Graphene-to-Substrate Energy Transfer through Out-of-Plane

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Graphene-to-Substrate Energy Transfer through Out-of-Plane Longitudinal Acoustic Phonons I-Ju Chen,† Pierre-Adrien Mante,† Cheng-Kai Chang,‡ Szu-Chi Yang,† Hui-Yuan Chen,† Yu-Ru Huang,† Li-Chyong Chen,‡ Kuei-Hsien Chen,‡,§ Vitalyi Gusev,∥ and Chi-Kuang Sun*,†,⊥,¶ †

Department of Electrical Engineering and GraduateInstitute of Photonics and Optoelectronics, ‡Center for Condensed Matter Sciences, National Taiwan University Taipei 10617, Taiwan § Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan ∥ Laboratoire d’Acoustique, LAUM, UMR No. 6613 associée au CNRS, LUNAM Université, Université du Maine, Avenue Olivier Messiaen, 72085 Le Mans, France ⊥ Molecular Imaging Center, National Taiwan University Taipei 10617, Taiwan ¶ Institute of Physics and Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan S Supporting Information *

ABSTRACT: Practically, graphene is often deposited on substrates. Given the major substrate-induced modification of properties and considerable energy transfer at the interface, the graphene−substrate interaction has been widely discussed. However, the proposed mechanisms were restricted to the two-dimensional (2D) plane and interface, while the energy conduction in the third dimension is hardly considered. Herein, we disclose the transfer of energy perpendicular to the interface of the combined system of the 2D graphene and the 3D base. More precisely, our observation of the energy dissipation of optically excited graphene via emitting out-ofplane longitudinal acoustic phonon into the substrate is presented. By applying nanoultrasonic spectroscopy with a piezoelectric nanolayer embedded in the substrate, we found that under photoexcitation by a femtosecond laser pulse graphene can emit longitudinal coherent acoustic phonons (CAPs) with frequencies over 1 THz into the substrate. In addition, the waveform of the CAP pulse infers that the photocarriers and sudden lattice heating in graphene caused modification of graphene−substrate bond and consequently generated longitudinal acoustic phonons in the substrate. The direct observation of this unexplored grapheneto-substrate vertical energy transfer channel can bring new insights into the understanding of the energy dissipation and limited transport properties of supported graphene. KEYWORDS: Graphene, THz coherent acoustic phonon, substrate effect, picosecond ultrasonics, nanoultrasonic spectroscopy

T

directly, different pictures for the role played by the substrate arise.12−17 Its effects on different phonon modes range from strong12,14,16,17 to negligible.13 To account for the differences, a clear understanding of the graphene−substrate interaction is demanded. Here, we focus on investigating the energy transfer of graphene under femtosecond laser excitation in the third dimension in the femtosecond to picosecond regime, when graphene and the supporting substrates can be highly out-ofequilibrium. Understanding the diverse coupling mechanisms between graphene and the adjacent materials is essential to control and improve its properties. In this Letter, we present our observation of the optically excited graphene dissipating energy in the perpendicular direction through generating longitudinal coherent acoustic

he properties of atomically thin materials like graphene are strongly influenced by interactions with the adjacent materials due to their high surface-to-volume nature. For instance, the presence of a substrate can induce gap opening in graphene’s electronic structure,1 create ripples,2 modify the phonon dispersion,3 the thermal expansion coefficient4 as well as the transport properties.3,5−8 For example, when graphene was placed on a typical substrate SiO2 a decrease of the charge mobility6 by a factor of 10 and of the thermal conductivity by a factor of 5 was observed.5 On the other hand, the graphene− substrate interplay also directly determines the heat spread in graphene-based devices.9−11 In the combined system of the 2D graphene and the 3D base, energy conduction in the third dimension emerge. Even though the graphene−substrate interactions have been widely investigated, the measurements particularly focused on the 2D plane and interface,3,5−10 leaving the vertical energy conduction in the far field unexplored. Additionally, when graphene phonon modes are observed © 2014 American Chemical Society

Received: November 20, 2013 Revised: January 24, 2014 Published: February 21, 2014 1317

