Ferroelectric gating of graphene 5

Chapter Quasi-periodic nanoripples in graphene grown by chemical vapor deposition and its impact on charge transport In the last chapter, we utilized mechanically exfoliated graphene to demonstrate a novel non-volatile memory device. However, it is impossible to use mechanically exfoliated graphene for large-scale applications. Ultimately, It needs to be replaced by large scale graphene, such as CVD graphene. This chapter will be devoted to a better understanding CVD graphene. We observed a new type of quasi-periodic nanoripple arrays in CVD graphene. The impact of these ubiquitous nanoripple arrays to the charge transport of CVD graphene was also studied. The results discussed in this chapter have been published in ACS Nano [100]. 61 62 5.1 Introduction and background The technical breakthrough in synthesizing graphene by chemical vapor deposition methods (CVD) has opened up enormous opportunities for large-scale device applications [44, 50]. In order to improve the electrical properties of CVD graphene grown on copper (Cu-CVD graphene), recent efforts have focussed on increasing the grain size of such polycrystalline graphene films to 100 micrometers and larger (Fig. 5.1) [44, 50]. While an increase in grain size and hence, a decrease of grain boundary density is expected to greatly enhance the device performance, here we show that the charge mobility and sheet resistance of Cu-CVD graphene is already limited within a single grain. We find that the current high-temperature growth and wet transfer methods of CVD graphene result in quasi-periodic nanoripple arrays (NRAs). Electron-flexural phonon scattering in such partially suspended graphene devices introduces anisotropic charge transport and sets limits to both the highest possible charge mobility and lowest possible sheet resistance values. Our findings provide guidance for further improving the CVD graphene growth and transfer process. Currently, CVD growth typically require high temperature of 1000-1050 ◦ C, very close to the melting point of Cu at 1083 ◦ C. This leads to Cu surface reconstruction and local surface melting [101, 102], during graphene growth, making high density Cu single-crystal terraces and step edges ubiquitous surface features. Taking into account the negative thermal expansion coefficient of graphene, this leads to new surface corrugations in CVD graphene during the cool down process [103]. Previously grain boundaries have been identified as one of the main limiting factors to degrade graphene quality [104]. While the heptagon and pentagon network [104, 105] at grain boundaries does disrupt the sp2 delocalization of electrons in graphene, it remains 63 b Graphene Cu ) 11 (1 b Cu (001) d [001] 35 µm Figure 5.1: (a) Scanning electron microscopy (SEM) image of CVD graphene on copper. By tuning the growth conditions, more than 100 µm graphene domain size is obtained. Cited from R. S. Ruoff group[106]. (b) Electron backscatter diffraction of sub-monolayer CVD graphene on Cu, revealing Cu(111) patch on Cu(001) surface. to be seen whether this is indeed the most relevant charge scattering source most relevant for device applications. Here, we show that Cu single-crystal step edges lead to the formation of quasiperiodic nanoripple arrays (NRAs) after transfer on Si/SiO2 substrates. Such surface corrugations suspend up to 20 % of the graphene and give rise to flexural phonon scattering [107]. In particular at room temperature and density levels of the order of 1012 /cm2 this leads to a strong anisotropy in the room-temperature (RT) conductivity depending on the relative orientation between NRA’s and current flow direction. More importantly, flexural phonon scattering within the nanoripples sets a lower bound on the sheet resistance and upper bound on the charge carrier mobility even in the absence of grain boundaries. Our findings provide guidance for further improving the CVD graphene growth and transfer process. 