Ultrafast hot-carrier-dominated photocurrent in graphene

Transcription

1 SUPPLEMENTARY INFORMATION DOI: /NNANO Ultrafast hot-carrier-dominated photocurrent in graphene Table of Contents: Dong Sun 1, Grant Aivazian 1, Aaron M. Jones 1, Jason S. Ross 2,Wang Yao 3, David Cobden 1, Xiaodong Xu 1,3* 1. Graphene device fabrication and characterization 2. Scanning photocurrent microscopy 3. Pump-probe spectroscopy 4. Gate dependence of pump-probe signal 5. Temperature dependence of photocurrent 6. Dynamics of exfoliated single layer graphene 7. Dynamics of CVD grown graphene 8. Temperature of pn junction and photocurrent 9. Cooling of the pn junction and photocurrent dynamics 10. Anomalous behavior of the PC signal as a function of gate voltages 11. Supplemental References NATURE NANOTECHNOLOGY 1

2 1. Graphene Device Fabrication and Characterization We fabricated graphene devices from both mechanical exfolatiation and chemical vapor deposition 1. We used the scotch tape method to exfoliate graphite flakes onto silicon oxide (285nm) on heavily n-doped silicon substrates 2. The number of graphene layers was identified by both optical microscope imaging and Raman spectroscopy 3. The sample presented in the main text is identified as trilayer graphene with ABA stacking 4 as determined from the Raman spectrum shown in Fig. S1a and b. Electrodes were patterned using a Heidelberg μpg mask writer. Titanium and gold were deposited using e-beam evaporation to (a) (c) After measurement Counts(a.u) Trilayer (b) Trilayer 2D peak Counts(a.u) After fabrication Before fabrication (e) (f) Counts(a.u) (d) Raman Shift (cm -1 ) Raman Shift (cm -1 ) Figure S1 Raman spectroscopy and device image. a, Raman spectra of exfoliated trilayer device. b Expand view of 2D peak which is fitted by 6 Lorentzian peaks with equal full-widthhalf-maximum of 25 cm -1 corresponding to ABA stacked order. c, Raman spectrum of exfoliated single layer graphene before fabrication (bottom), after fabrication (middle), and after measurements (top). A single Lorentzian fit yields a typical full-width-half-maximum of ~25 cm -1. d, Raman spectra of CVD grown graphene. e, Photograph of parallel fabrication with CVD graphene. f, Close-up image of CVD graphene device. 2

3 thicknesses of 5 nm and 60nm, respectively, and then lifted off. A large window was then patterned in photoresist exposing the whole graphene strip. 40nm of an ALD aluminum oxide was then deposited at 100 ⁰C to allow for easy liftoff. After liftoff, the gate was then patterned and metal was evaporated as described above. CVD graphene was grown on copper foil at 1000 ⁰C in flowing methane 1 and characterized as single layer using Raman spectroscopy (Fig. S1d). 40 nm of PMMA was then spin coated on top of the graphene as a support layer. The copper was etched away using a ferric chloride solution, leaving the graphene and PMMA support floating on top of the solution. This was transferred to several subsequent water baths to rinse the membrane clean. Finally the membrane was scooped up with a silicon oxide on heavily n-doped silicon substrate and allowed to dry. The PMMA was removed through calcification in a tube furnace at 350 ⁰C for 4 hours in ambient air, leaving a very clean a) graphene sheet on the substrate. Graphene strips were patterned using photolithography in an AB-M mask aligner and etched in an RIE for 15 seconds in mild oxygen plasma. Electrodes were patterned in the same way; titanium and gold contacts were Intensity (A.U.) b) c) d) Graphene Electrode Top Gate Electrode evaporated as described above. Gates were then patterned, again in the mask aligner. The gate dielectric was 80 nm SiO 2 evaporated in an e-beam evaporator, immediately followed by evaporation of titanium and gold as Time Delay (ps) Photocurrent (pa) Figure S2 Scanning photocurrent microscopy. a, Schematic of experimental setup. b, Autocorrelation measurement of two pulse interference gives pulse width of 250 fs. c, Reflection image of a typical device showing graphene strip bridged by the gate. d, PC map of typical device. We see prominent photocurrent generation in the graphene on both sides of the top gate. 3