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Figure 1. (a) Graphene on SiO2/Si was studied by picosecond ultrasonics with 800 nm pump lights and 400 nm probe lights in a reflection scheme. (b) In the measured transient reflection difference (ΔR) data, backward-Brillouin-oscillations in SiO2 and Si at 46 GHz (denoted by the red dashed line) and 224 GHz (denoted by the blue dashed line) (c), respectively, are observed. The orange arrow near 48.7 ps indicates the time when the graphene-generated acoustic pulse front entered the Si layer. (d) Graphene on GaN/InGaN SQW was studied by picosecond ultrasonics and nanoultrasonic spectroscopy under the same setup but in a transmission scheme. (e) In the measured transient differential transmission (ΔT/T) (black solid), a backward-Brillouin-oscillation at 103 GHz (f) is be observed. The green arrow near 4.8 ps indicates the time when the graphenegenerated acoustic pulse arrives at the SQW. Inset: the ΔT/T trace of graphene on GaN/InGaN-SQW measured by 800 nm degenerate femtosecond absorption spectroscopy (see Supporting Information).

phonons (CAPs) in the substrate. We first develop, based on classical mechanics, a model to describe the generation of longitudinal CAPs by a supported two-dimensional material like supported graphene. We then apply picosecond ultrasonics and nanoultrasonic spectroscopy to study supported graphene. With the picosecond ultrasonics approach, by observing the optical signal, we demonstrate that the optically excited graphene indeed generates out-of-plane longitudinal acoustic phonons into its substrate. Afterward, the application of nanoultrasonic spectroscopy with a piezoelectric nanolayer buried in the substrate enables temporally resolving the waveform of the phonon pulses. Thereby, the microscopic generation mechanism is unraveled and the roles of photocarriers and lattice heating are uncovered. Our observation discloses the unexplored energy conduction down into the substrate as well as a carrier−phonon and phonon−phonon scattering mechanism at graphene−substrate interface.

Under ultrahigh frequency optical or electrical excitations, a material is instantly heated and its carriers are driven out-ofequilibrium.11,13,16,17 Femtosecond laser pulses can conveniently be used to study the relaxation of thus excited materials.13,17,19,20 Under its excitation, hot photocarriers and sudden temperature rises are created, and consequently electronic and thermal stresses are established inside the materials, leading to the generation of CAPs.19−23 In the case of thin films on substrates, the stress induces breathing modes (ringing), which launch a compression strain followed by a tensile strain pulse propagating down into the substrates.20,21,23 In monolayer graphene, its single-atomic-layer nature forbids breathing mode in the normal direction. Yet, when graphene is under ultrafast laser excitation, nonequilibrium photocarriers and lattice heating give rise to driving stresses that modify the equilibration between graphene and the substrate. The stress induces ultrafast displacements of graphene and substrate 1318

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surface layers, which then lead to the generation of CAPs in the out-of-plane direction that transmit into the substrate. The driving stress σ(t) composed of both thermal and electronic stress can be represented by σ(t ) = γn(t ) + αΔθ(t )

ηs(t , z) =

−1 mω̅

t

∫−∞ σ(τ)e−(t−τ)(1/τ

loss + 1/ τIB)

sin(ω̅ (t − τ ))dτ (2)

with a normalized resonance frequency ω̅ =

2 ⎛ k β ⎞ k ⎟⎟ − ⎜⎜ − m 2m ⎠ ⎝ 2ρs cs

and a resonance damping time τloss

−1 ⎛ k β ⎞ ⎟⎟ = ⎜⎜ + 2m ⎠ ⎝ 2ρs cs

where m is the graphene layer mass density, cs and ρs are the substrate sound velocity and density, and β is the damping coefficient in the equation of motion. The resonance damping is subject to multiple mechanisms, including the transmission of energy to the substrate longitudinal CAP as discussed in this Letter as well as the loss of energy to the carriers, phonons, and defects of the substrate and graphene (phenomenologically represented by β). In addition, spatial lateral variations of graphene and the substrate (due to localized defects, corrugation, contamination, and so forth) have strong impact on the resonance frequency and phase and would thus give rise to inhomogeneous broadening of the resonance. The thus induced decay of the effective resonance and the observed acoustic signal is described by a phenomenological time constant, τIB. The substrate surface layer, being elastically bonded to graphene, undergoes a resonance with the same frequency and damping time and can be written as us(t, 0) =

