Study of the Substrate-Induced Strain of As-Grown Graphene on Cu

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Study of the Substrate-Induced Strain of the As-Grown Graphene on Cu(100) Using Temperature-Dependent Raman Spectroscopy: Estimating the Mode-Gruneisen Parameter with Temperature Ya-Rong Lee, Jian-Xiang Huang, Jiing-Chyuan Lin, and Jia-Ren Lee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b08170 • Publication Date (Web): 19 Nov 2017 Downloaded from http://pubs.acs.org on November 20, 2017

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The Journal of Physical Chemistry

Study of the Substrate-Induced Strain of the As-Grown Graphene on Cu(100) Using Temperature-Dependent Raman Spectroscopy: Estimating the Mode-Gruneisen Parameter with Temperature Ya-Rong Lee,† Jian-Xiang Huang,‡ Jiing-Chyuan Lin,*,† and Jia-Ren Lee*,‡

†

Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan

‡

Department of Physics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan

∗Corresponding author: E-mail: Jia-Ren Lee, [email protected] Jiing-Chyuan Lin, [email protected] 1

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ABSTRACT The strategy of using the thermal expansion of copper single crystal can provide an approach of homogenous strain along the basal plane to study the strain characteristic of graphene with temperature. Using an in-situ Raman measurement under a ultra-high vacuum (UHV) environment, the ability to remove contaminations allowed the direct observation of the strain property in as-grown chemical vapor deposition (CVD)-graphene with temperature on a Cu(100) substrate. In this study, the strain coefficients of G and G’ band with temperature were investigated from the in-situ temperature-dependent Raman spectra of the as-grown CVD-graphene on the single crystal of Cu(100) under UHV. By eliminating the minor contributions of the lattice expansion and anharmonic phonon scattering effects, we were able to estimate the strain coefficient of the G and G’ bands of graphene over a wide temperature from 100 K to 800 K. Based on the strain coefficients and the correlation map of the G- and G’-band frequencies, we made a reasonable presumption that a uniaxial-like strain manner exhibits in graphene on Cu(100). For a correction to magnitude of the uniaxial strain, the mode-Gruneisen parameters at room temperature are estimated about ~1.8 for the G bands, in reasonable agreement of the literature values. This strategy made it possible to estimate the temperature-dependent mode-Gruneisen parameters of the G and G’ bands for the first time.

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INTRODUCTION Strain is an important factor in the development of graphene-based optoelectronics and photonics devices, due to its capacity to destroy lattice symmetry and induce changes in the electronic band structure of material.1-3 Any difference in the thermal expansion coefficients (TEC) between graphene and the underlying substrate or overlayer invariably introduces an unwanted strain into the graphene film and produce a significant influence on both the electronic and phononic properties of graphene.4-6 The mode-Gruneisen parameter is an important fundamental parameter used to describe the sensitivity of the phonon frequencies to strain by quantifying changes in the frequency of the vibration modes as the volume of the unit cell is varied.2, 7 Theoretically, mode-dependent Gruneisen parameters can be calculated for a variety of phonon branches corresponding to different q-values.8-9 Experimentally, the mode-Gruneisen parameters

of

phonon

frequencies

can

be

estimated

from

the

pressure-

or

temperature-dependence of Raman spectra with the isothermal bulk modulus and thermal expansion coefficient, respectively.10

For graphene, the mode-Gruneisen parameters of the G and G’ bands (γg and γg’) have previously been determined at room temperature by applying stress with various designs.2-3, 7, 11-20

Unfortunately, there have been significant discrepancies among the reported values (γg

3



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~1.8-2.4 and γg’~2.4-3.8). Furthermore, to the best of our knowledge, no results have yet been published on the temperature dependence of mode-Gruneisen parameters pertaining to graphene. Only a related paper reported the mean Gruneisen parameter for graphite based on the measurements of the TEC in the temperature range of 20-273 K.21 The temperature-induced shift in the phonon frequency of graphene on substrate can be attributed to phonon scattering, changes in lattice structure under thermal expansion, and substrate-induced strain from a mismatch in the TEC between 2D material and substrate or overlayer.4-6, 10, 22-29 Therefore, how to disentangle the substrate-induced strain and the thermal-expansion-related band-structure change response from the temperature dependence of the Raman spectra of graphene is an interesting problem. Graphene has a negative TEC8, 30 ; however, there have been wide discrepancies theoretical8, 30-31 and experimental4, 22-23, 25, 27 TEC values of graphene with regard to magnitude as well as sign. For example, Mounet et al. used the ab initio density-functional theory (DFT) at the GGA-PBE level in conjunction with the quasiharmonic approximation to calculate the TEC of graphene. They reported negative values of much smaller magnitude in the temperature range of 0-1500 K.8 Sevik30 obtained similar results based on first principles using quasiharmonic approximation. However, Magnin et al. proposed the different TEC behaviors using different model potentials based on fully anharmonic Monte Carlo simulations.31