4 described above. This method allows for massive parallelization of the device fabrication as shown in Fig. S1c and d. 2. Scanning Photocurrent Microscopy In these experiments we excite the graphene devices using laser pulses generated from a Coherent MIRA- 900F. The MIRA is pumped by a 10 W Verdi and outputs a pulsed laser with pulse width of 250 fs (see Fig. S2b) at a repetition rate of 76MHz. In the experiment we set the laser to a wavelength of 800nm. The pulse is split into two at a beam splitter and fed through two optical pathways of equal length for pumpprobe spectroscopy (Fig. S2a). The pump beam path includes a delay stage to precisely vary the delay time between the two pulses. The probe beam path includes a two dimensional scanning mirror so the beam can be scanned over the sample. The two pulses are recombined with another beam splitter and focused through a microscope objective onto the sample. A mechanical chopper is used to modulate the pulses so that the photocurrent signals can be detected with a lock-in amplifier at the chopping frequency. The pump-probe experiments and chopping methods are further discussed in the next section. The sample is housed in a cryostat under vacuum at temperatures ranging from K. The device is electrically connected to a data acquisition board which allows us to bias the gates and read out photocurrent. For the scanning photocurrent measurements, the pump arm is blocked and the probe arm is chopped. Pulses are scanned two dimensionally over the sample and for each location the integrated photocurrent is electrically measured, as well as the intensity of the reflected light. This allows us to generate a 2D reflection image of our sample as well as a corresponding map of the areas where photocurrent generation occurs as shown in Fig. S2 (c) and (d). 3. Pump Probe Spectroscopy 4

5 Pump probe experiments are run by chopping the probe beam at 1.7 KHz. The length of the pump arm is varied to change the time delay between the two pulses. Generated photocurrent is first amplified by a preamp then connected to a lock-in amplifier. Since the probe is being chopped at the lock-in detection frequency, the lock-in actually measures the signal with and without the probe pulse: I pc =I pump on, probe on I pump on, probe off. Each pulse excites hot electrons based on the pulse power. The excited carriers then relax. If the two pulses are temporally separated enough so that the system has completely relaxed before the other pulse arrives, the lock-in signal is a constant given only by the photocurrent from the probe pulse. However, if the pulses are close enough so that the excited electrons have not yet decayed, the second pulse will excite more electrons in addition to the already excited ones. We have seen that the photocurrent saturates with increasing pump power (see Fig. S3a), so in this case the probe pulse will Photocurrent (A.U.) a) Probe Pump Without Saturation Combined Pulses Photocurrent (A.U.) b) Lock-in Signal Laser Power (A.U.) Probe Pump Time (A.U.) Normalized Photocurrent Photocurrent (A.U.) d) c) Without Saturation Lock-in Signal Time Delay (A.U.) PumpProbe Time (A.U.) Figure S3 Schematic illustration of pump probe experiment. a, Saturation of photocurrent with laser power. b, and c, Photocurrent as a function of time for different delay times. The shaded purple region is the signal measured with the lock-in amplifier. d, The lock-in signal as a function of delay time. 5

6 excite fewer electrons due to the presence of the already excited carriers. Therefore, while the two pulses are still interacting via the excited carriers there is a dip in the measured photocurrent corresponding to this saturation (see Fig. S3d). In the absence of saturation the two photocurrents would add linearly so the lock-in signal would be just the photocurrent from the probe pulse, and would be constant with respect to the time delay. In Fig. S3 we model the single-chopping detection technique. Here we assume that each pulse instantaneously generates a given amount of photocurrent depending on the pulse power, and that this photocurrent decays exponentially with a constant rate independent of the number of excited electrons. We point out that this is by no means an exact simulation of the data since the hot-carrier relaxation is much more complicated than a single or double exponential decay. Figure S3a shows the saturation behavior of the photocurrent with incident power. The red arrow has the combined power of the two yellow arrows. We see that the solid red arrow is smaller than the sum of the two solid yellow arrows corresponding to a saturated signal. This is unlike the case for the dashed arrows, where the dashed red arrow is equal to the sum of the two dashed yellow arrows. In Fig. S3b and c we plot the excited carriers as a function of time for the two pulse experiments with Photocurrent (pa) Bottom Gate Bias (V) 0-25 NP NN PP PN Top Gate Bias (V) 75µS 100µS Conductance Time Delay (ps) Figure S4 Photocurrent dynamics at different types of graphene junctions. 6