1 k /m ρs cs ω̅

t

∫−∞ σ(τ)e−(t−τ)(1/τ

(t − τ ) + φ)dτ

∂z

z cs

) (4)

To investigate the validity of the above hypotheses, picosecond ultrasonics,19,23 and nanoultrasonic spectroscopy24,25 were applied to study graphene deposited on a SiO2/ Si substrate and a wurtzite GaN substrate with an embedded InGaN single quantum well (referred as GaN/InGaN-SQW substrate) (Figure 1a,d). Mode-locked Ti:Sapphire laser (Coherent MIRA 900) pulses with a 76-MHz repetition rate and a 100 fs pulse-width were used in the experiments with one laser beam, the pump, used to excite the material, and another beam, the probe, to study the dynamics of the thus generated GHz−THz coherent phonons. The pump light wavelength was centered at 800 nm to exclusively photoexcite graphene. Yet, for the purpose of investigating phonon generation and propagation, a β-BaB2O4 crystal was used to generate second harmonic light at 400 nm as the probe to enable high detection sensitivity of longitudinal CAPs in the InGaN SQW24−26 and the SiO2/Si substrate.27 The transient transmission or reflection of the probe light was modulated by the CAPs through both backward-Brillouin-scattering and modulating the transmission of the SQW. The pump and probe beam had diameters of around 26 and 20 μm, fluences of 0.43 and 0.084 mJ·cm−2, and were at normal incidence. Considering the transparency of the substrate at the chosen probe wavelength, the transmissivity scheme was adopted for graphene on GaN/InGaN-SQW and the reflectivity scheme was adopted for graphene on SiO2/Si because Si is opaque for 400 nm lights. The graphene samples used in this study were fabricated by chemical vapor deposition (CVD) on copper foil and then transferred to both the SiO2/Si and GaN/InGaN-SQW substrate using PMMA as a carrier. Detailed fabrication procedures and the cleaning method can be found in ref 28. The Raman spectrum of the graphene on SiO2/Si sample was measured to verify that the sample is monolayer graphene with insignificant defects (Supporting Information).28 The SiO2/Si substrate has a 285 nm thick SiO2 layer grown by thermal oxidation of the silicon wafer. The wurtzite GaN/InGaN-SQW substrate consists of a 3 nm thick In0.1Ga0.9N SQW grown by metal−organic-chemical-vapor-deposition (MOCVD) above a 2 μm thick GaN buffer layer on a 300 μm thick sapphire substrate. On top of the InGaN SQW is a 38 nm thick GaN cap layer with a root-mean-square roughness around 1.2 Å on the Ga-terminated GaN(0001) surface. The GaN cap layer is ntype due to unintentional doping. The SiO2/Si substrate is the most common substrates for graphene because it allows visualizing graphene with high contrast29 and is also a typical structure in microelectronics.8 On the other hand, the GaN/ InGaN-SQW substrate was designed to achieve broadband detection of the CAPs. When the CAP pulse propagates across the InGaN nanolayer, the optical signal is modulated through the piezoelectric and quantum-confined-Franz-Keldysh effects.24−26 The 3 nm thick piezoelectric SQW provides a localized acoustic detection sensitivity function that enables detecting the waveform and spectrum of the generated CAPs with a 0.4 ps temporal resolution and ∼1 THz bandwidth.24 Moreover, the formation of graphene-graphite quilts on top of high power AlGaN/GaN transistors was demonstrated to be an efficient alternative heat escape channel that can be used to improve the thermal management in GaN electronic and optoelectronic devices.11 Thereby, understanding of the energy

(1)

where n(t) and Δθ(t) are the photocarrier density and lattice temperature change as functions of delay time (t), and γ and α are parameters that relate n(t) and Δθ(t) to electronic and thermal stresses.19,21 The parameter γ plays a similar role as deformation potential in bulk materials while α is related to the thermal expansion of the bond. Considering supported graphene as a simple harmonic oscillator bonded to an elastic bulk substrate with a force constant k, the displacement of graphene ug and the substrate us can be derived from the onedimensional equation of motion of graphene and the boundary condition at the surface of the elastic substrate (see Supporting Information). From the derivation, ug can be expressed as a convolution between the natural response of the graphene layer and the driving stress, σ(t) ug(t ) =