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Experimentally, Bao et al. obtained negative values for the TEC at low temperatures with a sign change approximation 350 K for graphene suspended across Si/SiO2 trenches by using the SEM measurement4 in a temperature range of 300-400 K. By measuring Raman scattering and carefully excluding the substrate effects, Yoon et al.22 estimated negative values for the TEC of exfoliated graphene on SiO2/Si within the temperature range of 200-400 K with no evidence for a sign change up to 400 K. Using measurements of Raman scattering, Wei et al.27 determined that the TEC of exfoliated graphene on Boron nitride (BN) is negative across a temperature range of 300-1200 K, which is in agreement with the theoretical results reported by Mounet et al.8 Recently, Linas et al.25 studied the TEC of graphene based on the Raman shift in the G band of CVD graphene/SiN/Si in the temperature range of 150-800 K under UHV or Argon (Ar) environment. They determined that the TEC of graphene is more likely to be positive above room temperature after correcting the measured Raman signal for the mismatch in the TEC of the substrate.32 Just recently, Shaina et al. estimated the TEC of the as-grown CVD graphene on copper foil over a temperature range of 90-300 K by Raman spectroscopy.23 They found that the TEC is negative (average value, -3.75x10-6 K-1) at temperatures of 100-300K and it approaches close to zero for T< 150 K, after considering a uniaxial strain profile and incorporating the temperature-dependent Gruneisen parameter of graphite corrections.21

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Due to a lack of experimental or theoretical results pertaining to the temperature dependence of the Gruneisen parameter of graphene, the TEC values in experiments have been estimated from the temperature-dependent Raman spectra under the assumption that the mode-Gruneisen parameter is temperature-independent.22-23 However, the mode-Gruneisen parameter may not be a constant with temperature, depending on the change of phonon shift with lattice change.21 Therefore, in this study, we used the thermal expansion of copper single crystal providing an approach of homogenous strain along the basal plane to study the strain characteristic of graphene with temperature. Raman spectroscopy is widely used in the study of TEC and strain in material, since it is a non-destructive and convenient tool to characterize the structure, symmetries, and optical phonon behavior. In this study, we conducted comprehensive analysis of the temperature-dependent phonons shift of as-grown CVD-graphene on Cu(100) over a wide temperature range from 100 to 850 K in the in-situ Raman measurement under a UHV environment. Using the correlation map of the G’-band frequency versus that of the G-band frequency, we observed a uniaxial-like strain manner in the as-grown CVD graphene on Cu(100). On the other hand, we also analyzed the frequency shifts in the G band as a function of temperature in accordance with the procedure laid out by Yoon et al.22 to disentangle the contribution of the substrate induced-strain. The fact that the TEC of copper33 far excess that of graphene,8, 31 enable us to estimate more exactly the temperature-dependent changes in the strain 6


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coefficient of graphene. In addition, in order to rule out the wide discrepancy of the calculated TEC, we also extracted the strain coefficient of G band with temperature range 100-800 K by comparing our data with the result of CVD graphene on SiN under UHV reported by Linas et al.25 Moreover, we also estimated the temperature-dependent mode-Gruneisen parameters of the G and G’ bands after considering a correction to magnitude of the uniaxial-like strain.

EXPERIMENTAL SECTION Graphene growth. The CVD graphene samples grown on a single crystal Cu(100) were prepared in a UHV chamber with a base pressure of ~4x10-10 Torr, as shown in Figure S1. Briefly, the Cu(100) surface was cleaned via several cycles of Ar-ion sputtering and annealing until a sharp (1x1) Low energy electron diffraction (LEED) pattern emerged. CVD-graphene samples were then deposited onto the heated Cu substrate by dosing the different precursors of m-diiodobenzene (mDIB), 3,5- and 2,4-dibromopydidine (3,5-DBP and 2,4-DBP) at a pressure of 1x10-8 ~ 2x10-7 Torr for 1~5 min. During growth, the Cu(100) substrate temperature was maintained at ~1100 K, except when studying the effect of growth temperature. The CVD-graphene/Cu(100) samples were cooled to 100 K before performing Raman measurements. The growth procedure is detailed in Supporting Information.

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In situ Raman measurement: In-situ Raman measurements were carried out in a home-built UHV chamber with a routine base pressure of ~4×10-10 Torr using a 514.5 nm Ar-ion laser or 532 nm diode laser as the excitation light source. More detailed description has been reported elsewhere.34-35 A laser-line filter was used to eliminate plasma emission lines adjunct. The laser beam was focused using a cylindrical lens and impinged, via a glass viewport, to the sample with an incident angle of 65°. The scattered radiation light, collected with a lens (f-number = 1), was sent through a long-pass filter to eliminate the excitation radiation and then to a 30-cm monochromator (1200 gr/mm grating, Horiba, TRIAX 320) equipped with a liquid-nitrogen cooled charge-coupled device for spectral analysis. The resulting spectral resolution and reproducibility were 8 and 1 cm-1, respectively. The laser power was kept ~45 mW, and the size of laser spot on the crystal was ~ 100 µm. Therefore, an average Raman signals across the laser spot area on Cu(100) were measured. The as-required Raman spectra of the as-grown graphene did not present a flat background due to the photoluminescence of copper, as shown in Figure S2. Thus, the Raman spectra were obtained via background subtraction. A schematic description of the setup is presented in the Supporting Information.