7 different time delays between the pulses. In each case the numbers of carriers present with (purple line) and without (blue line) the saturation effect is plotted. The shaded purple region is the lock-in signal, I pc =I pump on, probe on I pump on, probe off. In (b) the pulses are spaced so that the excited electrons have nearly decayed in between the pulses. In this case the saturation has little effect and we can see little difference between the purple and the blue curves. However, in (c) the second pulse comes in while there is still a significant amount of excited electrons present. At the time when the probe comes in we treat the remaining excited electrons as being a pulse of light with the (reduced) effective power required to excite the same number of electrons. This pulse power is added to the probe power and the subsequent saturated photocurrent is the second peak present in (c). We see here that the curves with and without the saturation effect are quite different, with the actual current being less than the case of no saturation. The integrated photocurrent is thus less for this time delay than the photocurrent in (b). Figure S3d plots the lock-in signal (integrated purple region of b and c) as a function of delay time using this model. We see that around timezero the photocurrent dips, corresponding to the delay times in which a) Photocurrent (pa) T=250K T=150K T=100K T=70K T=40K T=20K b) Photocurrent (na) Red: CW excitation Black: Pulse excitation Temperature (K) Pulse delay (ps) Figure S5 Temperature dependence of time dynamics. a, Full line traces of dynamics discussed in the paper. V t = 10V and V b =-25V. b, Temperature dependence of PN junction opposite the junction studied elsewhere in the paper. 7

8 the excited electrons from one pulse have not had time to decay before the arrival of the second pulse and the subsequent saturation that occurs. 4. Gate dependence of pump-probe signal The graphene strips were doped by changing the gate voltages as shown in the 2D conductance plot in Fig. S4. This conductance map was taken at the first cool down and Dirac point is slightly different from Fig 1c in main text, which was taken at the second cool down. The large purple spot represents the charge neutrality point of the graphene strip. We show representative pump-probe measurements from each of the four regimes of graphene interfaces (pn, pp, np, nn). In each case the dynamics appear largely the same, so while the measurements in this paper focus on pn junctions the data applies to other types of junctions as well. 5. Temperature dependence of photocurrent Here we present the full set of temperature dependent data taken on the exfoliated trilayer graphene device described in the paper. Notice in Fig. S5a that as temperature decreases the width of the dip increases corresponding to an increased decay time as described in the main text. In (b) we plot the temperature dependence of the generated photocurrent of a single beam at the opposite side of the junction presented in the paper. Notice the dramatic increase in CW photogenerated current with decreasing temperature, while that generated with the pulsed excitation is nearly constant. 6. Dynamics of exfoliated single layer graphene 8

9 In this section, we show the polarity reversal and enhancement regimes of an exfoliated single layer graphene with a mobility of ~1000 cm 2 /Vs. All of these behaviors are qualitatively the same as those of the trilayer sample presented in the main text. In Figure S6, we sweep the top gate with fixed V bg and the pump beam on and off (red and black curves respectively). Under most conditions the PC shows saturation behavior, i.e., it is reduced in the presence of the pump. This is illustrated in Fig. S6a, where at V bg = -40 V the PC with the pump at zero delay (red trace) appears to be a suppressed version of that with no pump (black trace). With certain gate configurations the presence of the pump can lead to a change in sign, or even to an enhancement of the PC near zero delay. Figure S6b shows the dependence of the PC on V tg with the pump at Figure S6 Gate dependent PC. a, Gate dependence of probe-induced photocurrent with (red) and without (black) pump at zero delay at V bg = -70 V. Here, the photocurrent is suppressed in the presence of the pump at all V tg consistent with saturation. (Probe power is 70 µw and pump power is 140 µw). b, As in a but at V bg = -40 V. Here the photocurrent can reverse polarity or be enhanced in the presence of the pump. zero delay (red trace) and without the pump (black trace), where the regimes of saturation, polarity reversal, and enhancement are indicated. 7. Dynamics of CVD grown graphene The CVD grown graphene was transferred to the SiO 2 substrate using the wet transfer method resulting in very strong p doping. Sweeping the back gate to 140V we still did not reach the charge neutrality point. The heavy doping results in a very small Seebeck coefficient for the graphene controlled by the back gate alone at V bg =0. As we sweep the top gate around the charge neutrality point we get big changes in photo-thermoelectric currents due to the large difference in the Seebeck coefficients of the two regions. In Figure S7 we plot the pump-probe time scan as function of top gate voltage. The data shows similar polarity reversal and enhancement regimes as we observed on an exfoliated sample. Also note the response time does not have a clear dependence on the top gate voltage. 9