64 5.2 Sample fabrications The detailed synthesis and transfer of large-scale CVD graphene are discussed in Chapter 3.2. Electron backscattering diffraction reveals that the annealed Cu(001) substrates have single-crystal patches of Cu(111) and Cu(101), BLG coverage up to 40% (Fig. 5.1b) or SLG-dominant samples (>95%). Raman spectra (Fig. 5.2c) show insignificant defect peaks demonstrating the high quality of both SLG and A-B stacked BLG. Except for areas with optically visible wrinkles, Raman imaging with micrometer resolution also shows that on this scale strain is negligible. GFET Hall bars and four-terminal devices ranging in size from 1.2×0.8 to 100×10 µm2 were patterned by e-beam lithography (EBL) for metal contacts (5 nm Cr/30 nm Au) and O2 plasma etching. The completed device image are shown in Fig. 5.2e. For very large-scale GFETs of 1.2× 1.2 mm2 devices, it were first etched into van der Pauw geometry by EBL followed by metal contact evaporation using shadow masks (Fig. 5.2d). To precisely define four contacts either perpendicular or parallel with the nanoripple arrays (NRAs), Au alignment mask arrays were pre-patterned using standard EBL processes followed by systematic non-contact mode atomic force microscopy (AFM) scanning. For the systematic investigation of the origin of NRAs, Au alignment mask arrays were also pre-patterned on Cu-CVD graphene using EBL processes followed by the systematic SEM and AFM scanning. For the AFM measurements, both high-resolution contact mode and tapping mode AFM technique have been utilized to characterize graphene morphology on top of copper and on top of the Si/SiO2 substrate. For contact mode AFM, ultrasharp tips with radii as small as 10 nm were used, limiting the error to be less than 10 % error when measuring the 100 nm nanorippled area in Fig. 5.3. However, the contact 65 mode AFM tips are more vulnerable to surface contaminations. Thus, for large-scale characterization, tapping mode AFM was used. The devices were finally thermally annealed at 400 K in high vacuum level (105 mbar) for hours to clean the graphene working channel. Electrical transport measurements were done in vacuum in a four-contact configuration using a lock-in amplifier with an excitation current of 100 nA. T-dependent measurements were done from 350 to K in varable temperature insert (VTI) using standard four-contact lock-in techniques. In total, eight SLG devices and three BLG devices have been measured. Here we discuss five (two) representative SLG (BLG) devices in more detail. 5.3 Results and discussions Utilizing these large grain size CVD graphene, we first compare the RT resistivity vs gate voltage (ρ vs VBG ) characteristics in four GFETs of very different dimensions, ranging from the µm scale to the mm scale. The resistivities of these devices, fabricated from the same batch of CVD graphene, are presented in Fig. 5.2f. Surprisingly, except introducing stronger charge inhomogeneity, increasing the device channel area by orders of magnitude does not significantly alter the charge carrier mobility; RT mobilities vary generally speaking independent of samples size between µ ∼ 40006000 cm2 /Vs. This excludes grain boundaries (10-20 per mm, see Fig. 5.2a) as the main limiting factor for µ in our CVD graphene, and strongly suggests that the main scatterers are identical to the ones in exfoliated graphene: adatoms and/or charged impurities. Similar conclusions have recently been reached also by others [108]. However, high resolution contact mode atomic force microscopy (AFM) of CVD graphene SiO2 with ultrasharp tips reveals a new type of surface corrugations (Fig. 66 a 20 µm c D Graphene 2D G Intensity (a.u.) Cu b >4L BLG Wrinkle 1600 20 µm d f 1.2 0.8 µm2 µm2 100 10 µm2 1.2 1.2 mm2 ρ (kΩ) 1.2 mm 2000 2400 2800 Raman Shift (cm-1) 60 σ−σmin e2/h e SLG 40 20 -4 -2 n (1012 cm-2) 0 50 VBG - VD (V) Figure 