(

∂us t −

loss + 1/ τIB)

cos(ω̅ (3)

with φ = tan−1[(k/(2ρscs)) − (β/(2m)]/ω̅ ). Finally, due to the substrate’s elastic nature, the displacements of the surface layer should transmit into inner layers and thus give rise to a propagating strain pulse, which can be derived from 1319

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Figure 2. (a) (Upper) After removal of the backward-Brillouin-oscillation background, the measured ΔT/T signal (black solid line) reveals the waveform of the longitudinal CAP pulse. The blue dashed line, a damped sine at the 240 GHz frequency of the resonance, provides a reference to the eye to distinguish the nonresonant abrupt change in the beginning of the acoustic pulse and the damped-oscillating part that follows. (lower) The simulation result based on the simple harmonic oscillator model (detailed equations see Supporting Information) with (b) the thermal (orange) and electronic (green) driving stresses, which were constructed with the information given by the ultrafast carrier and phonon dynamics studies (see Supporting Information), and fitting parameters α and γ. The negative and positive sign of the stresses were used in the derivation to represent attractive and repulsive forces between graphene and the substrate surface respectively. (c) The Fourier spectrum of the measured ΔT/T signal in (a), representing the spectrum of the acoustic pulse.

condition (Figure 1d) in the measured transient differential transmission (ΔT/T) trace (Figure 1e) an oscillation at 103 GHz was observed (Figure 1f). The frequency is consistent with the backward-Brillouin-oscillation frequency calculated with c = 7.95 nm·ps−1 and n = 2.56 for GaN.24 Observation of these oscillations affirm the emission of out-of-plane longitudinal-acoustic-phonons in the substrate by graphene optically excited with a femtosecond laser pulse. It not only discloses a distinct channel of substrate-assisted energy relaxation in supported graphene but also manifests the energy conduction in the third dimension in the combined system. The effect of substrate-assisted energy relaxation in supported graphene has been seen in different studies.9,12,16,17,31 For instance, the optical phonon lifetime of supported graphene has been universally observed to be shorter than suspended graphene due to substrate-assisted energy relaxation.16,17,31 Gao et al. observed a shorter optical phonon lifetime 1.2 ps for graphene supported by SiO2 compared to suspended graphene 1.8 ps.17 As for the graphene on GaN/ InGaN-SQW sample studied in this letter, an optical phonon lifetime 1.15 ± 0.15 ps was deduced from the femtosecond absorption spectroscopy measurement (Figure 1e inset) (Supporting Information). It was significantly shorter than the literature value 1.8 ps for suspended graphene17 and the calculated intrinsic lifetime31 2.65 ps, indicating that the GaN substrate provided considerable energy relaxation channels. The backward-Brillouin-oscillations in Figure 1b,e directly reveal a pathway of SiO2- and GaN-substrate-assisted relaxation of optically excited graphene, through coupling to the substrate longitudinal-acoustic-phonons. At the expected arrival time of the CAP pulse front at the SQW, 4.8 ps, a feature is observed in Figure 1e. It corresponds

transfer mechanism at the graphene−GaN and graphene−SiO2 interface would have important implications on a diversity of devices. In the transient reflection difference (ΔR) data of graphene on SiO2/Si measured by the picosecond ultrasonics technique (Figure 1b), a 46 GHz oscillation between 0 to 48.7 ps time delay (t) and a 224 GHz oscillation after 48.7 ps are observed (Figure 1c). The two oscillations have frequencies agreeing well with the expected frequencies of backward-Brillouin-scattering between the probe light (with wavelength λ) and the longitudinal-acoustic-phonons in SiO2 and Si, given by 2nc/ λ,19,23 with refractive index n and longitudinal-acoustic-phonon velocity c of the material. The ΔR signal not only unravels the generation of longitudinal CAPs but also enables temporally tracking the flow of the CAP pulse. After the pump excitation at t = 0, the CAPs were generated and transmitted into the SiO2 layer. Consequently, a backward-Brillouin-oscillation in ΔR at 46 GHz, close to the value calculated with c = 5.85 nm·ps−1 and n = 1.47 found in literature,23 was induced due to acousto-optic interaction. Until 48.7 ps (orange arrow in Figure 1d), when the longitudinal-acoustic-phonons crossed the 285 nm thick SiO2 layer and entered the Si layer, a stronger backwardBrillouin-oscillation at 224 GHz was observed. Once again, the frequency is in good agreement with the value calculated with c = 8.43 nm·ps−1 and n = 5.95 in Si found in the literature.23 Yet, because Si is not transparent at 400 nm, the observed backward-Brillouin-oscillation is damped. The damping time corresponds to the traveling time of the longitudinal CAP pulse across the penetration depth of 400 nm lights in Si (17.6 ps × 8.43 nm·ps−1 = 148 nm), as expected from the absorption coefficient in literature30 6.74−9.52 × 104 cm−1. Similarly, when graphene on GaN/InGaN-SQW was studied under the same 1320