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RESULTS AND DISCUSSION Fabrication and characterization of CVD-graphene. Figure 1a presents the Raman spectra of mDIB-based graphene grown directly on Cu(100) at four growth temperatures, measured at 100 K. For the growth temperature at 1000 K, the Raman feature shows a relatively large D band (~ 1373 cm-1) and a smaller G’ band (~ 2740 cm-1), indicating the graphene contains highly defective and/or disorderly structures. As the temperature increases to 1100 K, the signal of the D band of graphene nearly disappears and the intensity of the G’ band increases with respect to that of the G band (~ 1600 cm-1), indicating the formation of high-quality graphene. Meanwhile, as shown in Figure 1b, the LEED pattern comprises 12 sharp spots and 12 arcs, indicative of a polycrystalline structure with large range of in-plane orientations along some directions. The average lattice unit of the CVD-graphene was estimated at approximately 0.23±0.02 nm, which is slightly larger than a previously reported value of 0.21 nm obtained from scanning tunneling microscopy (STM) average line profile.36 Nonetheless, the average lattice unit of the CVD-graphene was still smaller than the normal lattice constant ~ 0.246 nm,37 which indicates an in-plane thermal contraction exhibits on the graphene grown directly on Cu(100). The similar results have also been obtained from precursors of pyridine derivatives, 3,5- and 2,4-DBP.

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(a)

(b)

Figure 1. (a) The Raman spectra of mDIB-based graphene features on Cu(100) at the growth temperature 850 , 900, 1000, and 1100K. (b) The LEED pattern of the DBP-based graphene film grown on Cu(100) at 1100 K was in situ measured with the electron energy of 110 eV. The sharp spots are the first-order diffraction from the Cu(100) surface. The faint ring at the same radius is corresponding to graphene.

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According to the changes in the Raman spectra as a function of exposure at the growth temperature~1100 K, we found that the G (G’) signals saturated quickly around ~30 L (1L=1 Langmuir =1x10-6 Torr sec), as shown in Figure S3. In addition, we observed no significant variations in any of the Raman features including the frequency, shape and the intensity ratio of the G’ band to G band (IG’/IG), with the exception of a small D band appearing after the saturation of G (G’) signals. These observations suggest that the growth of CVD-graphene grown on Cu(100) is self-limiting in the proposed UHV-CVD system. On the other hand, a single Lorentzian shape with a FWHM of ~ 50 cm-1 in the G’ band and an intensity ratio of IG’/IG ~0.9 were observed in the coupled CVD-graphene/Cu(100) system (see Figure S3). The feature of a single Lorentzian shape for the blueshift G’ band with full width half maximum (FWHM) of ~ 50 cm-1 is similar to that of turbostratic graphene, i.e., graphene layers of arbitrary stacking.38 The G’ band is known to be strongly influenced by the stacking of layers,38-39 excitation wavelength39 and the underlying substrate,40-41 which can alter the intensity ratio of IG’/IG. Lu et al. reported that the Raman features of the coupled as-grown monolayer graphene on Cu film can lead to the misidentification of the graphene as a bi-layer or few-layer structure prior to the decoupling or transfer of as-grown graphene.41 They found that the G’ FWHM narrows from a coupled monolayer CVD-graphene/Cu(100) system to one decoupled by a cuprous oxide interfacial-layer ( 43 to 29 cm-1 ), and the intensity ratio of IG’/IG increases from ~1.6 to 2.9 using 11



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an excitation wavelength of 473 nm.41 In the Raman spectrum of a coupled monolayer CVD-graphene/Cu(100) system fabricated under a cold wall UHV condition, it was observed that the width of the G’ band (~40 cm-1) is wider and the ratio of IG’/IG (~1.6) is lower than that of monolayer CVD-graphene/Cu(111) (~30 cm-1 and ~3.3, respectively).42-43 Those results clearly indicate that the underlying copper substrate can have a powerful influence on the width of the G’ band and the IG’/IG ratio.

On the other hand, few-layer graphene (FLG) prepared on

copper foils under atmospheric pressure CVD environment presented an IG’/IG ratio of ~0.5 with G’ FWHM of ~ 45 cm-1 at an excitation wavelength 532nm.44 In this study, the in situ Raman measurement of the coupled as-grown graphene on Cu(100) was averaged over an area of approximately ~100µm. Thus, our observations of the self-limited growth in our UHV-CVD growth system and the ratio of IG’/IG ~0.9 are suggestive of monolayer graphene with small regions of FLG on Cu(100) while the exposure is less than ~ 30 L. To further corroborate the results, we examine the growth of the mDIB-based CVD graphene on Cu(100) using STM. (see Supporting Information and Figure S4) According to the results of the STM study, the Cu(100) surface covered fully by bright protrusions with a size of ~1.2 nm at the deposition temperature ~1000 K, indicating that the carbon clusters form. It is consistent with the Raman observation which shows a relatively large D and G bands at the growth temperature ~1000K. As deposited onto Cu(100) at ~1080 K, superstructure pattern with the periodicity of 12


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bright protrusions (~0.4~0.5 nm) was observed, similar to that reported by Zhao et al.42 It has been reported that the formation of superstructure caused by interference effects between graphene lattices and the (100) facet of Cu.42 In addition, as increasing the exposure time, a meandering structure of excess carbon on graphene was observed, which is supported by the appearance of the D band shown in Figure S3a. The STM results are consistent with and confirm the finding of the Raman spectra analysis.

