Letter pubs.acs.org/NanoLett
Hot Phonon Dynamics in Graphene Shiwei Wu,*,†,⊥ Wei-Tao Liu,‡,⊥ Xiaogan Liang,†,# P. James Schuck,† Feng Wang,‡,§ Y. Ron Shen,‡,§ and Miquel Salmeron*,†,§,∥ †
The Molecular Foundry and §Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States ‡ Department of Physics and ∥Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, California 94720, United States S Supporting Information *
ABSTRACT: The dynamics of hot phonons in supported, suspended, and gated monolayer graphene was studied by using time-resolved anti-Stokes Raman spectroscopy. We found that the hot phonon relaxation is dominated by phonon−phonon interaction in graphene, and strongly affected by the interaction between graphene and the substrate. Relaxation via carrier−phonon coupling, known as Landau damping, is ineffective for hot phonons which are in thermal equilibrium with excited carriers. Our findings provide a basis for better management of energy dissipation in graphene devices. KEYWORDS: Graphene, hot phonons, ultrafast dynamics, time resolved, anti-Stokes Raman
S
yields contradictory interpretations.15,16 On the other hand, the time-resolved ASR spectroscopy directly probes the dynamics of zone-center optical phonons, the G mode phonon in graphene, whose ASR intensity is proportional to the phonon population.18 And it has recently been applied to other graphitic materials, such as carbon nanotube thin films19,20 and graphite.21,22 While the cross section of ASR scattering from monolayer graphene is relatively small, making a precise measurement on monolayer graphene is more challenging, as shown in ref 22. Using an ultrasensitive time-resolved Raman microscope, we measured the dynamics of hot phonons in supported, suspended, and gated monolayer graphene. This comprehensive study allows us to separate different hot phonon relaxation pathways, including phonon−phonon and carrier−phonon couplings within graphene and the interaction between graphene and the substrate. We found that the hot phonon lifetime shows no dependence on the gate voltage (or equivalently, the Fermi level) in graphene FET devices. This is in striking contrast to the dramatic gate-induced change of the line width observed by spontaneous Raman scattering on the same phonon mode at low temperatures.23,24 In the latter case, Landau damping, which describes phonon relaxation through coupling between phonons and resonant electron− hole pairs, was believed to be responsible for the change as the coupling is switched on or off by the gate voltage.23−25 Our result, however, showed that Landau damping is not an
ubstantial progress has been made in developing graphene devices recently,1−4 particularly for applications at very high frequencies5−7 and large current densities.8−10 Since graphene is merely one atomic layer thin, energy dissipation becomes a crucial issue.11 Phonons, the lattice vibrations of solids, play a central role in the relaxation of energetic electrons and dissipation of heat, which has profound impact on the performance of graphene devices through carrier−phonon and phonon−phonon interactions.9,10 For example, recent studies have shown that hot phonons, with a phonon temperature as high as 1570 K, were readily generated by the electrical current in graphene field effect transistors (FET),9,10 which led to current saturation under high source−drain voltages.8 However, relaxation dynamics of phonons and their interaction with other elementary excitations in graphene in the limit of large phonon populations (i.e., high effective phonon temperatures) remain poorly understood. Such understanding is essential for the future development of graphene devices. The lifetime of phonons is often implicitly taken from the inverse of the line width of the corresponding Raman mode, yet the Raman line width is affected by many other possible factors.12 In the case of resonant Raman scattering, such as that in graphene, the Raman line width is further complicated by the involvement of carrier lifetime.12 Here, we report a timedomain study on hot phonon dynamics in graphene using timeresolved anti-Stokes Raman (ASR) spectroscopy. This technique is different from other pump−probe techniques, such as transient reflectivity, in which the phonon lifetime is indirectly deduced from carrier dynamics and many different phonons could contribute to the relaxation of excited carriers.13−17 Thus, it complicates the results and sometimes © 2012 American Chemical Society
Received: May 27, 2012 Revised: October 21, 2012 Published: October 29, 2012 5495
