Supporting Information for Bilayer Graphene Grown on 4H-SiC (0001 ...
Supporting Information for
Bilayer Graphene Grown on 4H-SiC (0001) Step-Free Mesas L.O. Nyakiti*, R. L. Myers-Ward, V. D. Wheeler, E. A. Imhoff, F.J. Bezares, H. Chun, J.D. Caldwell, A. L. Friedman, B. R. Matis, J. W. Baldwin, P. M. Campbell, J. C. Culbertson, C. R. Eddy Jr., G. G. Jernigan, and D. K. Gaskill. U.S. Naval Research Laboratory, 4555 Overlook Ave. SW, Washington DC 203575 *Email: [email protected],mil *To whom correspondence should be addressed
Description of Mesa fabrication steps unique to our set of samples Mesas of 2 to 4 µm in height were fabricated by the following sequence. First 0.5-1.0 µm of aluminum was deposited by e-beam evaporation on a clean 76.2 mm diameter with a misorientation of 0.25o (nominally on-axis) 4H-SiC surface, as measured by X-ray diffractometry mapping. This masking material was then patterned by standard photolithographic techniques. The exposed aluminum was wet etched (acetic acid, phosphoric acid, nitric acid, and water; 4:4:1:1), then the photoresist pattern was removed with solvents and plasma ashing. Next the exposed SiC was etched by inductively coupled plasma reactive ion etching (ICP-RIE). The ICP-RIE tool used in this work is an STS MP-0566 with 1
backside wafer cooling. The etch chamber pressure was 5 mTorr and the etch gases were sulfur hexafluoride and oxygen at 50 sccm and 5 sccm, respectively. At an ICP-RIE RF power of 1000 W for the coil and 100 W for the platen, the etch rate was 0.5-0.6 µm/min. Etch sidewalls approaching 90° with no sputter micro-masking was easily achieved with these etch conditions. The final step was removal of the aluminum pattern with the acid mixture outlined above.
Homoepitaxial growth of n-doped 4H-SiC/ n+4H-SiC substrates Briefly, the growth method involved the use of silane and propane (C3H8) as silicon and carbon containing gas species diluted in hydrogen carrier gas. An Aixtron VP508 SiC chemical vapor deposition (CVD) reactor was used; this reactor utilizes a horizontal laminar flow of hydrogen gas to deliver growth precursors to the inductively heated substrate contained in a high purity graphite hot zone. To remove residual oxide and impurities before growth, in-situ H2 etching of the mesas were performed during ramp to growth temperature (1580oC) by flowing 80 standard liters per minute (slpm) of Pd-purified H2 into the growth chamber1 where the pressure was controlled by a throttle valve (MKS) on an Ebara dry process pump. After attaining a temperature of 1580oC, as measured by a two-color pyrometer focused on the graphite susceptor adjacent to the location of the sample, 4.1 standard cubic centimeters (sccm) of propane was added to the 80 slpm Pd-purified H2 flow into the growth chamber for the first 10 seconds before starting the SiC growth which involved the simultaneous gas flow of 4.1 sccm propane and 398 sccm of 2% silane in high purity H2 and 5 sccm of high purity N2 (an n-type dopant). We estimate the partial pressures would result in an epitaxial doping of 3.8x1016 cm-3 on unpatterned substrates misoriented by 4 degrees towards the [11-20] direction; doping is expected to be reduced as the misorientation approaches zero. The thin SiC films were grown for a total of 0.443 hours at a constant pressure of 100 mbar and a rate of 2 µm hr-1, where the growth rate is based upon results for unpatterned substrates misoriented by 4 degrees. 2
2
EG Growth Description Epitaxial graphene growth is performed in a different cell of the same CVD reactor. Quarters of the processed wafers were diced into ~ 16 x 16 mm2 coupons before being loaded into the growth chamber. Prior to dicing a 1.8 µm layer of Shipley’s S-1818 photo resist is spin-coated over the quarter wafers at speeds of 4500 RPM and hard baked in an oven at 90oC for 30 minutes to minimize adherence of dicing debris. The diced samples were subjected to ex-situ wet chemical cleaning that involves the following steps; 5 min. of acetone and isopropanol to remove oil and grease, 10 min. piranha, to removes surface organic contaminants, 15 min. of the Standard Clean 1 (SC-1), and then dipped in a solution of deionized water, ammonium hydroxide and hydrogen peroxide mixed in the ratio of 5:1:1. To remove the surface impurities after being exposed to ambient, in situ hydrogen etching is performed by flowing 50 – 80 standard liters per minute (slpm) of H2 during temperature ramp up to 1400oC; based upon prior etching rate experiments the etch depth is estimated to be 200 nm. The ambient was then switched to Ar with a stabilization period of 3-5 min during which pressures oscillated by ±50% with reference to 100 mbar, the temperature was then increased at a constant rate to 1620oC. The subsequent 2.5 hour graphene growth process was conducted under a flowing Ar ambient of 20 slpm at 100 mbar at a growth temperature of 1620oC. Samples were cooled in Ar to 800 °C for 60 minutes in order to suppress Si sublimation and limit contaminants that may adhere to the surface. The samples are left under vacuum until they attained room temperature. This recipe is known to yield uniform graphene with ~ 2.3% sheet resistance variations across a vicinal 76.2 mm diameter wafer.