Temperature coefficients of the G and G’ band. Numerous studies have sought to acquire the temperature-dependent Raman spectra of graphene;6,

26, 45-49

however, the reported

temperature coefficients of frequencies are inconsistent, ranging from -0.015 to -0.07 cm-1/K for the G band. Moreover, researchers have also observed that an irreversible change of the temperature coefficient of graphene exists before and after the first heating under air, Ar and even under vacuum environments.26, 46-47, 49 Therefore, the in-situ measurement under a UHV environment in this study made it possible to eliminate the contaminations in reexamining the temperature coefficient of the graphene on Cu(100) using temperature-dependent Raman spectroscopy.

Figure 2 shows the temperature dependence of the G and G’ band frequencies of as-grown

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CVD-graphene on Cu(100), measured in the range from 100 K to 850K. (The Raman spectra were shown in Figure S5-S6.) Black (red) color represents the mDIB-based (35DBP-based) graphene grown at ~1100K (~1100 and ~1050 K) and shown individually in Figure S7. Apparently, the trends of the G and G’ bands shift to low frequency with increasing temperature and can be fitted using simple linear lines. A roughly linear form can be derived from the following relation: ω=ω0+χT, where ω0 is the frequency of the G (G’) band when temperature T is extrapolated to 0 K, and χ is the first-order temperature coefficient defining the slope of the dependence. As listed in Table 1, the extracted negative value χ of the G (G’) bands for mDIB-based graphene is -0.044 (-0.074) cm-1/K, as listed in Table 1, which are slightly lower than that of the 3,5- and 2,4-DBP-based graphene (-0.06 cm-1/K for the G band and -0.10 cm-1/K for the G’ band). We repeated the measurements several times to verify the reproducibility of our results. No irreversible shifts in the G and G’ bands were found during the thermal cycles in the temperature range from 100 to 850 K, thereby demonstrating the stability of the CVD-graphene on Cu(100) as well as a good adhesion between the as-grown CVD graphene and the Cu(100) surface.41, 43

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Figure 2. The trends of Raman thermal frequency shift of (a) the G band and (b) the G’ band for CVD-graphene on Cu(100), fabricated with different temperature. Black (red) color represents the mDIB-based (35DBP-based) graphene grown at ~1100K (~1050 and 1100 K).

The reported discrepancies in the Raman shift with temperature may be attributed to the number45, 48 and quality,46, 48-49 of the graphene layers or the type of substrate.24 It may also be due to the interaction between the graphene and the substrates41,

43

and the environment.47

Compared with the literature results, the temperature coefficient of the G band in mDIB-based graphene (-0.044 cm-1/K) is lower than that of the CVD-graphene on copper foil (-0.101 cm-1/K) 15



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reported by Wang et al.,26 and larger than the theoretical32 and experimental24 results obtained from freestanding graphene (~ -0.016 cm-1/K). In regard to the G’ band, the temperature coefficient of the G’ band is approximately 1.67x that of the G band. Moreover, to scrutinize the temperature coefficients of frequency χ in Table 1, we find that the temperature coefficients do not vary considerably, regardless of whether the graphene contained the defect peak. This means the slope is insensitive to the initial number of defects in the film. In addition, we also find the temperature coefficient of the G’ band obtained here is almost twice of that of the D band, as shown in Table 1. However, this contradicts other studies that reported no significant shift in the D peak frequency with changes in temperature from 15-400 K.48, 50 It has been reported that in cases where the substrate-induced strain is dominated, the temperature-dependent frequency shift in the D band is close to that of the G band.11 We therefore presume that the temperature coefficients observed in this study probably depend on the substrate-induced strain due to the large mismatch between the TEC of the graphene and the underlying copper substrate. This issue is detailed below.

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Table 1. Comparison between values of the temperature coefficient of frequency for the D, G, and G’ bands measured at the temperature ranges of 100-850 K for CVD-graphene fabricated by different conditions. χ (cm-1/K)

graphene

D band

G band

G’ band

mDIB

1100K

--

-0.044±0.002

-0.074±0.003

1100K

--

-0.061±0.002

-0.112±0.005

1050K

-0.050±0.005

-0.061±0.002

-0.107±0.005

1000K

-0.060±0.005

-0.063±0.004

-0.121±0.030

1100K

--

-0.048±0.003

-0.087±0.005

1050K

-0.071±0.004

-0.068±0.003

-0.123±0.007

1000K

-0.054±0.005

-0.050±0.003

--

3,5-DBP

2,4-DBP

Correlation map of G’- and G-band frequencies. The ω0 of the G band for the mDIB, 3,5and 2,4-DBP-based graphene samples on Cu(100) (1607, 1622, and 1614 cm-1, respectively) revealed a strong blue shift, compared to the intrinsic value of 1581.6 cm-1 expected for charge17