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Figure 3. The schematic representations that denote the motions of the graphene layer and the substrate surface layers at different time delays after laser pulse excitations. (a) Before laser excitations, graphene and the substrate are at their equilibrium positions. (b) The pump laser excitation generates photocarriers in graphene, which induce an attraction force between graphene and the substrate surface layer, generating a dilatation strain in the substrate. (c) After the photocarriers relax, hot phonons are generated, causing an expansion of the graphene−substrate bond, which gives rise to the compressive strain in the substrate. (d) Being disturbed by the stresses, graphene and the substrate surface layer begin to resonate at the normalized resonance frequency of the bond ω̅ until they are damped out. The resonance gives rise to the damped sinusoidal waveform of the longitudinal CAP pulse. Owing to the elastic nature of the substrate, the displacements of the surface layer transmit into the inner layers and consequently generate the propagating strain pulse.

to the detection of the CAP pulse through the piezoelectric and quantum-confined-Franz-Keldysh effects in the SQW.24−26 By subtracting the backward-Brillouin-oscillation background, the acoustic pulse waveform is revealed (Figure 2a). A study of the SQW sensitivity function (see Supporting Information) reveals that compressive strains induce positive ΔT/T, while tensile strains induce negative ΔT/T in the SQW. Thereby, the ΔT/T signal in Figure 2a implies that over the excited area, a succession of dilatation and compression strains were launched into the substrate. Similar CAP pulses can be generated by exciting breathing modes of thin-film acoustic transducers deposited on bulk materials,20,21,23 however, such modes do not exist in monolayer graphene. The damped-oscillating strain pulse can therefore only be induced by the ultrafast displacements and resonance of graphene and the substrate surface layer, as proposed in our derivation. Compared to the main frequency of the oscillation (denoted by blue dashed line in Figure 2a), the beginning of the acoustic pulse undergoes a faster change. This nonresonant signal reflects the motions of graphene and the substrate surface layer near t = 0, which follow the features of the driving stresses. The initial waveform is constituted by an abrupt tensile dip (green arrow in Figure 2a). According to the ultrafast carrier dynamics study (ref 17 and Supporting Information), the lattice temperature rises with a time constant of around 1 ps, therefore, this leading dilatation can only be attributed to the electronic stress. The tensile dip is followed by a bigger compression (orange arrow), which is also faster than the resonance and can be attributed to the temperature increase occurring between 0.5 and 2 ps (see refs 17 and 31, and Supporting Information). Thus, the electronic and thermal stress each plays a considerable role in generating the acoustic pulse. The acoustic pulse waveform is well simulated by the simple harmonic oscillator model we derived (Figure 2a) with σ(t) shown in Figure 2b, where n(t) and Δθ(t) were extrapolated from the ultrafast carrier dynamics measurement (Supporting Information) and γ and α were fitting parameters. Additional fitting parameters include the damping terms and the force constant k. The carrier dynamics measurement of the same sample indicated that within 500 fs after the pump excitation energies still mostly resided in the photocarriers (see Supporting

