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Dirac fermion relaxation and energy loss rate near the Fermi surface in monolayer and multilayer graphene

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Dirac fermion relaxation and energy loss rate near

the Fermi surface in monolayer and multilayer

graphene

C. W. Luo,*aP. S. Tseng,aH.-J. Chen,aK. H. Wuaand L. J. Lib

Ultrafast dynamics of Dirac fermions near the Fermi surface in monolayer and multilayer graphene are revealed using optical pump mid-infrared probe spectroscopy. The energy loss rate of Dirac fermions is also determined via energy-resolved transient trans-missivity spectra, which is significantly suppressed as the number of layers in graphene increases.

Recently, 2D materials, such as graphene,1 MoS

2, WS2 and MoSe2,2have become attractive because of their unique physical properties. Of these 2D materials, graphene is the simplest, composed of only a single element, carbon. Since the discovery of graphene by Novoselov and Geim,1 many studies have

demonstrated its unique properties of a high mobility of2  105 cm2 V1 s1for both electrons and holes,3 a high trans-mittance of97.7% in the visible range4 and a high Young's modulus of 1 TPa.5 Different graphene-based devices have also been developed for various applications, such as FETs6and sensors.7Therefore, the issues associated with electron–phonon interaction, carrier lifetime, carrier dynamics and energy loss rate are very important for optimizing the device performance. In 2008, Dawlaty et al.8rst measured the ultrafast dynamics of photoexcited carriers in graphene using degenerate optical pump-probe spectroscopy. Similar measurements for mono-and multilayer epitaxial graphene have also been carried out by non-degenerate pump-probe spectroscopy, such as a dual-color optical pump probe,9,10an optical-pump infrared-probe,11–13an

optical-pump THz-probe14 and a THz-pump optical-probe.15

However, the Dirac fermion–phonon coupling or energy loss rate in the vicinity of the Fermi level has not been studied. In this study, graphene is pumped by 800 nm and probed with a tunable mid-infrared to determine the Dirac fermion–phonon coupling and energy loss rate near the Fermi level.

The graphene samples were synthesized using CVD on a copper substrate. By carefully controlling the airow of a

mixture of methane and hydrogen in a heated furnace, mono-layer graphene was uniformly grown on a copper substrate. The samples were then spin coated with poly(methyl methacrylate) (PMMA). PMMA/graphene was detached from the copper substrate by etching copper with an aqueous nitric acid solu-tion. The detached PMMA/graphene was then transferred and deposited on the sapphire substrate by direct contact. PMMA was subsequently dissolved, leaving monolayer graphene on the target substrate. PMMA residues on the sample were then eliminated by annealing. N-layer graphene samples were obtained by repeating this process with N times on the same sapphire substrate. In this study, p-type graphene samples were used on the sapphire substrate, with N¼ 1, 2, 3 and 5, respec-tively. The number of layers in each sample was conrmed by the quantized absorption level for each sample, as noted in the optical transmission measurement using broadband visible light.

For optical pump mid-infrared probe (OPMP) spectroscopy,16

the light source was provided by a regenerative amplier (Legend, Coherent Inc.) operating at a central wavelength of 800 nm, with a repetition rate of 5 kHz, a spectral width of 35 nm and a pulse duration of 30 fs. A beam splitter reected 40% of the light into the pump path, with the remainder being trans-mitted to serve as a probe. In the probe path, a 0.7 mm thick GaSe crystal generated mid-infrared (MIR) pulses with tunable wavelengths from 9.0 (138 meV) to 14.1 mm (88 meV) via differential frequency generation (DFG). In order to ensure the spot size of the pump beam was larger than that of the probe beam, the optical pump beam was focused on the sample to provide a spot with a diameter of 485mm, using a 150 mm lens. The typical pumpinguence used in this study was 68 mJ cm2. The mid-infrared probe beam was focused on the sample surface to produce a spot with a diameter of 392mm through an Au coated off-axis parabolic mirror with f ¼ 200 mm. This beam was collimated and refocused onto a liquid-nitrogen cooled HgCdTe detector using an Au coated off-axis parabolic mirror with a focal length of 50 mm.

aDepartment of Electrophysics, National Chiao Tung University, Hsinchu 30010, Taiwan. E-mail: cwluo@mail.nctu.edu.tw

bInstitute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan Cite this:Nanoscale, 2014, 6, 8575