Strain Equation Gruneisen parameter is used to determine the rate of change of phonon frequency with strain in a crystal structure 3 and is defined by the equation, SEq 1.
3
Where
is the hydrostatic component of the strain.
and
correspond to phonon frequency of
2D band peak of exfoliated bilayer graphene (unstrained) and in SiC respectively. The hydrostatic strain can be resolved into
, where l and t represent directions that are parallel and perpendicular
to applied strain respectively. For bilayer EG, Gruneisen value is β2D = 2.73. Since bilayer EG couples well with the underlying SiC, Poisson’s ratio is used in the strain calculations instead of an in-plane Poisson’s ratio for the bulk graphite. Inserting these definitions into SEq. 1 for uniaxial strain yields the following4. SEq. 2
But, for uniaxial strain;
and
where ν is Poisson’s ratio for SiC (ν = 0.183) SEq. 3
SEq. 4
μ – Raman spectroscopy. Confocal micro-Raman spectroscopy, using a 514.5 nm excitation laser wavelength, 7cm-1 spatial resolution and 0.7 µm Gaussian spot size, was utilized to probe the presence, thickness and lattice strain variation in epitaxial graphene grown on 4H-SiC SFMs, using the 2D band; for example, multilayer or bilayer EG on SFM was identified by fitting the 2D spectra to two or four Lorentzian functions, respectively. This method has been widely used by various groups
5-7
. The spatial spectral data were
collected using a step size that ranged from 0.4 to 1 µm in the x and y direction with an integration time of 10 – 60 seconds.
4
Raman spectral maps from a 10 x10 µm2 graphene region near the mesa center but different from the location of the SFM discussed in the main text are shown in Fig S1-S4. These maps show 2D band full width at half maximum (FWHM) that are 40 - 60 cm-1 and average peak position of 2707.4±5.6 cm-1. Figure S5 is a representative Raman 2D band spectra from the edge region of SFMs described as region 1 in the main text; it has been fitted by two Lorentzian functions. Spectra that can be fit by two Lorentzians correspond to ≥ multilayer graphene6. To demonstrate the veracity of our fits, a 2D band spectra from the center region of a EG/4H-SiC SFM was fit by one, two, and four Lorentzian functions, shown in figures S6, S7, and S8 in that order. The sum of the Lorentzian components (red color) does not fit with the experimental spectrum (in black color) for either the one or two Lorentzian function fits (blue colored) but four Lorentzian functions fit the data well. The inability to fit the sum of one Lorentzian component with the experimental spectrum means that it is not a monolayer graphene. The experimental value of the FWHM, ~60 cm-1, is also not consistent with monolayer graphene as it is much larger than that found by others for a monolayer film, ~25-40cm1 8, 12
, using a similar excitation wavelength. Epitaxial graphene layers > 2 with turbostratic stacking can
also be fit with one Lorentzian function7, 9, however, the peak width is much broader (>40cm-1). The attempts to fit the experimental 2D mode data from the center of SFM region by two Lorentzian components also failed. This implies that there is absence of graphitic-type of EG layers with AB stacking10. Fitting the 2D data to a sum of the four Lorentzian functions converged perfectly to experimental data, and given the uniformity of the FWHM in the Raman spatial maps, demonstrates complete Bernal bilayer graphene coverage. The splitting of electronic bands in bilayer graphene is responsible for the splitting of the 2D peak into four components 10. We did not attempt to fit the data to a sum of 6 Lorentzians (required for 3 monolayers of graphene) as a false positive may result. Instead, we note that the 2D FWHM for 3 monolayers is ~70 cm-1 for the excitation wavelength used here 11, larger than experimentally measured. Likewise, for 4 or more layers, even larger FWHM would be 5