10 140 a) V t = 1.5v 8. Temperature of pn-junction and photocurrent Photocurrent (pa) V t = 1v V t = 0.5v V t = 0v V t = -1.5V The laser-excited electrons equilibrate in a timescale of tens of femtosecond by electron-electron interaction, after which the electronic system can be described by local temperatures 5-8. Photocurrent has two contributions which are both related to the elevated temperature at the pn-junction. The first contribution is from the built-in electric field effect: the photo-generated electrons and holes are accelerated by the built-in electric field of the Photocurrent (pa) Pulse Delay (ps) 100 b) k Red: pump on Black: pump off Orange: Resistance -200 measurement 6k Top gate voltage (V) Figure S7 PC dynamics in CVD graphene a, Pump probe scans for various top gate voltages. b, Continuous gate scans for line cuts shown in (a). Saturation, sign flip, and enhancement regions clearly shown. 8k Resistance (Ohm) PN-junction which drives the electric current in the circuit 9 : I PV η = e Vnx (S1) σ R o where η is the mobility, σ o is the local conductivity at the PN-junction, R is the Source-Drain resistance, eδv gives the energy offset of the Dirac points between the two sides of the junction, and n x is the density of the photo-generated carrier. n x is a function of the local electron temperature at the junction. It scales quadratically with T e if the Fermi energy is close to the Dirac point, so the photocurrent also scales quadratically with the junction electron temperature at such gate configurations. The second contribution to photocurrent is from the photo-thermoelectric effect, where the inhomogeneous local electron temperature distribution generates thermoelectric current: 10

11 L/2 1 I = S( x) T x dx, PTE R L/2 e ( ) (S2) S ζ T e is the Seebeck coefficient, where π dσ ζ = is a function of the carrier 3e σ de 2 k 2 b 1 EF density 10. We can assume a nearly uniform local temperature in the small length scale of the pnjunction (~ 40 nm). Then the thermoelectric current is given by: 2 2 ζ L ζ R Te (0) Te ( L/ 2) I = (S3) R 2 where T e (0) is the electron temperature at the pnjunction and T e (L/2) is the electron temperature far from the junction which is equal to the Figure S8 Schematic of two PC generation mechanisms. Top: conventional photo-voltaic effect. Hot electrons and holes at the PN junction are accelerated by the built-in electric field which generates the photocurrent I PV. In the meantime, the local temperature of the PN junction decreases as these hot carriers move out. Bottom: schematic illustration of the Seebeck and Peltier coefficients. Hollow arrows indicate the energy current and solid arrows indicate the electrical current. lattice/environmental temperature. Thus, the photocurrent by the thermoelectric effect scales quadratically with the local electron temperature at the junction. The electronic energy as a function of temperature is of a larger nonlinearity. Near the neutrality point, the electron specific heat (per unit area) is 7 : C e Σ T e = = π 22 ( v ) F 2 kt 3 2 b (S4) where Σ e is the energy density of the electrons. The initial temperature of the pn-junction after photoexcitation is determined from Σ e = αp where P is the energy flux of the laser and α is the fraction of the energy that is transferred to the electron system. Thus, we expect the scaling of the electron temperature with the incident laser power density as T e ~ P 1/n where n >= 3 (considering that at higher power excitation, the phonon system may take a larger portion of the energy during the excitation). Since laser power has a higher nonlinear dependence on T e than PC, PC shows saturation behavior with the increase 11