Received 24th April 2014 Accepted 14th May 2014 DOI: 10.1039/c4nr02205j www.rsc.org/nanoscale

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Fig. 1 shows the optical pump mid-infrared probe spectra for all of the samples in this study. At low probe photon energy (Ep), a negative peak is clearly observed in the transient trans-missivity changes,DT/T. This negative peak gradually dimin-ishes as the probe photon energy increases (in Fig. 1(a)). Noticeably, an additional positive peak appears at a greater probe photon energy of Ep > 126 meV, which is close to the Fermi energy, EF(here, we take the Dirac point energy, ED, to be zero). In order to elucidate the origins of both positive and negative signals, a model for the optical pumping and mid-infrared probing processes in the schematic energy band structure of the graphene is shown in Fig. 1(b). Since the photon energy of the MIR probe pulse ranges from 88 to 138 meV, the interband transitions between the valence band (VB) and the conduction band (CB) in the vicinity of the Fermi surface of graphene can be clearly observed. Aer pumping, the smearing effect causes the transient occupation probability above (below) EFis to be larger (smaller) than that before pumping. Therefore, DT/T induced by the pump pulses is positive (negative) for the probe transitions above (below) EF, which is consistent with the results for n-type graphene.11

This phenomenon is also demonstrated by the transient spectra, as shown in Fig. 2(a). For monolayer graphene,DT/T at 1.0 ps changes from negative to positive and crosses zero at around 132 meV. Aer 1.0 ps, the transient spectra gradually shrink with increasing delay time. Similar results are also observed for samples with two, three andve layers, as shown in Fig. 2(b)–(d). The variation in the transient spectra at 1.0 ps increases when the number of layers is increased. Additionally, the zero crossing point gradually shis to the lower probe photon energy as the number of layers increases, which indi-cates that the Fermi surface is moving away from the Dirac point. The inset in Fig. 2 further presents the dependence of EF on the number of layers in graphene. EFlinearly decreases as the number of layers increases, which is consistent with the results in ref. 11 and 17, in which the graphene samples were prepared by thermal desorption on SiC substrates. It is worth emphasizing that the Fermi level of graphene produced using CVD in this study is smaller than that of those produced by

thermal desorption on SiC substrates.11,17 This indicates that graphene grown by CVD has a smaller doping effect from substrates and is close to the intrinsic graphene.

The decay time (s) of DT/T above EFsignicantly depends on the probing photon energy, as shown in Fig. 3(a). For monolayer graphene,s is larger and remains constant at 2 ps when the probed regime is closer to EF. A similar energy dependence ofs is also observed in multilayer graphene (bilayer, trilayer and ve-layer). However, all of the s values for multilayer graphene are larger than those for monolayer graphene, because the cooling of photoexcited hot carriers in multilayer graphene is slower than that in monolayer graphene. Additionally, the slope of s(E) in the range of >5 meV is also larger than that for multilayer graphene. This implies that the smearing effect around EFinduced by optical pumping is signicant in mono-layer graphene.

Phonons are thought to be the main medium for the relax-ation of photoexcited hot carriers in graphene.9,11,12,14Here, we

follow this approach. The dependence of the relaxation time on the photon energy implies that the coupling strength (l) between Dirac fermions and phonons varies at different posi-tions on the Dirac cone. According to the second moment of the Eliashberg function,18l is inversely proportional to the

relaxa-tion time (s) of excited electrons, lu2f1

s (1)

whereu is the phonon energy, which couples with the electrons. For the estimate of hu2i, some vibrational modes are more efficiently coupled to Dirac fermions than others are. In the case of graphene, the E2gmode (which is the so-called G peak in the Raman spectra) of195.9 meV is coherently excited by photo-excitation and efficiently coupled.19 Aer pumping, the

temperature of the electrons (Te) suddenly rises due to the smaller coefficient of heat capacity. Taking Te ¼ 2162 K (obtained from ref. 20 at the pumpinguence, as mentioned Fig. 1 (a)DT/T for monolayer graphene at various photon energies,

from 88 to 138 meV. (b) The schematic energy band structure of graphene with the optical pump mid-IR probe processes.

Fig. 2 The transient spectra at different delay times for the graphene samples with (a) monolayer, (b) bilayer, (c) trilayer and (d)five-layer. Inset: the energy difference between the Fermi level (EF) and the Dirac

point (ED) as a function of the number of graphene layers.