exhibited, again not found experimentally here. As the EG layers approaches five layers, the intensity of the two lower wave number components out of the four, further decreases while the intensity of the higher wave number components increase. Above a threshold of five graphene layers, the determination of the layer thickness with Raman becomes rather complex, as the shape of the 2D mode is increasingly similar to that of bulk graphite, therefore it was not necessary to continue fitting for example with six lorentzian components as was reported by 11. The four Lorentzians components for the bilayer EG are markedly comparable to the 2D band components reported by others
7, 8-11
with the two middle bands
having higher intensity relative to the outer two functions. In addition, the positions of the four fit components are consistent with the theoretical predictions for bilayer graphene, see Table S1, where the difference between experiment and theory is mainly due to the resolution of our spectrometer. This implies the sample is Bernal-stacked bilayer graphene. Comparing the 2D mode FWHM for EG on SFM to other reports
7, 11
of BLG show peak widths within a similar range i.e. 41-60 cm-1. Robinson J. A. et
al.13, successfully used Raman spectroscopy technique to identify bilayer EG on step-bunched SiC(0001), and validated their results by use of High Resolution transmission Electron microscopy (HRTEM). The extrapolated 2D FWHM reported13, 8 for bilayer graphene is ~50 cm-1. In addition, the peak shape (FWHM) for bilayer EG on SiC is very similar to what we have measured. As the number of layers increases from monolayer, bilayer, and multilayer graphene, the corresponding 2D FWHM becomes substantially larger and falls within the range of 25-40cm-1, 41-60cm-1 and >70cm-1 respectively. 7, 11.
6
Figure S1 - S4: 2D band FWHM (used to extract out thickness) and peak position (used to extract out strain) spectral maps showing the variation of these parameters from two different center regions of a step free mesa different from the example shown in the main text. Surface particles are believed to cause the poor resolution of 2D band peaks which result as the (discontinuous) single point tetragonal blue data contained in the maps S1, S2, and S4; otherwise the overall pattern is supportive of the discussion and conclusion in the main text.
7
Figure S5: A representative Raman 2D band spectra from the edge region of SFM after EG growth, fitted with a set of two Lorentzian functions confirming presence of ≥ 3 monolayers of EG.
8
Figure. S6-S8: Demonstrates fitting of experimental 2D band spectra (black in color) to four, two, and one Lorentzian functions. A fit by four Lorentzian functions, i.e. S6, provides the best fit since all four functions sum to match (sum, red) the experimental spectra (black).
9
Table S1. A shift of Raman 2D Lorentzian component functions relative to the average wave number of the two main components.