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and strain-free graphene.51 In general, the blueshifts can be caused by both changes in doping and strain.2-3,

20, 52

Doping effect tend to induce a large shift in the G-band but a far less

significant shift in the G’-band.52 The ratio of the G’-band shift to the G-band shift (△ωg’/△ωg) is reported approximately ~ 0.75.51 With respect to the strain effect, the shift of the G’ band is larger than that of the G band at a ratio of 2.0~2.8.2, 11, 15-17, 20, 51 This make it possible to disentangle contribution of strain and doping through the correlation analysis of the Raman Shift in G and G’ band.51

Using the G-and G’-band frequency (ωg, ωg’) correlation method,51 we analyzed the frequencies of the G and G’ bands to extract the information pertaining to the effects of the strain and doping on the as-grown CVD-graphene on Cu(100). Figure 3a shows the correlation map of the G-and G’-band frequency (ωg, ωg’) in the mDIB-based graphene (measured at ~300 K) and the 3,5- and 2,4 DBP-based graphene (measured at ~250 K), all of which were fabricated at the growth temperature of ~1100 K. Black, red, and green open circles represent the data obtained from the Raman spectra of mDIB-, 3,5DBP- and 2,4DBP-based graphene, respectively. The black solid circles were obtained from the previous reports for a freestanding graphene, which is assumed not to be affected by strain or charge doping.51, 53 However, it is to note that the native strain in graphene can also lead to non-negligible variations in (ωg, ωg’). The red stars were

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obtained from the report on expitaxial graphene on SiC.51 Based on a review of the literature, the ratio (△ωg’/△ωg) of the graphene is expected to lie in the range of 2.02-2.44 under uniaxial stress2, 16-17 and 2.25-2.8 under biaxial stress by experimental11, 15, 20, 51 and theoretical values.2 The black dashed line with a slope of ~2.2 represents a prediction of (ωg, ωg’) for charge-neutral graphene under randomly oriented uniaxial stress, following the same method advocated by Lee et al.51 The red dashed line is an average of experimental values for strain-free graphene with varying hole doping from the Refs.52, 54 The arrows indicate the vectors for strain- (black) and doping- (red) induced movement of (ωg, ωg’), i.e., approximately 0.5% compressive strain and 5x1012 cm-2 hole-doping.51 It is well-known that the G band of the graphene Raman is a first order Raman scattering associated with Brillouin zone center phonons, which means that the G frequency (ωg) does not vary with the excitation wavelength. By contrast, the G’ band of graphene is generated through a second-order process, which results in a highly dispersion behavior.39, 55 Thus, all of the G’ frequencies (ωg’) data shown in Figure 3 were calibrated to account for an excitation wavelength at 532 nm using the excitation energy dispersion factor of ~88 cm-1/eV.39, 55

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(a)

(b)

Figure 3. Correlation between the frequencies of the G and G’ bands (ωg, ωg’): The data were obtained from Raman spectra of mDIB-, 3,5- and 2,4-DBP-based graphene (denoted by black, red, green open circles, respectively) fabricated at 1100 K (a) measured at 250~300 K. (b) measured at 100-850 K. The black solid circles obtained from a freestanding graphene from Ref. data.51, 53 The black and red dashed lines represent the (ωg, ωg’) for charge-neutral graphene under randomly oriented uniaxial stress and for graphene doped with varying density of holes. 12

-2

The black and red arrows represent the vector for 0.5% compressive strain and 5x10 cm hole doping, respectively. 20


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In the (ωg, ωg’) correlation map51, the (ωg, ωg’) upshift (downshift) from the origin along strain lines corresponds to an increase in compressive (tensile) strain.51 The yellow-shaded region indicates a “forbidden area” because the electron and hole doping both lead to increase in ωg. Obviously, the (ωg, ωg’) points of 3,5- and 2,4-DBP-based graphene (red and green open circles) are shifted up and slightly to the right hand side, whereas the (ωg, ωg’) points of the mDIB-based graphene (black open circles) are scattered only along the strain line corresponding to the compressive strain. According to the result of the adsorption and reaction of DBP on Cu(100),56 it indicates that carbon and nitrogen atoms remained on the copper surface even after flashing the surface to 980 K. Meanwhile, the XPS of N1s (C1s) revealed multiple binding energies at 398.2 and 400.4 eV (284.3, 283.4 eV), which are indicative of extended, nitrogen-containing carbon structures on the surface. Therefore, the offset of the (ωg, ωg’) points of 3,5- and 2,4-DBP-based graphene (shifted toward higher ωg values) was presumably considered in terms of the doping effect induced by the insertion of the nitrogen atoms (N) of the pyridine precursor into the graphene. This is similar to the reports in which N-doped CVD graphene was synthesized on Cu using pyridine as a precursor.57-58 It is for this reason that DBP-based graphenes exhibit the effects of slightly doping and considerable compressive strain. According to the correlation of (ωg, ωg’) scattering along the line with a slope of 2.2, it shows the mDIB-based CVD graphene grown on Cu(100) exhibits a compressive strain corresponding to ~ 0.6±0.1%, close to that 21



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reported by Boyd et al.59 for the plasma-enhanced CVD-graphene on the Cu(100) surface (0.5~0.6%). In previous discussions,5, 29 compressive strain has been attributed to the mismatch in the TEC between copper and graphene following a decrease in temperature from the growth temperature down to room temperature.