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previously) to estimate the coefficient of (pkBTe/3ħ) in eqn (1), the photon energy dependence of the Dirac fermion–phonon coupling strengthl is shown in Fig. 3(b). The Dirac fermion– phonon coupling strength, measured using OPMP, becomes signicantly smaller near EF, which is in close agreement with the theoretical results ofl  3  103,21obtained by using a continuum model to calculate the self-energy of phonon Green's function in graphene.

Fig. 3(b) shows thel value for graphene as a function of the energy difference above EF. For multilayer graphene (including two, three andve layers), the value of l is around 1.5  103 below 5 meV and then slightly increases above 5 meV. Similar results are also observed in monolayer graphene. However, the value ofl  1.65  103is higher than that of multilayer gra-phene below 5 meV and rises much signicantly to close to the theoretical value of 3 103as the energy increases above 5 meV.21 These results demonstrate that the Dirac fermion–

phonon coupling strength above the Fermi level in monolayer graphene is higher than that in multilayer graphene. Moreover, the Dirac fermion–phonon coupling strength in monolayer graphene exhibits marked energy dependence above the Fermi level.

Finally, a closer examination ofDT/T as a function of photon energy at various delays in Fig. 2 reveals that the absorption peak (marked by arrows in Fig. 2) experiences a red shi (rela-tive to the zero crossing point, EF) with the time delay. This implies the unoccupied density of states in the Dirac cone shi as a function of time, i.e., the energy loss of carriers as a func-tion of time. According to therst moment,

 ðDT T EphotondEphoton  ðDT T dEphoton  (2) the rate of energy loss for the carriers in the Dirac cone is estimated. As shown in Fig. 4, the dots represent the rst moment at a different time, which is associated with the red shi in the absorption peak shown in Fig. 2. An exponential t to the time-dependent rst moment shown in Fig. 4 gives a relaxation time of 0.35 ps within the range of 6.2 meV in monolayer graphene. Therefore, the rate of energy loss for Dirac fermions in the Dirac cone of monolayer graphene is17.7 meV ps1, which is much larger than that of 1 meV ps1in topo-logical insulators.16,22 For bilayer, trilayer and ve-layer gra-phene, the rate of energy loss for Dirac fermions in the Dirac cone is 16.8, 8.6 and 3.8 meV ps1, respectively. This demon-strates that the number of layers in graphene is an important parameter for control of the energy loss rate, which is

Fig. 3 The relaxation time for Dirac fermions as a function of the distance from the Fermi surface (EF) for various graphene samples with

monolayer, bilayer, trilayer and five-layer. (b) The Dirac fermion– phonon coupling constant as a function of the distance from the Fermi surface (EF) for various graphene samples with monolayer, bilayer,

trilayer andfive-layer. The solid lines and gray areas are a guide for the eyes.

Fig. 4 The time-dependentfirst moment as a function of the delay time for various graphene samples with monolayer, bilayer, trilayer and five-layer. The solid lines are the exponential fitting curves.

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signicantly decreased when the number of layers increases. Consequently, this parameter, measured by OPMP, is extremely important for optoelectronic design, especially in the IR and THz range.

Conclusions

The Dirac fermion ultrafast dynamics in the vicinity of the Fermi surface in monolayer and multilayer graphene are studied using optical pump mid-infrared probe spectroscopy. The Fermi level of graphene with different numbers of layers is clearly identied by the change of sign of DT/T. From the probe energy-dependent relaxation time, the Dirac fermion–phonon coupling strength is obtained as a function of energy near the Fermi surface using the two-temperature model. Additionally, the energy-resolved transient transmissivity spectra disclose that the rate of energy loss for Dirac fermions at room temperature is strongly dependent on the number of layers and it is signicantly reduced as the number of layers in graphene increases.

Acknowledgements

This work was supported by the Ministry of Science and Tech-nology, Taiwan, Republic of China (Contract no. 101-2112-M-009-016-MY2, 103-2923-M-009-001-MY3, and 102-2112-M-009-006-MY3), the Grant MOE ATU Program at NCTU.

Notes and references

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C. Lian, K. Tahy and H. Xing, Nano Lett., 2010,10, 1308. 10 K. M. Dani, J. Lee, R. Sharma, A. D. Mohite, C. M. Galande,

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數據

Fig. 1 shows the optical pump mid-infrared probe spectra for all of the samples in this study
Fig. 4 The time-dependent first moment as a function of the delay time for various graphene samples with monolayer, bilayer, trilayer and five-layer

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