5.2: (a) SEM image of submonolayer graphene on Cu foil. (b) Optical image of high BL coverage CVD graphene on 300 nm SiO2 . The black, red, and blue circles indicate the Raman measurement (0.4 µm in spot size) locations. Black arrows indicate wrinkles formed during growth. (c) Raman spectroscopy of SLG, BLG, and multilayer graphene. Raman on optical visible wrinkle shows significant broadening in G and 2D peaks, indicating non-negligible strain. (d) Optical image of a millimeter size GFET with van der Pauw geometry and (e) of micrometer size. Scale bar: µm. (f) Electrical measurements of square millimeter and square micrometer devices at RT. Each curve is shifted by 20 V. Inset show the corresponding σ-σmin vs n. 5.3), whose influence on charge transport is not known. Distinct from the well known low density strain-induced wrinkles (∼ per µm), we observe nanoripples of ∼ 3±1 nm in height of much higher density (∼ 10 per 5µm), which are typically arranged in a quasi-periodic fashion (Fig. 5.3b). Each nanoripple location contains multiple peaks of 10-20 nm width (Fig. 5.3e), thus making it possible that overall a section of up to ∼ 100 nm, i.e. up to 20 % of the graphene sheet becomes effectively suspended. 67 a b c Z (nm)   Distance (µm) e Z (nm) d (nm) Figure 5.3: (a) AFM image of Cu surface, showing single-crystal terraces and step edges (color scale, 0-60 nm; scale bar = µm), and (b) CVD graphene on SiO2 , showing high-density nanoripples induced by Cu step edges (color scale, 0-15 nm; scale bar = µm). (c) Top: AFM cross section of Cu terraces. The typical width of step edges is 100 nm. Bottom: AFM line scans of graphene after transfer to Si/SiO2 reveal nanoripple arrays which are closely correlated with the Cu terraces. (d) Illustration of nanoripple formation, structure, and periodicity. (e) High-resolution scan with ultrasharp tips shows that the nanoripple consists of multiple peaks of 10-20 nm width. Systematic AFM studies on centimeter size samples further confirm that quasiperiodic nanoripples arrays (NRAs) are a general feature of the CVD graphene-onSiO2 surface morphology. To find out the origin of these NRAs, we did systematic comparative SEM and AFM studies of the Cu films before transfer and the CVD graphene sheets after transfer. The patterning of Cu substrate after graphene growth with Au alignment mark arrays allows a direct comparison of the local Cu step edge orientation and their density with the surface morphology of CVD graphene, once it is transferred to Si/SiO2 substrates. Systematic SEM studies before transfer (more than 30 locations) on centimeter size Cu substrates confirm that single crystal step 68 edges and terraces are a ubiquitous surface feature of Cu foils after CVD graphene growth. Here we pick two specific locations for illustration. In Fig. 5.4, we show the comparison of CVD graphene morphology before and after wet transfer from two different positions (namely Left and Right). Left-(a) shows an overview of an asgrown CVD graphene on copper foil. The feature in the bottom right corner is Au alignment mark. After wet transfer graphene to Si/SiO2 substrate, the morphology of CVD graphene in the same location were examined using AFM (Left-(b) and Left(c)). Both the nanoripple orientation and density follows closely the Cu-step edge profile, as indicated by the dotted square region in Left-(a). Using the same strategy, another different location was examined, as shown in the Right images. Right-(a) shows the SEM image of CVD graphene before wet transfer. The black dotted square indicates the zoom-in region shown in (b). Right-(c) shows the AFM image of CVD graphene of the same location after transfer to a Si/SiO2 substrate. The blue dotted square indicates the zoom-in region shown in Right-(d) and Right-(e), respectively. A direct relation between nanoripple array orientations, density with Cu step edges is clearly seen. Thus, we conclude