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Figure 1. (a) Schematic showing the principle of this pump−probe technique. (b) 2D plot of ASR spectra as a function of the time delay between pump and probe beams, measured from a monolayer graphene supported on a SiO2/Si substrate. For clarity, a few selected spectra at different time delays are also shown in (c). The pump and probe fluences were 3.7 and 0.2 J/m2, respectively. (d) Stokes (red curve) and anti-Stokes (blue curve) Raman spectra of the G mode phonons measured with femtosecond probe pulses at time delay of 0.6 ps. The broad photoluminescence background was subtracted. (e) The integrated intensity of the ASR peak at ∼1585 cm−1, corresponding to the G mode phonons in graphene, was extracted and plotted as a function of time delay. The dynamic measurement is fitted with a simple model that considers finite durations of the pump and probe pulses and an abrupt but time-delayed phonon population rise, shown in the red solid curve. The fitting yields a lifetime of 1.5 ± 0.1 ps for a supported monolayer graphene. For reference, the cross correlation between the pump and probe pulses is also shown in a black dashed line. (f) Comparison of the phonon dynamic measurements at different pump fluences (red for 5.0 J/m2 and black for 2.5 J/m2, respectively). Negligible change in the phonon lifetime was observed.
dynamic studies (Figure 1a). The stronger pump beam at 830 nm from a femtosecond Ti:Sapphire oscillator (∼150 fs, 76 MHz) excited carriers and created a high density of hot phonons from carrier relaxation similar to what happens in high field graphene devices.9,10 A time-delayed weaker probe beam at 565 nm from a synchronously pumped optical parametric oscillator (∼200 fs, 76 MHz) was then used to probe the population of hot zone center optical phonons via ASR scattering. We defined zero time delay between pump and probe by the maximum four-wave mixing signal emitted from the Si substrate that supported the graphene samples. Both pump and probe pulses were focused on the sample at normal incidence through the microscope objective ( ×100, NA = 0.95). The probe beam was adjusted to a spot ∼2.5 μm in diameter inside a larger spot of the pump beam. The backscattered ASR signal was collected by the same objective and recorded with a liquid nitrogen cooled CCD detector after passing through a spectrograph with appropriate filters. Our detection system was sufficiently sensitive for us to obtain timeresolved ASR spectra from even monolayer graphene with 0.1 ps time resolution. Figure 1b shows a 2D plot of ASR spectra as a function of the time delay between pump and probe beams, obtained from a monolayer graphene supported on a Si wafer covered by a 300 nm oxide layer. A few selected spectra at different time delays are presented for clarity in Figure 1c. An ASR peak at ∼1585 cm−1 was clearly observed on a broad photoluminescence background,26 and its intensity changed with the time delay. This peak comes from the zone-center G mode phonon in graphene.27,28 The phonon population n of the G mode can be
effective decay mechanism for a system of hot phonons and carriers in thermal equilibrium as in the case of high field graphene devices;10 instead, the hot phonon relaxation is dominated by phonon−phonon coupling in graphene. The result also confirms an earlier speculation that the phonon− phonon interaction dominates the relaxation of hot phonons in graphite.21 We also observed notable differences in phonon lifetimes between supported monolayer and multilayer graphene and between suspended and supported monolayer graphene. The results reveal additional relaxation channels for hot phonons provided by the substrate, which can account for ∼25% increase of the overall phonon relaxation rate in graphene. The result corroborates the substrate effect recently observed by transient reflectivity in ref 16, although the hot phonons probed in that paper are not limited to the G mode phonons. Furthermore, we found that the hot phonon lifetimes for bi- or trilayer graphene are very close to 2.1 ps as found in graphite.21,22 The experiment was conducted on mechanically exfoliated graphene at room temperature using a diffraction-limited optical microscope and a tunable femtosecond light source (for the experimental setup, please refer to the Supporting Information).26 The system allowed time-resolved imaging and characterization of the graphene samples with both photoluminescence26 and Raman spectroscopy.27,28 Raman spectra taken from our samples exhibited no measurable D peak at ∼1320 cm−1, indicating that the samples had a minimal amount of defects.27 The samples were also protected by continuously purging with dry nitrogen. The pump and probe beams were sent collinearly through the microscope onto the sample for 5496