12 of laser power. Taking I pc ~T e 2 and T e 3 ~P, it leads to I pc ~P 2/3, which agrees with measured I pc ~P 0.7 in Fig. 2c. 9. Cooling of the pn-junction and photocurrent dynamics The laser-induced temperature distribution at the pn-junction will relax by two mechanisms. The first is energy relaxation by optical phonons 5,8,11 which typically occurs in a timescale of several picoseconds. The second is through the transport of electrons/holes which take away energy. We analyze the latter below. By the built-in electric field effect, the photocurrent at the pn-junction corresponds to the flow of hot electrons and holes which carry an average energy of ~ k b T e (measured from Fermi level). Therefore, this photocurrent contribution corresponds to an energy current: W = η η Vn k T V Σ PV x b e e σor σor (S5) By the continuity equation of the energy flow, d ( 2Σ dw) e dt η = WPV + WPV = 2 VΣ x= d x= d e (S6) σ R o where w is the channel width and 2d is the length of the PN junction. Therefore, the electron energy density Σ e at the PN-junction decays with the rate η Γ= V (S7) wdσ R o For mobility η ~ cm 2 V -1 s -1 and w ~ 5 µm. Assuming σ o R ~ 4, d ~ 0.02 µm, ΔV ~ 50 mv, we find Γ~ ps -1, which corresponds to a decay time of ps. This time scale describes how fast the hot carriers are moved out of the active region (i.e. pn junction here) by the built in electric field. 12

13 Due to the inhomogeneity of the Seebeck coefficient, the photocurrent due to the thermoelectric power also cools the pn-junction by the Peltier effect. The energy current is related to the electric current by W PTE = Π I where Π = ST is the Peltier coefficient. We have the continuity equation: PTE /2 dt d 2 1 L dt Ce = ζt ζt dx dt dx wr dx L/2 (S8) The cooling effect is most significant at the pn-junction since ζ has an abrupt change there (see Fig S8). We numerically simulated the dynamics for the configuration illustrated in Fig. S8, where we assume 1 x ζ ( x) = erf ( ) in units of µv/k 2 and source drain resistance R = 9 kω (erf stands for the error 3 d function). We assume the electron specific heat is given by Eq. (S4). The energy transferred to the electron system per unit area by each pulse excitation at its peak position is assumed to be Figure S9 Calculated photocurrent dynamics of the thermoelectric effect. Left: Photocurrent as a function of time after the pulsed excitation (probe only). Middle: Temperature distribution as a function of time after the pulsed excitation (probe only). Right: Integrated photocurrent in the pump-probe measurement as a function of the pump-probe delay time, showing saturation behavior at small delay i 22 ( ) 3π v F 2 k (1000) 3 3 b results are presented in Fig. S9., and the environmental temperature T e (L/2) is taken as 300 K. The simulation 13

14 In summary, both contributions to the photocurrent are associated with cooling of the PN junction which determines the dynamics of the photocurrent after the pulsed optical excitation. As the temperature of the PN junction cools down, the photocurrent decays. These dynamics are studied by the pump-probe Seebeck Coefficient (µv/k) ΔS= S b -S t (µv/k) a) b) Top Gate Voltage (V) Figure S10 Calculated Seebeck coefficient. a, Calculated Seebeck coefficient as modulated by top gate, found using the Mott formula from a line trace of Fig 1c with V b = V. b, Difference of Seebeck coefficients between bottom gate and top gate modulated graphene. measurements as described in the main text and are related to the response time of the graphene PN junction as a photo detector. A common feature to these cooling processes is that the timescale is proportional to the source-drain resistance R while the current integrated over the decay time is independent of R. This is consistent with the two observations that the integrated photocurrent is independent of the environmental temperature while the timescale of the dynamics decreases as environmental temperature increases from 20K to 300K, since R decreases. The measured value of R does show correlation with the timescale as a function of environmental temperature (see Fig. 3b in the main text). The timescale of the cooling by the built-in electric field effect is about one or two orders of magnitude longer than the observed dynamics, while the timescale of the Peltier cooling effect is in reasonable agreement with the observation. Top Gate Voltage (V) 10. Anomalous behavior of the PC signal as a function of gate voltages We calculated the thermoelectric power difference at the pn junction using the Mott formula (Fig. S10). If we define S = Sb St, the calculation yields that the thermoelectric power difference at the pn junction 14

