SiO 2 and a doped silicon substrate. The silicon serves a back gate to control the Fermi level in the graphene flake. The graphene is covered by an exfoliated flake of hexagonal boron nitride (1-2 nm) and a chromium-gold top gate that locally controls the Fermi level of the graphene sheet. Further fabrication details are given in Ref. S1. The transparent substrate device contains an exfoliated flake with a monolayer region, connected to a bilayer region, which in turn is connected to a graphite region. The monolayer and graphite regions are each connected to titanium-gold contacts (made using laser writing and evaporation) that serve as source and drain contacts. Figure 1 shows the details of this device, with characterization by Raman spectroscopy to identify the monolayer, bilayer and graphite regions. The substrate of this device is a 1 mm thick crystal of SiO 2, which is used to avoid any graphene absorption enhancement due to reflections at the interface of SiO 2 and doped Si in typically used substrates (see main text). The suspended device contains an exfoliated flake on top of a substrate of 3 nm SiO 2 and Si, where the oxide underneath the flake is etched away in a BOE solution for 7 seconds, thus producing a suspended flake. The distance between the graphene flake and the oxide is estimated to be 24 nm. The flake is contacted with gold contacts, made using e-beam lithography. II. TIME-RESOLVED PHOTOCURRENTSCANNING MICROSCOPY SETUP Here we describe in detail the time-resolved photovoltage microscopy setup with 3 fs time resolution (see Fig. 1c of the main text). We use a broadband Titanium Sapphire laser (Octavius 85M, Menlo Systems) tuned to a central wavelength of 8 nm with a bandwidth of 12 nm combined with a liquid crystal based spatial light modulator (SLM) pulse shaper arranged in a 4f-configuration. After propagating through the shaper, the laser 2 NATURE NANOTECHNOLOGY Macmillan Publishers Limited. All rights reserved

3 DOI: 1.138/NNANO a SUPPLEMENTARY INFORMATION b 3 Photon counts (a.u.) 2 1 Graphite Bilayer graphene Monolayer graphene 5 µm Raman shift (cm ) Supplementary Fig. 1: a) Raman spectrum of three different locations on the Device B, showing monolayer graphene, bilayer graphene and graphite. b) Microscope image of the device with indications where the Raman spectra of panel a are taken. The dashed lines indicate the monolayer and bilayer graphene areas. beam is spectrally split using a dichroic filter (Semrock, 83 nm Edge Basic) into two parts: the pump (<8 nm) and the probe (>8nm), each with a bandwidth of 55nm. Due to this spectral separation, the two pulses do not show any coherent artefact when they overlap in time. One of the beams travels through a motorized delay line that is used to control the delay time t between the pulses. The other beam is modulated with a mechanical chopper. The two beams are recombined through the same dichroic filter, propagated collinearly into an inverted microscope (Zeiss Axiovert 2) and focused with a.65na objective (Olympus LCPLN-5X-IR) onto the graphene device. The studied devices are mounted ontoa3d piezo-scanner that allows for measuring spatially resolved photovoltage maps. Both beams are linearly polarized, parallel to each other. The reflected laser light is collected through the same objective and sent to an avalanche photo-diode (APD) that allowes for confocal optical imaging of the device, in addition to the photovoltage detection. In order to obtain transform limited pulses we use the MIIPS method in combination with second harmonic nanoparticles, an approach described in detail elsewhere [S2]. Briefly, NATURE NANOTECHNOLOGY Macmillan Publishers Limited. All rights reserved

4 DOI: 1.138/NNANO the second harmonic signal from BaTiO 3 nanoparticles (few hundred nanometers in size) is used to detect the phase dispersion of the laser pulses. An appropriate phase mask is then applied onto the SLM to compensate for the dispersion. This allows for obtaining transform limited pulses in the focal spot of the microscope objective. The same nanoparticles are used to measure the cross-correlation signal of the two pulses. The generated photovoltage is detected using a lock-in amplifier locked to the driving frequency of the chopper and recorded as a function of the delay line position. III. ANALYSIS OF THE TIME-RESOLVED PHOTOVOLTAGE SIGNALS The reason we are able to resolve the dynamics of hot electrons is that there is an intrinsic nonlinearity between the amount of created photovoltage and the amount of power absorbed in the graphene sheet (see Fig. 2a): The signal is smaller for excitation with 4 µw than twice the signal for excitation with 2 µw. Here we are dealing with the strong excitation regime ( T el >> T ), in contrast to the weak excitation regime that applies to our spectrally resolved measurements. The reason for this nonlinearity is the nonlinear relation between the amount of absorbed power and the electron temperature for pulsed excitation, which has an approximate square-root dependence [S3]. This follows from the electronic heat capacity C el = α T and Q = T el T C el dt, which gives T el = T Q. α Here C el is the electronic heat capacity, α = 2πE F k 2 3 h 2 vf 2 B (with E F the Fermi energy, h the reduced Planck constant, v F the Fermi velocity and k B Boltzmann s constant), and Q the amount of power absorbed from the incident light. Furthermore, T el saturates at higher fluences due to the lower heating efficiency [S4]. As a result, the photovoltage decreases around t = and forms the photovoltage dip I PC with dynamics that reflect the dynamics of the electron temperature, as explained in the main text. Interestingly, we closely recover the original heating dynamics from our photovoltage dip I PC by taking its time derivative. We show this numerically in Fig. 2b, where we use two different heat dynamics curves and use these to calculate the photovoltage dip, following the procedure described in the Methods section. The heat dynamics contain an exponential heating time and an exponential cooling time. We find that taking the time derivative of 4 NATURE NANOTECHNOLOGY Macmillan Publishers Limited. All rights reserved