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determined from the intensity ratio of anti-Stokes and Stokes Raman peaks, IAS/IS = (ωAS/ωS)4[n/(n + 1)]. If the phonons are in quasithermal equilibrium, then the effective phonon temperature T is obtained from the Bose−Einstein distribution, n = [eℏωG/kBT − 1]−1, where ℏωG is the G mode phonon energy. In our experiment on the monolayer graphene, a pump fluence of 3.7 J/m2 yielded a maximum IAS/IS ratio of 0.294 at ∼0.6 ps (Figure 1d), corresponding to a phonon population and the effective phonon temperature of 0.17 and 1320 K, respectively. Figure 1e depicts the rise and decay of the integrated antiStokes peak intensity (and hence the hot phonon population). The probe beam also created hot phonons, which contributed to the signal as a weak, time-independent background, and was subtracted in the dynamic plot. The data in Figure 1e show that the phonon population builds up rapidly in the first few hundred femtoseconds and then decays away in the next few picoseconds. Fitting the decay section with a single exponential curve yields a lifetime of 1.5 ± 0.1 ps for the hot G mode phonons in the supported monolayer graphene. The same result was obtained by taking into account the finite duration of pump and probe pulses and an abrupt but time-delayed rise on the phonon population section,20,22 as shown by red solid lines in Figure 1e. We also observed negligible change in the phonon lifetime as the pump and probe beams were varied from 2.5 to 5.0 J/m2 and 0.08 to 0.20 J/m2, respectively. For example, comparison of the phonon dynamic measurements at different pump fluences is shown in Figure 1f. The limited range of laser fluences was chosen to avoid damage of the sample and ensure good signal-to-noise ratios. The values of lifetime reported in the following at various conditions (monolayer vs few-layers, supported vs suspended, and different gate voltages) are all reproduced within an error of 0.1 ps by using different clean samples and choosing different area of samples. Similar measurements were carried out on supported multilayer graphene samples. Figure 2 shows the results from mono-, bi-, tri-, and quad-layer graphene on an oxidized Si substrate. The lifetimes of the hot G mode phonons deduced from the curves are 2.0, 2.2, and 2.3 ps for bi-, tri-, quad-layer graphene, respectively, in comparison with 1.5 ps for monolayer graphene (Figure 2b). We note that the observed lifetimes for multilayer graphene are similar to the 2.1 ps G phonon lifetime we and others21,22 found in graphite but is noticeably different from that of the supported monolayer graphene. To see how the supporting substrate may affect the hot phonon lifetime, we did the measurement on a monolayer graphene suspended over a 5 μm hole on the SiO2/Si substrate (Figures 3a,b). Figure 3c displays the Raman spectra from the suspended and supported regions of the sample. The intensity ratio of the 2D mode at ∼2640 cm−1 to the G mode appears much larger in the suspended region, consistent with previous studies.29 From the pump−probe measurement, the lifetime of the hot G phonons was found to be 1.5 ps in the supported region but 2.0 ps in the suspended region (Figure 3d). The latter is nearly the same as that in multilayer graphene but slightly shorter due to possible structural defects in suspended graphene such as ripples.30 Clearly, the interplane relaxation of hot phonons is negligible compared to intraplane relaxation in graphene, but the relaxation through coupling between graphene and the substrate is not. If the substrate is in contact with the monolayer graphene, it provides an additional pathway for hot phonons in graphene to relax.22 We now examine effects of carrier−phonon coupling on the dynamics of hot phonons in graphene. Previous spontaneous
Figure 2. (a) Optical microscopy image showing mono-, bi-, tri-, and quad-layer graphene on a SiO2/Si substrate. The scale bar is 10 μm. (b) Phonon dynamic measurements on the above shown graphene layers of different thicknesses. The fittings indicate the lifetime of G mode optical phonons to be 1.5, 2.0, 2.2, and 2.3 ps for mono- (black), bi- (blue), tri- (green), quad-layer (red) graphene, respectively. The data for bi-, tri-, and quad-layer graphenes are scaled correspondingly for clarity.