We went ahead and plotted the correlation map of the G and G’ bands from the temperature-dependent Raman spectra of the mDIB-, 3,5- and 2,4-DBP-based graphene fabricated at 1100 K, respectively depicted as black, red, and green open circles in Figure 3b. To clearly observe the results of the DIB- and DBP-based graphene, we also presented them individually in Figure S8. As mentioned above, the (ωg, ωg’) distributions of the pyridine-based graphene (green and red open circles) are off the strain line shifted slightly to the right, which is indicative of a slight doping effect. It is worth mentioning that we did not observe any difference in the doping effects on as-grown CVD-graphenes after annealing to 850 K under UHV, comparing with the previous reports6, 46 that exhibit a change in the doping effect after annealing to 700 K even under vacuum environment (~10-1 torr). To scrutinize the (ωg, ωg’) distribution, we find that the distribution of the data points in the upper-right are along the slope of the “strain” line (~2.2), whereas the distribution of the data points in the left bottom are off the “strain” line and shifted slightly to a slope ~1.7. It has been reported that the △ωg’/△ωg ratio of freestanding

22


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graphene with temperature change is about ~1.68 over the temperature range of 100-800 K.6 The (ωg, ωg’) distribution revealed that a decrease in the slope of the data points at the temperature up to ~ 400 K can be reasonably explained by the contribution of the lattice expansion and anharmonic phonon scattering described by the Bonini et al..32 This issue is discussed in greater detail in the following section. Obviously, the correlation analysis of the G’ and G Raman band of graphene can help to disentangle the contributions of the strain-induced, doping-induced and the thermal-induced effects.

Estimate the strain coefficient of the G and G’ bands. Figure 4a presents a comparison of the frequency redshift of the G band with temperature for the mDIB-based graphene and the result calculated by Bonini et al.32 The black line corresponds to the best fit lines in Figure 2. Apparently, the experimental result of the frequency downshift of the G band (open circles) with temperature is larger than that calculated by Bonini et al.32 for a freestanding graphene (red line). In addition, we also found that it cannot be ignored the contributions from the thermal expansion of the lattice and phonon anharmonic effects when temperature is up to ~350 K. It does help to explain our observation of slight change in the slope of the (ωg, ωg’) distribution from ~2.2 to ~1.7 when the temperature of the graphene was increased to ~ 350 K, as shown in Figure 3b.

23



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(a)

(b)

Figure 4. Comparison between temperature dependence of the frequency shift (a) for the G band and (b) for the G’ band obtained from the mDIB-based graphene results. The theoretical result for a freestanding graphene is depicted by red real lines.32, 60 The blue dashed lines represent the result obtained from the fitting line of experimental data (black line) subtract the theoretical result (red line).

24


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As mentioned previously, the temperature-dependent shifts in the frequency of the G band on Cu(100) (△ωg(T)) can be attributed to the thermal expansion of the lattice (△ωlatt(T)), phonon anharmonic effect (△ωanh(T)) and the strain effect induced by the TEC mismatch between the substrate and graphene (△ωstrain (T)), which can be represented using the following equation:

△ωg(T) =△ωlatt(T)+ △ωanh(T)+ △ωstrain (T)

(1).

The contribution from the substrate-induced strain △ωstrain (T)22 on the Raman shift can be expressed as follows:

∆ω strain (T ) = βε (T ) T

= β ∫ (α Cu (T ) − α graphene (T ))dT

(2)

T0

Where β is the strain coefficient of the G band; and αCu and αgraphene are the temperature-dependent TECs of copper and graphene, respectively. In general, the substrate-induced strain in an epitaxial film depends on the difference of the TEC between the film and the substrate, and the difference between the epitaxial temperature and room temperature. Equation (2) is a simple model by which to estimate the frequency shift of a very 25



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thin epitaxial film on substrate caused by the substrate-induced strain, wherein most of the strain is assumed to retain in the film.27, 61 This means that the interaction between the film and the substrate must be strong enough to allow for the transfer of the strain to the film. The Raman spectrum of an as-grown monolayer CVD graphene on Cu presents a blue shift in the G’ band frequency, a wider FWHM of the G’ band, and a lower IG’/IG ratio, which are indicative of a strong interaction between the as-grown graphene layer and the copper substrate.23,