Information), therefore the electronic stress was the primary driving stress. The initial tensile dip (green arrow) of the acoustic pulse indicates that an attraction force was induced between graphene and the substrate surface layer, which caused contraction of the graphene−substrate bond and generation of a dilatation strain in the substrate (Figure 3b). This photocarrier-induced attraction force can be understood by considering the electrostatics force between graphene and the substrate. Because of band bending, a high density of holes accumulates near the n-type GaN surface.32 Under the effect of the surrounding charges, the electrons in π and π* bands of graphene are subject to the electrostatic force and become polarized.33 Consequently, when photoexcitations generated carriers with high kinetic energies into the π and π* bands, the charged GaN surface created an even stronger polarization and drew the graphene layer and the substrate surface layer toward each other. After 500 fs, while the electronic temperature decreased, the lattice temperature rose and a compressive signal is observed in Figure 2a (orange arrow). This observation suggests that the graphene lattice heating caused graphene− substrate bond expansion (Figure 3c). Because of the opposite natures of the electronic and thermal stresses, the graphene− substrate bond underwent a sudden contraction followed by an expansion, thus launching the initial sharp phonon pulse into the substrate, contributing to frequency components up to more than 1 THz (Figure 2c). The disturbed graphene and substrate surface layers were then prompted to resonate until they were damped out (Figure 3d), which gave rise to the main 240 ± 40 GHz frequency in the spectrum and dampedoscillating waveform of the strain pulse. The graphene−GaN force constant k obtained by comparing the experimental trace with the simulation, considering m as graphene-mass-density34 0.76 × 10−6 kg·m−2, is 14.6 ± 0.2 eV· nm−4, of the same order as but smaller than the reported graphene-SiO2 force constant35 56 eV.nm−4. Yet, unintentional adsorptions are commonly found on graphene exposed to air.36 Underestimating the layer’s mass density leads to a lower estimated k value, therefore, the value obtained here sets the lower bound for the graphene-GaN force constant. With the extracted k, the damping time, given by τ = 2csρs/k if only coupling to substrate longitudinal CAPs is considered, is ∼40 ps. However, experimentally, a 3.5 ps damping time was 1321

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layer graphene.12,13 Lui et al. observed,12 through combination Raman scattering, the layer-breathing mode in few-layer graphene. Through comparing suspended and supported bilayer graphene, Lui et al. found that the substrate induced substantial damping of these phonon modes, especially those involving out-of-plane layer displacements, yet, the nature of the coupling with substrate remain undetermined.12 Our discovery, by studying monolayer graphene, that out-of-plane displacements of graphene couple to substrate longitudinalacoustic-phonon directly identifies one origin of the substrateinduced damping they observed. In a different study, Boschetto et al. observed13 with femtosecond pump−probe technique, coherent interlayer shearing modes of few-layer graphene in real time and found no significant substrate effect on the frequency. Despite the similarity between the experimental technique used by Boschetto et al. and us, the results are substantially different. The interlayer shearing mode observed in ref 13, by definition, does not exist in monolayer graphene, and contrarily to that mode we excited vertical displacements of graphene. Moreover, in our experiment the detection was performed in the substrate or in the SQW. In our experimental scheme, the detection was designed to be spatially separated from the excitation in graphene to improve the observation of energies transmitted into the substrate. Our results consequently demonstrated that the out-of-plane vibrational energy of graphene was vertically transferred into the substrate. On the other hand, Boschetto et al. observed the modulation of the optical dielectric function of the few-layer graphene induced by their own vibrations.13 From their result, the shearing mode frequency showed insensitivity to the external environment, nevertheless they suggested that for strongly bonded graphene−substrate, changes could be observed.13 Yet, the substrate effect on the damping time, which was left undiscussed, could provide implications on the transmission of shearing mode vibrational energy to the substrate. Jointly, all these results form an increasingly complete picture of how adjacent materials influence phonon dynamics in graphene and provide critical information for future applications of supported two-dimensional materials. In summary, we observed the generation of substrate longitudinal acoustic phonons by graphene under pulsed-laser excitations, revealing an unexplored energy leakage channel at graphene−substrate interfaces and energy conduction in the third dimension of the combined system of the 2D graphene and 3D substrate. For graphene on GaN/InGaN-SQW, the piezoelectric nanolayer allows retrieving the waveform and spectrum of the longitudinal CAP pulse, and the generation mechanism was studied in detail. Interestingly, our study indicates that both the photocarriers and the temperature increases in graphene contribute to the CAP generation. It implies that both graphene carriers and phonons scatter with substrate out-of-plane longitudinal acoustic phonons and thereby pose a limitation on the thermal and electrical transport properties of supported graphene.