Experimental
-40
-11
+11
+32
Experimental7
-44
-10
+10
+25
Theory7
-44
-11
+11
+41
References 1. VanMil, B.L.; Lew, K.-K.; Myers-Ward, R.L.; Holm, R.T.; Gaskill, D.K.; Eddy Jr, C.R.; Wang, L.; Zhao, P. Journal of Crystal Growth 2009, 311 (2), 238–243. 2. Myers-Ward, R.L.; Nyakiti, L.O.; Hite, J.K.; Glembocki, O. J.; Bezares, F.J.; Caldwell, J.D.; Imhoff, G. A.; Hobart, K. D.; Culbertson, J.C.; Picard, Y. N.; Wheeler, V. D.; Eddy, C. R. Jr.; Gaskill, D. K. Materials Science Forum 2011, 679-680, 119. 3. Grimvall, G. Thermophysical properties of materials. North Holland (1999). 4. Mohiuddin, T.; Lombardo, A.; Nair, R.; Bonetti, A.; Savini, G.; Jalil, R.; Bonini, N.; Basko, D.; Galiotis, C,; Marzari, N.; Novoselov, K.; Geim, A.; Ferrari, A. Phys. Rev. B 2009, 79 (20), 205433. 5. Robinson, J. A.; Puls C. P.; Staley N. E.; Stitt J. P.; Fanton, M. A.; Emtsev, K. V.; Seyller, T.; Liu Y. Nano Lett. 2009, 9 (3), 964-968. 6. Ferralis, N,; Maboudian, Roya.; Carraro C. Phys. Rev. Lett. 2008, 101 (15), 156801. 7. Ferrari, A. C.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.; Mauri, F.; Piscanec, S.; Jiang, D.; Novoselov, K. S.; Roth, S.; and Geim, A. K. Phys. Rev. Lett. 2006, 97 (18), 187401. 8. Röhrl, J.; Hundhausen, M.; Emtsev, K. V.; Seyller, Th.; Graupner, R.; Ley, L. Appl. Phys. Lett. 2008, 92(20), 201918. 9. Lespade, P.; Marchand, A.; Couzi, M.; Cruege, F.; Carbon 1984, 22, 375. 10
10. Ferrari, A,; Robertson, J.; Phys. Rev. B 2000, 61, 14095 11. Malard, L. M.; Pimenta, M. A.; Dresselhaus, G.; Dresselhaus, M. S.; Physics Reports 2009, 473, 51-87 12. Graf, D.; Molitor, F.; Ensslin, K.; Stampfer, C.; Jungen, A.; Hierold, C.; Wirtz, L.; Nano letters 2007, 7( 2), 238-242 13. Robinson, J. A.; Fanton, M. A.;
Wetherington, M.; Frantz, E.;
Tedesco, J. L.;
Snyder, D.;
Campbell, P. M.;
Vanmil, B. L.;
Jernigan, G. G.;
Eddy, C. R., Jr.; Gaskill, D. K. Nano Lett. 2009, 9(8), 2873-2876.
11
Weng, X.;
Stitt, J.;
Myers-Ward, R. L.;
Bilayer Graphene Grown on 4H-SiC (0001) Step-Free Mesas L.O. Nyakiti*, R. L. Myers-Ward, V. D. Wheeler, E. A. Imhoff, F.J. Bezares, H. Chun, J.D. Caldwell, A. L. Friedman, B. R. Matis, J. W. Baldwin, P. M. Campbell, J. C. Culbertson, C. R. Eddy Jr., G. G. Jernigan, and D. K. Gaskill. U.S. Naval Research Laboratory, 4555 Overlook Ave. SW, Washington DC 203575 *Email: [email protected],mil *To whom correspondence should be addressed
Description of Mesa fabrication steps unique to our set of samples Mesas of 2 to 4 µm in height were fabricated by the following sequence. First 0.5-1.0 µm of aluminum was deposited by e-beam evaporation on a clean 76.2 mm diameter with a misorientation of 0.25o (nominally on-axis) 4H-SiC surface, as measured by X-ray diffractometry mapping. This masking material was then patterned by standard photolithographic techniques. The exposed aluminum was wet etched (acetic acid, phosphoric acid, nitric acid, and water; 4:4:1:1), then the photoresist pattern was removed with solvents and plasma ashing. Next the exposed SiC was etched by inductively coupled plasma reactive ion etching (ICP-RIE). The ICP-RIE tool used in this work is an STS MP-0566 with 1
backside wafer cooling. The etch chamber pressure was 5 mTorr and the etch gases were sulfur hexafluoride and oxygen at 50 sccm and 5 sccm, respectively. At an ICP-RIE RF power of 1000 W for the coil and 100 W for the platen, the etch rate was 0.5-0.6 µm/min. Etch sidewalls approaching 90° with no sputter micro-masking was easily achieved with these etch conditions. The final step was removal of the aluminum pattern with the acid mixture outlined above.