that the quasi-periodic nanoripple arrays in CVD graphene indeed originate from the Cu step edges and rule out any other potential factors during the fabrication processes. We now focus on T-dependent electrical transport measurements. In micron size devices the QHE is well developed for both SLG and BLG, as shown in Fig. 5.5a and 5.5b, respectively. As we expected, SLG shows the anomalous quantization plateaux of ±4e2 /h(N +1/2), while BLG has the typical ±4Ne2 /h quantization signatures. From an application point of view, the zero field measurements of conductivity (σ) vs charge density (n) are more relevant. They show a pronounced sublinear behavior, 69 Left: Right: b a a Au marker 5.0 µm d Au marker 1.0 µm c 8.0 µm 2.5 µm b c 640 nm e 36 nm 600 nm 270 nm 1.6 µm nm Figure 5.4: Two specific examples of CVD graphene morphology before and after wet transfer. Left: SEM and AFM images of CVD graphene before and after wet transfer. (a) Overview image of CVD Cu foil. The Au alignment markers (”11”) is clearly visible. The dotted square indicates the zoom-in region shown in (b). (b) SEM image of CVD graphene morphology at the boundary of two different Cu crystals. (c) AFM image of CVD graphene of the same location after transfer to a Si/SiO2 substrate. Both the nanoripple orientation and density follows closely the Cu-step edge profile. Note that the upper dotted region is shown in more detail in (d), while the lower dotted region refers to the image shown in (e). The Right panel shows another location on the same sample before and after transfer. not only in CVD SLG but also in CVD BLG devices. The sublinearity is strongest at RT and diminishes gradually with decreasing temperature, as shown in Fig. 5.5c and 5.5d, respectively. This is best studied by plotting the T-dependent part of the resistivity instead and represents the key finding of our experiments. Our data reveal a superlinear T-dependent resistivity for T>50 K. Remarkably, such a metallic behavior is observed in both SLG and BLG (Fig. 5.5e). Note that the dashed lines correspond to a two-parameter fit to the data using ρ= ρ0 + 0.1T + γT /ne, and 70 SLG 16 B=9T T = 3.5 K c e 1.8 SLG 60 1.6 40 -0.3 0.0 40 -3 60 d -8 20 VBG (V) 40 60 -2 -2 12 -2 3.8 (10 cm ) 0.2 0.4 50 150 250 -2 350 50 150 250 T (K) f BLG 400 BLG BLG σ (e2/h) 300 -4 -20 -1 SLG 120 σxy(e2/h) ρxx(kΩ) -2 12 BLG B = 16 T T=2K 12 0.5 (10 cm ) 0.8 12 Charge Density (10 cm ) VBG(V) b BLG 1.2 2.8 (10 cm ) 100 K 50 K 5K ρs (Ω) 20 0.5 (10 cm ) 1.4 0.3 350 K 300 K 200 K -20 -2 1.0 20 -8 -40 12 0.5 1.4 SLG ρ (kΩ) σ (e2/h) σxy(e2/h) ρxx(kΩ) a 80 40 -2 -1 100 300 K 250 K 200 K 5K 50 K 100 K 12 -2 Charge Density (10 cm ) 200 SLG 12 -2 Charge Density (10 cm ) Figure 5.5: (a) and (b) QHE of CVD SLG and BLG graphene on Si/SiO2 substrate, respectively. (c) and (d) T-dependent sub-linear behavior of a SLG and a BLG. Inset of (c) and (d): Insulating behavior with n < × 1011 /cm2 and AFM image of a flower shaped CVD BLG, respectively. The scale bar is µm. (e) ρ(T) at different doping level for both SLG and BLG. (f) At RT, ρS vs. n for both CVD SLG and CVD BLG. The solids curves correspond to fits of the form ρS = a/n, where ρS arises from both FPs and RIPs. We used a = 1.57×1018 Ω/m2 and 2.87×1018 Ω/m2 for SLG and BLG, respectively. serve as guide to the eyes. Previous studies on supported exfoliated samples only reported such a T-dependent resistivity in SLG, while BLG samples did not show any T dependence away from the charge neutrality point (CNP) [109]. Such behavior for BLG is expected only for suspended samples, where the T-dependent contribution to ρ (n, T) scales as T2 /n and is generally associated with electron-flexural phonon (FP) scattering [110]. Indeed, the high density NRAs effectively decouple up to 20 % of CVD graphene sheets from the substrates, activating low energy FP excitations in both SLG and BLG even when the samples are overall supported on