5 DOI: 1.138/NNANO SUPPLEMENTARY INFORMATION the dip very closely reproduces the original heat dynamics. a Photocurrent (na) I PC I PC Power ( W) T -T (K) el 4 2 b d/dt( I PC ) (norm.) 1 5 fs 1.3 ps 25 fs 1.3 ps Delay time t (ps) Supplementary Fig. 2: a) Photocurrent I PC (left vertical axis) as a function of power, showing the nonlinear dependence. The fit is the hot electron temperature increase T el T directly after laser pulse absorption and electron thermalization (right vertical axis), calculated using E F =.2 ev, a spot size of 1.5 µm and an absorption of 1%. The agreement shows that the photocurrent is proportional to the hot electron temperature, as expected. b) Time derivative of the modeled photocurrent dip d/dti PC (solid lines) together with the heat dynamics that served as input into the model (dashed lines). The black (red) lines correspond to a heating time of 5 (25) fs and a cooling time of 1.3 ps. IV. ENERGY-RESOLVED PHOTOCURRENT SCANNING MICROSCOPY SETUP The energy-resolved photovoltage microscopy setup uses a pulsed laser (NKT Photonics SuperK Extreme) and an acousto-optic tunable filter (NKT Photonics SpectraK Dual) to select the desired wavelength between 5 and 15 nm. The laser has a repetition rate of 4 MHz, and the pulses have a duration of 4 ps, as determined using time-correlated photon counting (using a PicoHarp) of the reflected signal. The light is focused onto the device using a broadband long working distance objective with a numerical aperture of.65 (Olympus LCPLN-5X-IR). The device is mounted in a closed cycle Helium cryostat (Janis) with x,y,z-manipulation using piezo-controllers (Attocube). The current generated in the device passes through a current pre-amplifier (Femto DLPCA-2) and an AD-card. NATURE NANOTECHNOLOGY Macmillan Publishers Limited. All rights reserved

6 DOI: 1.138/NNANO V. ANALYSIS OF WAVELENGTH-RESOLVED PHOTOVOLTAGE SIGNALS As we discuss in the main text, in the case of efficient electron heating the wavelength (λ) dependence of the responsivity is solely determined by the wavelength-dependent absorption coefficient A(λ). We compare the responsivity for all three devices with the (scaled) absorption, which is numerically calculated taking into account the full layered system (using Lumerical FDTD Solutions software). We also show what the responsivity would look like in the case of photovoltaic current generation or (equivalently) PTE current generation with low electron heating efficiency. In those cases the responsivity would depend on absorbed photon density R PC A(λ) N ph, rather than on absorbed power R PC A(λ) N ph hf (see Fig. 3a-c). Clearly, the agreement between data and model is best when assuming that the responsivity scales with absorbed power. This indicates that the current generation mechanism is the photo-thermoelectric effect and that electron heating is efficient. To further illustrate efficient heating we show the absorbed photon densitynormalized photovoltage vs. photon energy hf in Fig. 3d-f for the dual-gated device, the transparent substrate device and the suspended device, respectively. Linear scaling through the origin shows that a higher photon energy gives a proportional increase in photovoltage, which is the result of efficient electron heating through carrier-carrier scattering [S5]. 6 NATURE NANOTECHNOLOGY Macmillan Publishers Limited. All rights reserved

7 DOI: 1.138/NNANO SUPPLEMENTARY INFORMATION a 1.5 d b RPC(1 A/W) -4 (1 A/W) -4 RPC Photocurrent ratio 5 15 Wavelength (nm) SLG-BLG transparent PN junction 285 nm SiO 2 e IQE (a.u.) IQE (a.u.) c f.6 (1 A/W) -4 RPC.4.2 PN junction suspended IQE (a.u.) Wavelength (nm) Initial energy (ev) Supplementary Fig. 3: a-c) Wavelength dependent responsivity for the transparent substrate device (a), the dual-gated device (b), and the suspended graphene device (c), together with the numerical model where the photovoltage scales with the calculated graphene absorption coefficient (solid red line) and the model where the photovoltage scales with the calculated absorbed photon density (dashed red line). The former model corresponds to photovoltage generation through the PTE and efficient electron heating, whereas the latter corresponds to photovoltic photovoltage generation or PTE current generation with low heating efficiency. The inset of panel b shows the photocurrent ratio, where the photocurrent with the laser at the graphene-metal interface is divided by the photocurrent with the laser at the pn-junction. The flat ratio above 6 nm, together with the PTE origin of the photocurrent at the pn-junction, shows that the origin of the photocurrent at the graphene-metal interface is likely also photo-thermoelectric. d-f) The photovoltage normalized by the absorbed photon density as a function of initial electron energy E i = hf/2 for Device B (d), Device A (e), and Device C (f). 7 NATURE NANOTECHNOLOGY Macmillan Publishers Limited. All rights reserved

8 DOI: 1.138/NNANO Supplementary References [S1] Gabor N.M. et al. Hot Carrier-Assisted Intrinsic Photoresponse in Graphene. Science 334, (211) [S2] Accanto, N., Nieder, J.B., Piatkowski, L., Castro-Lopez, M., Pastorelli, F., Brinks, D. and van Hulst, N.F., Light: Science & Applications 3, e143 (214) [S3] Graham, M.W., Shi, S.-F., Ralph, D.C., Park, J. & McEuen, P.L. Photocurrent measurements of supercollision cooling in graphene. Nature Phys. 9, (213). [S4] Jensen, S. et al. graphene. Nano Lett. 14, (214) Competing ultrafast energy relaxation pathways in photoexcited [S5] Tielrooij, K.J. et al. Photoexcitation cascade and multiple hot-carrier generation in graphene. Nature Phys. 9, (213) 8 NATURE NANOTECHNOLOGY Macmillan Publishers Limited. All rights reserved