Homoepitaxial growth of n-doped 4H-SiC/ n+4H-SiC substrates Briefly, the growth method involved the use of silane and propane (C3H8) as silicon and carbon containing gas species diluted in hydrogen carrier gas. An Aixtron VP508 SiC chemical vapor deposition (CVD) reactor was used; this reactor utilizes a horizontal laminar flow of hydrogen gas to deliver growth precursors to the inductively heated substrate contained in a high purity graphite hot zone. To remove residual oxide and impurities before growth, in-situ H2 etching of the mesas were performed during ramp to growth temperature (1580oC) by flowing 80 standard liters per minute (slpm) of Pd-purified H2 into the growth chamber1 where the pressure was controlled by a throttle valve (MKS) on an Ebara dry process pump. After attaining a temperature of 1580oC, as measured by a two-color pyrometer focused on the graphite susceptor adjacent to the location of the sample, 4.1 standard cubic centimeters (sccm) of propane was added to the 80 slpm Pd-purified H2 flow into the growth chamber for the first 10 seconds before starting the SiC growth which involved the simultaneous gas flow of 4.1 sccm propane and 398 sccm of 2% silane in high purity H2 and 5 sccm of high purity N2 (an n-type dopant). We estimate the partial pressures would result in an epitaxial doping of 3.8x1016 cm-3 on unpatterned substrates misoriented by 4 degrees towards the [11-20] direction; doping is expected to be reduced as the misorientation approaches zero. The thin SiC films were grown for a total of 0.443 hours at a constant pressure of 100 mbar and a rate of 2 µm hr-1, where the growth rate is based upon results for unpatterned substrates misoriented by 4 degrees. 2
2
EG Growth Description Epitaxial graphene growth is performed in a different cell of the same CVD reactor. Quarters of the processed wafers were diced into ~ 16 x 16 mm2 coupons before being loaded into the growth chamber. Prior to dicing a 1.8 µm layer of Shipley’s S-1818 photo resist is spin-coated over the quarter wafers at speeds of 4500 RPM and hard baked in an oven at 90oC for 30 minutes to minimize adherence of dicing debris. The diced samples were subjected to ex-situ wet chemical cleaning that involves the following steps; 5 min. of acetone and isopropanol to remove oil and grease, 10 min. piranha, to removes surface organic contaminants, 15 min. of the Standard Clean 1 (SC-1), and then dipped in a solution of deionized water, ammonium hydroxide and hydrogen peroxide mixed in the ratio of 5:1:1. To remove the surface impurities after being exposed to ambient, in situ hydrogen etching is performed by flowing 50 – 80 standard liters per minute (slpm) of H2 during temperature ramp up to 1400oC; based upon prior etching rate experiments the etch depth is estimated to be 200 nm. The ambient was then switched to Ar with a stabilization period of 3-5 min during which pressures oscillated by ±50% with reference to 100 mbar, the temperature was then increased at a constant rate to 1620oC. The subsequent 2.5 hour graphene growth process was conducted under a flowing Ar ambient of 20 slpm at 100 mbar at a growth temperature of 1620oC. Samples were cooled in Ar to 800 °C for 60 minutes in order to suppress Si sublimation and limit contaminants that may adhere to the surface. The samples are left under vacuum until they attained room temperature. This recipe is known to yield uniform graphene with ~ 2.3% sheet resistance variations across a vicinal 76.2 mm diameter wafer.
Strain Equation Gruneisen parameter is used to determine the rate of change of phonon frequency with strain in a crystal structure 3 and is defined by the equation, SEq 1.
3
Where
is the hydrostatic component of the strain.
and
correspond to phonon frequency of
2D band peak of exfoliated bilayer graphene (unstrained) and in SiC respectively. The hydrostatic strain can be resolved into
, where l and t represent directions that are parallel and perpendicular
to applied strain respectively. For bilayer EG, Gruneisen value is β2D = 2.73. Since bilayer EG couples well with the underlying SiC, Poisson’s ratio is used in the strain calculations instead of an in-plane Poisson’s ratio for the bulk graphite. Inserting these definitions into SEq. 1 for uniaxial strain yields the following4. SEq. 2
But, for uniaxial strain;
and
where ν is Poisson’s ratio for SiC (ν = 0.183) SEq. 3
SEq. 4
μ – Raman spectroscopy. Confocal micro-Raman spectroscopy, using a 514.5 nm excitation laser wavelength, 7cm-1 spatial resolution and 0.7 µm Gaussian spot size, was utilized to probe the presence, thickness and lattice strain variation in epitaxial graphene grown on 4H-SiC SFMs, using the 2D band; for example, multilayer or bilayer EG on SFM was identified by fitting the 2D spectra to two or four Lorentzian functions, respectively. This method has been widely used by various groups
5-7
. The spatial spectral data were
collected using a step size that ranged from 0.4 to 1 µm in the x and y direction with an integration time of 10 – 60 seconds.