41

The

interaction would be far less pronounced if the grapheme were wet-transferred onto the Cu23 or decoupled by Cu2O.41 In our case, according to the correlation between the frequencies of the G and G’ band shown in Figure 3a, it also indicates that the as-grown CVD graphene on Cu(100) exhibits a compression strain. Therefore, the Eq. (2) seem to be valid for roughly estimating the substrate-induced strain of the as-grown CVD graphene on Cu.23, 62 Of course, the simple Eq. (2) can not sufficiently describe the complex strain between the grapheme and the substrate. However, it can provide us a simple guide on the estimation of the substrate-induced strain for an epitaxial thin film on substrate.23, 62 As shown in Figure 4, we can observe that the thermal expansion of lattice and anharmonic phonon-phonon scattering effects contribute to the frequency shift far less than the observation of the frequency shifts of the G band with temperature does. According to Eq. (1), the △ωstrain (T) can be obtained by eliminating the contributions of △ωlatt(T) and △ωanh(T) according to the result 26


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by Bonini et al.,32 depicted as a blue dashed line in Figure 4a. We adopted the calculated result reported by Bonini et al.32 for our quantitative analysis due to the fact that it32 is in good agreement with the experiment result of freestanding graphene.24 Then, by assuming that the TEC of graphene is similar to that of a free-standing one and the strain is mostly retained in the film, we can estimate an extreme (minimum) value of the strain coefficient from the Eq. (2), depicted as a black line shown in Figure 5a Here, the TEC of graphene was taken from the theoretical result of a free-standing graphene,8 while the TEC of copper was taken from the Ref.33 ( see Figure S9) In fact, with respect to the graphene TEC (αgraphene), it exhibits a broad variety of thermal expansion behaviors, depending on the calculation method8, 31 and the experimental method.4, 22, 63

In addition, the TEC of graphene is sensitive to the interaction between the graphene and the

supporting substrate.64 However, for the graphene/copper system, the αCu is always much larger than the wide-ranging values of αgraphene reported in the literatures for different situations both theoretically8, 31 and experimentally.4, 22, 63 Therefore, the term of the αgraphene in the Eq. (2) does not strongly influence the estimation about the trend of the strain coefficient with temperature, although the actual TEC of as-grown graphene does not be really known. The estimation of the strain coefficients of the G band as a function of temperature by ignoring the contribution of the TEC grapheme in Eq. (2) is shown in Figure S10. 27



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However, in order to rule out the possibility of deviation from the term αgraphene, the strategy of using the temperature-dependent Raman shift of graphene on different substrates is considered. Meantime, the Eq. (2) can be rewritten as follows:

strain strain ∆ωdiff = ∆ωsub 1 (T ) − ∆ωsub 2 (T ) T

T

T0

T0

(3)

= β ' [ ∫ α sub1 (T )dT − ∫ α sub 2 (T )dT ]

Herein, we estimated the temperature-dependent strain coefficient β’ of the G band by comparing our results with that in a previous report by Linas et al.25 on CVD-graphene on SiN under UHV, according to Eq. (3) using the well-known TEC of copper33 and SiN,25, 65 (see Figure S9). The result is shown in Figure 5a, depicted as red open circles. It is similar to the strain coefficient β estimated from our data when the contributions of △ωlatt(T) and △ωanh(T) were eliminated from the theoretical calculation by Bonini et al.32 in accordance with Eq. (2) using the αgraphene from the theoretical calculation presented by Mounet et al.,8 depicted as a black line in Figure 5a. The results obtained using the two approached methods differ only slightly over a temperature range of 100-800 K.

28


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(a)

(b)

Figure 5. (a) The strain coefficient of the G band as a function of temperature estimated following Eq. (2) using the copper TEC33 and the calculated graphene TEC8 (black line) and estimated as comparing our data and Ref. data25 on SiN just only using the well-known TEC of copper and SiN. (red circles) (b) In the same way as above to estimate the strain coefficient of the G’ band as a function of temperature. 29



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According to the results in Figure 5a, the strain coefficients for the G band at room temperature are -26 and -30 cm-1/% for β and β’, respectively. These results are close to that reported by Shainan et al. (-23 cm-1/%) for the as-grown CVD-graphene on copper film.23 Supposedly, if graphene lies flat on a single crystal with isotropic thermal expansion characteristic, then the strain profile in graphene can be taken to be biaxial. Nevertheless, the value is notably lower than that obtained in numerous experiments on biaxial strain in the range of ~ -57~-65 cm-1/% for the G band.2, 14 This means that the value of the strain coefficient compares favorably with that for uniaxial strain. As mentioned previously, the data points scatter along the slope of the strain line (~2.2) in the (ωg, ωg’) correlation map (Figure 3b). This also has the appearance of the uniaxial strain (slope: 2.02~2.44), although the presence of biaxial strain or mix of both could not be excluded.51 The phenomenon of the uniaxial-like strain has been explained due to the unidirectional quasi-periodic nanoripples ubiquitously in CVD graphene grown on copper, causing from the anisotropic compression.23 The morphology of parallel quasi-one-dimensional wrinkles in graphene flakes on a Cu surface has been observed in SEM images.5, 23 Similar uniaxial-like strain has also been observed in the CVD graphene grown on a cobalt film associated with the nonequibiaxial strain from the wrinkle edges.29

In general, the mode-Gruneisen parameter can be estimated from the Raman frequency shift