a substrate. For CVD BLG, this clearly demonstrates that at RT NRAs will limit both R✷ and µ due to FP scattering. However, the CVD SLG case is more ambiguous. Its 71 resistivity has additional T dependent contributions due to scattering from remote interfacial phonons (RIP) of the SiO2 substrate [34, 111] and possibly high energy FPs arising from quenched 10 nm-wide nanoripples [112, 113]. On SiO2 substrates both the FP and RIP scattering mechanisms lead to a very similar T and n dependent behavior over 50-350 K and 1012 cm−2 ranges (Fig. 5.5e and 5.5f) [34]. a c 60 12 e -2 2.0 x 10 cm , S1 400 50 40 12 -2 12 -2 12 -2 12 -2 2.0 x 10 cm , S2 200 400 20 2.5 x 10 cm 100 -3 -4 -2 -1 12 150 200 250 T (K) -2 Charge Density (10 cm ) 12 -2 Charge Density (10 cm ) d b 200 300 10 10 100 60 400 3.0 x 10 cm 100 200 40 10 400 3.4 x 10 cm 20 Parallel NRAs Perpendicular NRAs 0.1 -4 -3 -2 -1 12 -2 Charge Density (10 cm ) 0.1 10 200 100 100 150 200 250 300 350 T (K) Figure 5.6: (a-b) T-dependent σ for both ⊥ and ∥ NRAs configurations. Inset: AFM image of graphene channel with clear ⊥ and ∥ NRAs orientations. The scale bar is µm. (c) Anisotropic resistivity results obtained with sample set S1 at n = 2.0 ×1012 /cm2 . (d) Estimate of the NRA impact on CVD SLG R and µ at n = ×1012 /cm2 . (e) ∆ρ(T) obtained from a second set of devices S2 for different charge densities ranging from 2.0 ×1012 /cm2 to 3.4 ×1012 /cm2 . To explicitly measure the influence of NRAs on CVD SLGs resistivity, we have fabricated GFETs where the orientation of the electrodes is such that the current is either perpendicular (⊥) or parallel (∥) to the NRAs (Fig. 5.6a and 5.6b). We analyzed the corresponding transport data by assuming a resistivity ρ of the form: ρ(n, T) = ρ0 (n) + αT + ρS (n,T), where ρ0 (n) is the T-independent residual resistivity, αT is the acoustic phonon (AP) induced resistivity (α= 0.1 Ω/K), and ρS (n,T) the 72 superlinear part of the resistivity. In Fig. 5.6e, we directly compare ρS (n,T) for the ⊥ and ∥ devices by computing ∆ρ⊥ (n, T) =ρ⊥ (n, T) - ρ⊥ (n, 100K) - α(T-100K) = ρS⊥ (n,T) - ρS⊥ (n,100K) and ∆ρ∥ (n, T) = ρ∥ (n,T) - ρ∥ (n, 100K) - α(T-100K) = ρS∥ (n,T) - ρS∥ (n,100K). Strikingly, ∆ρ⊥ remains always significantly greater than ∆ρ∥ . In other words, the RT CVD graphene resistivity is anisotropic. This is in sharp contrast with the isotropic resistivity of exfoliated samples and clearly shows that the phonon scattering rate is higher in the devices with the ⊥ configuration. Since FPs are the only phonons which are activated upon suspension, this demonstrates that NRAs contribute also in CVD SLG importantly to the T-dependence of ρ. Assuming a simple resistor-in-series and resistor-in-parallel model, we estimate the impact of NRAs on key figures of merit such as µ and R✷ . In Fig. 5.6d, The solid red and black curves represent the RT mobility µ against liquid Helium T mobility µ0 for CVD SLG in both ⊥ (solid red) and ∥ (solid black) NRAs configurations, assuming electron-RIP scattering is suppressed. The dashed dotted curves represent the FP-induced increase in R in ⊥ (red) and ∥ (black) orientations. Note that in our model ρS (n,T) arises from both electron-FP scattering (in the nanoripples) and electron RIP-scattering events (between the nanoripples) independent of the NRAs orientation. With this we write ρS⊥ = f·ρFP + (1-f)·ρRIP and ρS∥ = (f/ρFP + (1f)/ρRIP )−1 , where f is the ratio of the typical ripple width w and the mean inter-ripple spacing a. Besides, we assume ρFP is of the form γT /ne [13, 113, 114] and ρRIP can be written as (A/n)(g1 /(Exp(E1 /(kB T))-1) + g2 /(Exp(E2 /(kB T))-1)), where g1 = 3.2 meV and g2 = 8.7 meV are the respective coupling strengths of the SiO2 RIP modes of energies E1 = 63 meV and E2 = 149 meV. We can now estimate the two free parameters A and γ setting the magnitude of ρFP and ρRIP by fitting the 12 curves 73 of Fig. 5.6e. This leads to A = 3·1017 kΩ/(eV