observed, reflecting that the resonance damping resulted from complex effects. The vibrational energy could dissipate through coupling to graphene’s and substrates’ carriers, phonons, ripples, contaminations, and defects.37 In addition, the localized defects and roughness on GaN surface, together with graphene’s corrugation, caused lateral inhomogeneity of the graphene-substrate bonding and can contribute to the decay of the observed signal. The uncertainty of the relative importance of the energy dissipation effect and inhomogeneous broadening on the signal decay results in uncertainties in fitting parameters k, γ, and α. Via deconvolving the signal in Figure 2a with the sensitivity function, a peak strain amplitude of 2.2 × 10−5 under a 0.43 mJ· cm−2 pump fluence was obtained. The strain amplitude generated by supported graphene on GaN per unit absorbed energy was around 5 times smaller than by a 3 nm Au film deposited on the same substrate. We then estimated the electronic and thermal stresses peak amplitude under current pump intensity to be 12.5 ± 0.1 and 12.8 ± 0.1 MPa respectively. By reconstructing n(t) and Δθ(t) following the ultrafast carrier dynamics measurement and graphene parameters from literatures (Supporting Information), γ = −0.85 ± 0.11 × 10−10 Pa·m2 and α = 0.23 ± 0.02 MPa·K−1 were extrapolated for graphene on GaN. Considering 0.335 nm graphene thickness,5 the γ value is equivalent to 0.18 ± 0.02 eV. In addition, our analysis unravels that the graphene−GaN bond has contracted and expanded up to 1.7 and 8.4 picometer, predominantly owing to graphene displacements. Maximum displacements of the GaN surface layer were found to be only 0.049 picometer toward and 0.110 picometer away from graphene, respectively. Our observations bring new insights on the scattering of graphene electrons and phonons with substrate phonons especially in the low temperature limit, where acoustic phonons become predominant. The discrepancy between the calculated electron−phonon coupling for transverse and longitudinal acoustic phonons, and the experimentally measured deformation potential9,18,34 suggests undiscovered channels for electron-acoustic-phonon scattering. By incorporating the coupling to substrate longitudinal-acoustic-phonons, a more complete picture of the substrate-limited electrical transport properties can be obtained. On the other hand, scattering of graphene phonons, mainly ZA modes, with the substrate phonons and defects was demonstrated to cause severe phonon leakage at the interface and thus reduced the in-plane thermal conductivity.5 Here, we observed directly the coupling of graphene phonons to longitudinal-acoustic-phonons in the SiO2 and GaN substrate. Our design of the GaN/InGaN-SQW substrate demonstrates a method to quantitatively analyze the coupling strength and allow a better understanding of the phonon−phonon scattering process at the graphene−substrate interface that is essential for heat spread issues in graphenebased devices and for the control of the in-plane thermal conductivity in supported graphene. Additionally, the graphene−substrate bonding strength and the displacement amplitude that reflect the structure stability under ultrafast modulations are discussed, providing essential parameters for graphene-based devices including resonators and NEMS.38,39 Finally, the observation can lead to the application of graphene as a simple-to-use, stamplike opto-acoustic transducer for nanoacoustic imaging and sensing. It is also interesting to compare the result of our study of monolayer graphene with the phonon modes reported in few-

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ASSOCIATED CONTENT

S Supporting Information *

The derivation of the displacements of graphene and the substrate surface layers, the derivation of the strain pulse, the carrier dynamics of graphene on GaN/InGaN single-quantumwell substrate, the time-dependent photocarrier density and lattice temperature rise, the Raman spectrum of graphene on SiO2/Si, the detection sensitivity function of the InGaN 1322

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piezoelectric nanolayer. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: (886-2) 33665085. Fax: (886-2) 33663614. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Bluestone Global Tech for providing the samples as well as its characterization with the Raman spectroscopy and Yun-Wen Chen and Jer-Lai Kuo for discussion about the graphene−GaN interface. This work was sponsored by the National Science Council of Taiwan, R.O.C., under Grant 1012120-M-02-005.

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dx.doi.org/10.1021/nl404297r | Nano Lett. 2014, 14, 1317−1323