Raman scattering studies indicated efficient phonon relaxation through Landau damping.23−25 This relaxation process is particularly efficient in graphene because of the unique band structure of graphene. It allows a G phonon to annihilate into an electron−hole pair with both energy and momentum conserved, when the separation between the Fermi level and the Dirac point is smaller than half of the phonon energy. On the other hand, shifting the Fermi level away from the Dirac point by more than half of the phonon energy suppresses this phonon decay channel. Such an effect was observed in the spontaneous Raman line width of the G mode when the gate voltage on a graphene monolayer was varied to shift the Fermi level up and down.23,24 One may think that the same effect would also contribute to hot phonon relaxation (for example, in ref 9). We prepared gated monolayer graphene devices to study the effect of carrier−phonon coupling. The samples were in the form of three-terminal FETs that allowed electrical transport measurement. The heavily doped silicon substrate covered by a 300 nm oxide layer acted as the back gate, and tuning of the Fermi level was achieved by varying the gate voltage Vg.23,24 Figure 4a shows the source−drain resistance as a function of Vg, which reaches the maximum at 39 V when the Fermi level in 5497
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Figure 3. (a) Optical image of a monolayer graphene on a holepatterned SiO2/Si substrate. The monolayer graphene over the holes is suspended from the substrate. The size of the patterned holes is ∼5 μm in diameter. The scale bar is 20 μm. (b) Side-view schematic of the sample geometry. (c) Spontaneous Raman spectroscopy of monolayer graphene suspended over the holes (red) and supported on the substrate (black). The excitation wavelength is 532 nm. (d) Phonon dynamic measurements on suspended (red) and supported (black) monolayer graphene. The data are scaled correspondingly for clarity. The phonon lifetime is 2.0 ps for suspended monolayer graphene, instead of 1.5 ps for supported monolayer graphene. For comparison, result on a supported bilayer graphene is also shown in blue, and its phonon lifetime is 2.0 ps.
Figure 4. (a) Transport measurement of a three-terminal monolayer graphene field effect transistor. The graphene was supported on a SiO2/Si substrate with the heavily doped silicon acting as a back gate. The peak at a gate voltage of 39 V indicates the charge-neutral point of graphene. The electronic structure of graphene at different gate voltages is also schematically shown. (b) Phonon dynamic measurements at gate voltages of 0 V (black), 39 V (red), and 90 V (green), respectively. The data are scaled correspondingly for clarity. Phonon lifetime is 1.5 ps, independent of gate voltage, or equivalently the Fermi energy in graphene. (c) Phonon population as a function of gate voltage at two different time delays, 1.0 ps (red) and 2.4 ps (black). The phonon population remains a constant.