4
Raman spectral maps from a 10 x10 µm2 graphene region near the mesa center but different from the location of the SFM discussed in the main text are shown in Fig S1-S4. These maps show 2D band full width at half maximum (FWHM) that are 40 - 60 cm-1 and average peak position of 2707.4±5.6 cm-1. Figure S5 is a representative Raman 2D band spectra from the edge region of SFMs described as region 1 in the main text; it has been fitted by two Lorentzian functions. Spectra that can be fit by two Lorentzians correspond to ≥ multilayer graphene6. To demonstrate the veracity of our fits, a 2D band spectra from the center region of a EG/4H-SiC SFM was fit by one, two, and four Lorentzian functions, shown in figures S6, S7, and S8 in that order. The sum of the Lorentzian components (red color) does not fit with the experimental spectrum (in black color) for either the one or two Lorentzian function fits (blue colored) but four Lorentzian functions fit the data well. The inability to fit the sum of one Lorentzian component with the experimental spectrum means that it is not a monolayer graphene. The experimental value of the FWHM, ~60 cm-1, is also not consistent with monolayer graphene as it is much larger than that found by others for a monolayer film, ~25-40cm1 8, 12
, using a similar excitation wavelength. Epitaxial graphene layers > 2 with turbostratic stacking can
also be fit with one Lorentzian function7, 9, however, the peak width is much broader (>40cm-1). The attempts to fit the experimental 2D mode data from the center of SFM region by two Lorentzian components also failed. This implies that there is absence of graphitic-type of EG layers with AB stacking10. Fitting the 2D data to a sum of the four Lorentzian functions converged perfectly to experimental data, and given the uniformity of the FWHM in the Raman spatial maps, demonstrates complete Bernal bilayer graphene coverage. The splitting of electronic bands in bilayer graphene is responsible for the splitting of the 2D peak into four components 10. We did not attempt to fit the data to a sum of 6 Lorentzians (required for 3 monolayers of graphene) as a false positive may result. Instead, we note that the 2D FWHM for 3 monolayers is ~70 cm-1 for the excitation wavelength used here 11, larger than experimentally measured. Likewise, for 4 or more layers, even larger FWHM would be 5
exhibited, again not found experimentally here. As the EG layers approaches five layers, the intensity of the two lower wave number components out of the four, further decreases while the intensity of the higher wave number components increase. Above a threshold of five graphene layers, the determination of the layer thickness with Raman becomes rather complex, as the shape of the 2D mode is increasingly similar to that of bulk graphite, therefore it was not necessary to continue fitting for example with six lorentzian components as was reported by 11. The four Lorentzians components for the bilayer EG are markedly comparable to the 2D band components reported by others
7, 8-11
with the two middle bands
having higher intensity relative to the outer two functions. In addition, the positions of the four fit components are consistent with the theoretical predictions for bilayer graphene, see Table S1, where the difference between experiment and theory is mainly due to the resolution of our spectrometer. This implies the sample is Bernal-stacked bilayer graphene. Comparing the 2D mode FWHM for EG on SFM to other reports
7, 11
of BLG show peak widths within a similar range i.e. 41-60 cm-1. Robinson J. A. et
al.13, successfully used Raman spectroscopy technique to identify bilayer EG on step-bunched SiC(0001), and validated their results by use of High Resolution transmission Electron microscopy (HRTEM). The extrapolated 2D FWHM reported13, 8 for bilayer graphene is ~50 cm-1. In addition, the peak shape (FWHM) for bilayer EG on SiC is very similar to what we have measured. As the number of layers increases from monolayer, bilayer, and multilayer graphene, the corresponding 2D FWHM becomes substantially larger and falls within the range of 25-40cm-1, 41-60cm-1 and >70cm-1 respectively. 7, 11.