15 is always positive and reaches a minimum around V tg = 0 V (where S b (S t ) denotes the Seebeck coefficient of the graphene controlled by the bottom (top) gate). FromV = S T, the electric field for electrons always points towards the top-gate. In our experimental configuration, it means I PTE is always positive at fixed V b =-24.2V. Since the intrinsic Dirac point for the top gate is ~0V, the device is in the pn (pp) configuration when V t is larger (smaller) than 0V. In the pn configuration, the built-in electric field points from the p to the n side and has the same direction as the photo-thermoelectric field. Photocurrent response is the addition of both effects, and we observe the saturation effect. When V tg is smaller than 0V, the junction switches from pn to pp, where the graphene outside top gate is less p doped. The built-in electric field switches signs and points away from the top gate, i.e. in the opposite direction as the photo-thermoelectric effect, and thus gives negative photocurrent (Fig. 4a&c). The net photocurrent is a subtraction of the two effects (I pc = I PTE - I PE ). At large negative V t, PC excited by one laser beam could be positive (Fig. 4b) or negative (Fig. 4c) depending on relative strength of I PTE and I PE. Figure 4c shows a scenario of negative photocurrent. This means the absolute value of I PE is slightly larger than I PTE at this gate configuration. The absolute photocurrent is further enhanced in the presence of the pump. This tells us the photothermoelectric effect has a higher nonlinear dependence on T e than the built-in electric field, i.e. the photo-thermoelectric effect has a stronger saturation under pulse excitation. In the regime when Photocurrent (pa) µw 130 µw 30 µw Time Delay (ps) Figure S11 Sign flip region of pump probe signal with various pump powers. V t =-2 V V b =45 V. the built-in electric field just switches sign, I PTE reaches a minimum and is slightly larger than I PE, and the net photocurrent is positive (Fig. 4c). However, the presence of the pump induces further saturation of I PTE. I PE stands out and yields a net negative photocurrent at zero time delay (Fig. 4a&c). We are able to control the amount of photocurrent in the opposite direction by varying the pump power as shown in 15

16 Figure S11. Our data demonstrate that both built-in electric fields and photo-thermoelectric effect contribute significantly to photocurrent generation at a graphene pn junction under pulse excitation. The above explanation qualitatively agrees with the experimental results. It is difficult to exactly reproduce the gate dependent data since the conductance measurement is a bulk effect. Charge inhomogeneities could strongly affects local charge density so as to change the effective Seebeck coefficient and the built-in electric field strengths. This problem could be overcome by local conductance measurement techniques such as EFM, or STM. 11. Supplemental References 1 Li, X. et al. Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science 324, (2009). 2 Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, (2005). 3 Ferrari, A. C. et al. Raman Spectrum of Graphene and Graphene Layers. Phys. Rev. Lett. 97, (2006). 4 Lui, C. H. et al. Imaging Stacking Order in Few-Layer Graphene. Nano Lett. 11, (2011). 5 Bistritzer, R. & MacDonald, A. H. Electronic Cooling in Graphene. Phys. Rev. Lett. 102, (2009). 6 Butscher, S., Milde, F., Hirtschulz, M., Malic, E. & Knorr, A. Hot electron relaxation and phonon dynamics in graphene. Appl. Phys. Lett. 91, (2007). 7 Lui, C. H., Mak, K. F., Shan, J. & Heinz, T. F. Ultrafast Photoluminescence from Graphene. Phys. Rev. Lett. 105, (2010). 16

17 8 Sun, D. et al. Ultrafast Relaxation of Excited Dirac Fermions in Epitaxial Graphene Using Optical Differential Transmission Spectroscopy. Phys. Rev. Lett. 101, (2008). 9 Liu, M. et al. A graphene-based broadband optical modulator. Nature 474, (2011). 10 Xu, X., Gabor, N. M., Alden, J. S., van der Zande, A. M. & McEuen, P. L. Photo- Thermoelectric Effect at a Graphene Interface Junction. Nano Lett. 10, (2009). 17