30


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(∆ω) using applied uniaxial strain related to strain (ε), as follows: ∆ω ε ≈ −γω0 , where γ is the mode-Gruneisen parameter. In accordance with the relationship, the mode-Gruneisen parameter of the G band at room temperature is estimated at approximately 1.88 (1.62) with the β’ (β) -30 (-26) cm-1/% and the ω0 is 1596±5 cm-1, which is in agreement with the results presented in the literature (~1.8).2, 7, 14

Similarly, the strain coefficients β of the G’ band with temperature have also been roughly estimated using Eq. (1) and Eq. (2) with the contributions of △ωlatt(T) and △ωanh(T) for the G’ band from the theoretical result by Apostolov et al.60 and the αgraphene based on the theoretical calculation by Mounet et al.8 We adopted the result reported by Apostolov et al.60 for quantitative analysis because it is consistent with the experimental result of unsupported graphene.66 In Figure 4b, the blue dashed line indicates the temperature-dependent frequency shift in the G’ band caused by substrate-induced strain after eliminating the contributions (red line) of △ωlatt(T) and △ωanh(T) according to the literature results.60, 66 According to Eq. (2) and Figure 4b, the strain coefficients and mode-Gruneisen parameter for the G’ band of graphene over a wide temperature from 100 K to 850 K were estimated, as shown in Figure 5b. Then, the mode-Gruneisen parameter of the G’ band at room temperature was estimated to be approximately 2.13, while the β(G’) is -58 cm-1/% and the ω0 is 2723±5 cm-1. The estimated

31



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value is close to the result reported by Metten et al.(2.4),13 but smaller than the results reported in others studies (2.8~3.8).2, 14

As mentioned previously, Eq. (2) provides a simple way to obtain a rough estimate of the strain coefficient resulting from the substrate-induced strain in the as-grown CVD-graphene on Cu(100), under the assumption that most of the strain is retained in the epitaxial film. Despite the fact that we do not know the actual αgraphene of the CVD-graphene, this is not a concern because it has only a negligible effect on estimates of the strain coefficient, due to the fact that αgraphene is always far less than αCu. Thus, this strategy can be used to capture the trend of the mode-Gruneisen parameter of CVD-graphene over a wide range of temperature from 100 K to 850 K. As shown in Figure 5, the trends indicate the mode-Gruneisen parameter is not as a constant, but rather a function of temperature. Obviously, the mode-Gruneisen parameter of the G and G’ bands decreased rapidly with the temperature and then flattened out beyond 300 K. The mode-Gruneisen parameter of the G and G’ band for graphene has previously been determined at room temperature;2-3,

7, 11-20

however, to the best of our knowledge, no results have been

published on the temperature dependence of mode-Gruneisen parameter.

32


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CONCLUSIONS In this study, we examined the in-situ temperature-dependent Raman shift of the as-grown CVD-graphene on Cu(100) produced under UHV. The strategy of using the thermal expansion of copper crystal with temperature can provide an approach of homogenous strain along the basal plane. The reproducibility of the temperature coefficients indicate the stability of the as-grown CVD-graphene on Cu(100) with good adhesion between the as-grown CVD graphene and the Cu surface. It is important for us to investigate the substrate-induced strain effect over the temperature range from 100 to 850 K. The results demonstrate that the contribution of the substrate-induced strain plays an important role in the frequency shift of the G and G’ bands with temperature. By separating the effects of thermal phonon scattering, lattice effect and subtract-induced strain, we are able to determine the strain coefficient of the G and G’ bands as a function of temperature. The fact that the TEC of graphene is far lower than that of copper makes it possible to obtain a precise estimate of the temperature-dependent strain coefficient for graphene in a graphene/copper system. There was only a slightly difference in the temperature-dependent strain coefficients obtained using the two approach methods. The correlation map of (ωg, ωg’) and strain coefficient revealed the existence of uniaxial-like strain in as-grown CVD-graphene on Cu(100). For a correction to magnitude of the uniaxial strain, the temperature-dependent Gruneisen parameter of G and G’ bands can first be estimated at the 33



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temperature range from 100 K to 850K. However, up to now, there is no experimental data or theoretical estimates of the temperature-dependent Gruneisen parameter of the G and G’ modes for graphene. Therefore, our results provide important insight into the change of strain coefficients of G and G’ bands with temperature in CVD-graphene.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: The as-acquired Raman spectra of m-DIB-based graphene grown on Cu(100) using 532 nm excitation. The temperature-dependent Raman spectra of m-DIB-based and 3,5-DBP-based graphene features grown on Cu(100) (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. *E-mail: [email protected]. Notes The authors declare no competing financial interest. 34


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ACKNOWLEDGMENT The authors would like to gratefully thank Y. K. Hsieh for assistance in the STM measurements and Professor C. Su for fruitful discussions. We would also like to thank Professor J. -L. Lin for early assistance in graphene preparation and helpful discussions. The authors highly acknowledge the financial support by the Academia Sinica in Taiwan, the National Science Council (NSC 102-2113-M-001-014 and NSC 103-2113-M-001-012) and the Ministry of Science and Technology (MOST 106-2633-M-017-001) in Taiwan.

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Study of the Substrate-Induced Strain of As-Grown Graphene on Cu

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