6
Figure S1 - S4: 2D band FWHM (used to extract out thickness) and peak position (used to extract out strain) spectral maps showing the variation of these parameters from two different center regions of a step free mesa different from the example shown in the main text. Surface particles are believed to cause the poor resolution of 2D band peaks which result as the (discontinuous) single point tetragonal blue data contained in the maps S1, S2, and S4; otherwise the overall pattern is supportive of the discussion and conclusion in the main text.
7
Figure S5: A representative Raman 2D band spectra from the edge region of SFM after EG growth, fitted with a set of two Lorentzian functions confirming presence of ≥ 3 monolayers of EG.
8
Figure. S6-S8: Demonstrates fitting of experimental 2D band spectra (black in color) to four, two, and one Lorentzian functions. A fit by four Lorentzian functions, i.e. S6, provides the best fit since all four functions sum to match (sum, red) the experimental spectra (black).
9
Table S1. A shift of Raman 2D Lorentzian component functions relative to the average wave number of the two main components.
Experimental
-40
-11
+11
+32
Experimental7
-44
-10
+10
+25
Theory7
-44
-11
+11
+41
References 1. VanMil, B.L.; Lew, K.-K.; Myers-Ward, R.L.; Holm, R.T.; Gaskill, D.K.; Eddy Jr, C.R.; Wang, L.; Zhao, P. Journal of Crystal Growth 2009, 311 (2), 238–243. 2. Myers-Ward, R.L.; Nyakiti, L.O.; Hite, J.K.; Glembocki, O. J.; Bezares, F.J.; Caldwell, J.D.; Imhoff, G. A.; Hobart, K. D.; Culbertson, J.C.; Picard, Y. N.; Wheeler, V. D.; Eddy, C. R. Jr.; Gaskill, D. K. Materials Science Forum 2011, 679-680, 119. 3. Grimvall, G. Thermophysical properties of materials. North Holland (1999). 4. Mohiuddin, T.; Lombardo, A.; Nair, R.; Bonetti, A.; Savini, G.; Jalil, R.; Bonini, N.; Basko, D.; Galiotis, C,; Marzari, N.; Novoselov, K.; Geim, A.; Ferrari, A. Phys. Rev. B 2009, 79 (20), 205433. 5. Robinson, J. A.; Puls C. P.; Staley N. E.; Stitt J. P.; Fanton, M. A.; Emtsev, K. V.; Seyller, T.; Liu Y. Nano Lett. 2009, 9 (3), 964-968. 6. Ferralis, N,; Maboudian, Roya.; Carraro C. Phys. Rev. Lett. 2008, 101 (15), 156801. 7. Ferrari, A. C.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.; Mauri, F.; Piscanec, S.; Jiang, D.; Novoselov, K. S.; Roth, S.; and Geim, A. K. Phys. Rev. Lett. 2006, 97 (18), 187401. 8. Röhrl, J.; Hundhausen, M.; Emtsev, K. V.; Seyller, Th.; Graupner, R.; Ley, L. Appl. Phys. Lett. 2008, 92(20), 201918. 9. Lespade, P.; Marchand, A.; Couzi, M.; Cruege, F.; Carbon 1984, 22, 375. 10
10. Ferrari, A,; Robertson, J.; Phys. Rev. B 2000, 61, 14095 11. Malard, L. M.; Pimenta, M. A.; Dresselhaus, G.; Dresselhaus, M. S.; Physics Reports 2009, 473, 51-87 12. Graf, D.; Molitor, F.; Ensslin, K.; Stampfer, C.; Jungen, A.; Hierold, C.; Wirtz, L.; Nano letters 2007, 7( 2), 238-242 13. Robinson, J. A.; Fanton, M. A.;
Wetherington, M.; Frantz, E.;
Tedesco, J. L.;
Snyder, D.;
Campbell, P. M.;
Vanmil, B. L.;
Jernigan, G. G.;
Eddy, C. R., Jr.; Gaskill, D. K. Nano Lett. 2009, 9(8), 2873-2876.
11
Weng, X.;
Stitt, J.;
Myers-Ward, R. L.;