graphene appears at the Dirac point. The carrier density and the Fermi level at each Vg can be determined from the gate capacitance of the oxide layer and the Fermi velocity of graphene.23 For our sample at Vg = 0 V, the graphene was holedoped, and the Fermi level EF was about 187 meV below the Dirac point. In this case, because |EF| was well above half of the G mode phonon energy (ℏωG = 196 meV), G mode phonon relaxation via Landau damping was prohibited. At Vg = 39 V (| EF| = 0 V), the same relaxation process should become possible. However, as seen in Figure 4b, the dynamic measurements at different Vg yielded nearly the same lifetime of 1.5 ps. The result was further illustrated by monitoring the G mode phonon population while sweeping Vg at a fixed pump/probe time delay. Figure 4c shows that at both time delays of 1.0 and 2.4 ps, the phonon population is independent of Vg. The lifetime of 1.5 ps we observed is equivalent to a line width of 3.6 cm−1, which is close to the G mode line width measured in spontaneous Raman scattering from gated graphene in the region where Landau damping is prohibited. This therefore indicates that Landau damping is not effective even when the Fermi level is near the Dirac point, and relaxation of the hot G mode phonons is essentially the same as the usual phonon relaxation in graphene dominated by phonon−phonon coupling. To understand the results, it is essential to understand the dynamics of this coupled carrier−phonon system. The femtosecond pump pulse first generates a highly nonequilibrium population of carriers, which thermalizes through carrier−carrier interaction and reaches an effective temperature of a few thousand degrees in the first tens of femtoseconds.13 In
the next few hundred of femtoseconds, the carrier temperature drops rapidly as the hot carriers relax into zone-center (or G mode) and zone-edge optical phonons.14 The phonon population peaks as carriers and phonons approach thermal equilibrium, but not with the acoustic phonons.10 With a pump fluence of 3.7 J/m2, the equilibrated carrier and optical phonon temperature is as high as 1320 K at the time delay of ∼0.6 ps. At such high carrier temperatures, the excitation probability of low-energy electron−hole pairs drops,9,24,25 and the annihilation of G mode phonons through Landau damping is less likely. According to the calculations in refs 9, 24, and 25, the G mode line width broadening due to Landau damping becomes ∼4.5 cm−1 at 1300 K. This value is much lower than that of ∼11 cm−1 at low temperatures.24,25 However, the temperature effect still cannot account for the negligible gate dependence in the phonon lifetime that we observed. Furthermore, the independence of phonon lifetime on the pump fluence also indicated that the temperature effect is not appreciable. To comprehend the phenomenon, we noted that upon thermal equilibrium, the energy exchange between carriers and optical phonons becomes bidirectional. The G mode phonons can annihilate into low-energy electron−hole pairs, and conversely, the excited electrons and holes can recombine and generate G 5498
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mode phonons. Hence there is no net decrease of phonon population via carrier−phonon coupling in graphene, and Landau damping cannot be effective for the equilibrated system of hot carriers and phonons. While the carrier−phonon coupling within graphene is no longer efficient, the dominant relaxation mechanism of the coupled hot carriers and phonons is via scattering to low-energy phonons. In suspended graphene, it leads to a phonon lifetime of ∼2 ps, but for supported graphene, the SiO2 substrate creates additional relaxation channels that increases the overall relaxation rate of phonons in monolayer graphene by ∼25% and reduces the phonon lifetime to 1.5 ps. Such channels can be the direct scattering between graphene phonons and substrate phonons.31 In addition, the remote scattering of graphene carriers by the substrate polar phonons can also accelerate the cooling of the equilibrated system of hot carriers and phonons.32 Although a theoretical calculation favors the latter mechanism,33 we could not determine this from the current experimental results. Since high currents readily induce a significant overpopulation of phonons,9,10 the decay of hot phonons imposes a fundamental limit to the switching rate of high field graphene devices. Recently, fast graphene transistors have been demonstrated with a cutoff frequency of hundreds of GHz.5−7 Though the resonant coupling between phonons and low-energy electron−hole pairs can be strong, our study shows that Landau damping is not an effective decay channel for hot phonons. The phonon−phonon coupling dominates the decay process on the time scale of ∼2 ps. This sets a limit to the switching rate of about 500 GHz. On the other hand, our results suggest that the relaxation of hot phonons can be expedited by supporting graphene on appropriate substrates, whose strong interaction with graphene can provide additional relaxation pathways for hot phonons in graphene.
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REFERENCES
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ASSOCIATED CONTENT
S Supporting Information *
Detailed description of the experimental setup and measurement. This material is available free of charge via the Internet at http://pubs.acs.org.
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Letter
AUTHOR INFORMATION
Corresponding Author
*Email:
[email protected];
[email protected] Present Addresses ⊥
Department of Physics, Fudan University, Shanghai, 200433, China. # Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was done at the Molecular Foundry and supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, of the U.S. Department of Energy under contract no. DEAC02-05CH11231. Manuscript finalization was also supported by NSFC under contract no. 11104036. 5499
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