cm2 ), in reasonable agreement with Refs ([111],[34]), and γ = 6∼ 10−6 Vs/(mK)2 . Interestingly, this extracted value of γ matches well the experimental values recently obtained for fully suspended graphene samples. With the extracted value of γ, its now possible to predict FP-induced limits on CVD SLG µ and R✷ . Fig 5.6d shows the calculated RT mobility as a function of the Helium-T mobility µ0 for CVD graphene with f = 20 % both in ⊥ and ∥ orientations. As µ0 is unaffected by phonons, this is a convenient variable to gauge the influence of FPs [115]. Including AP scattering NRAs limit the RT mobility to 40,000 cm2 /Vs in ⊥ orientation and 80,000 cm2 /Vs in ∥ orientation, independent of the choice of substrate. In contrast, RT mobilities greater than 100,000 cm2 /Vs have already been achieved for exfoliated graphene encapsulated in h-BN [116]. 5.4 Conclusion In summary, we show that the current growth and transfer methods of CVD graphene lead to a quasi-periodic nanoripple arrays in graphene. Such high density NRAs partially suspend graphene giving rise to flexural phonon scattering. This not only causes anisotropy in charge transport, but also sets limits on both the sheet resistance and the charge mobility even in the absence of grain boundaries. At room temperature NRAs are likely to play a limiting role also for the mobility of ultra-clean samples, in particular when the graphene sheets are transferred onto ultraflat BN substrates [35, 108]. On the other hand the controlled rippling of graphene may be useful for graphene-based sensor applications as the ripples are more prone to adsorptions than flat graphene [117]. Controlled rippling may also be instrumental for spin-based device applications requiring surface modifications [118]. [...]... phonons (RIP) of the SiO2 substrate [34, 111] and possibly high energy FPs arising from quenched 10 nm-wide nanoripples [112, 113] On SiO2 substrates both the FP and RIP scattering mechanisms lead to a very similar T and n dependent behavior over 50 - 350 K and 1012 cm−2 ranges (Fig 5. 5e and 5. 5f) [34] a c 12 e -2 2.0 x 10 cm , S1 -2 -2 12 -2 12 400 50 40 12 12 60 -2 2.0 x 10 cm , S2 200 0 400 20 2 .5 x 10 cm... 0 1 2 12 150 200 3 250 T (K) -2 Charge Density (10 cm ) 12 0 -2 Charge Density (10 cm ) d b 200 300 10 1 10 100 60 400 3.0 x 10 cm 100 200 40 0 1 10 400 3.4 x 10 cm 20 Parallel NRAs Perpendicular NRAs 0.1 0 -4 -3 -2 -1 0 1 12 2 -2 Charge Density (10 cm ) 0.1 1 10 200 1 100 100 150 200 250 300 350 T (K) Figure 5. 6: (a-b) T-dependent σ for both ⊥ and ∥ NRAs configurations Inset: AFM image of graphene channel... orientation, independent of the choice of substrate In contrast, RT mobilities greater than 100,000 cm2 /Vs have already been achieved for exfoliated graphene encapsulated in h-BN [116] 5. 4 Conclusion In summary, we show that the current growth and transfer methods of CVD graphene lead to a quasi-periodic nanoripple arrays in graphene Such high density NRAs partially suspend graphene giving rise to... the absence of grain boundaries At room temperature NRAs are likely to play a limiting role also for the mobility of ultra-clean samples, in particular when the graphene sheets are transferred onto ultraflat BN substrates [ 35, 108] On the other hand the controlled rippling of graphene may be useful for graphene- based sensor applications as the ripples are more prone to adsorptions than flat graphene [117]... obtained for fully suspended graphene samples With the extracted value of γ, its now possible to predict FP-induced limits on CVD SLG µ and R2 Fig 5. 6d shows the calculated RT mobility as a function of the Helium-T mobility µ0 for CVD graphene with f = 20 % both in ⊥ and ∥ orientations As µ0 is unaffected by phonons, this is a convenient variable to gauge the influence of FPs [1 15] Including AP scattering... respective coupling strengths of the SiO2 RIP modes of energies E1 = 63 meV and E2 = 149 meV We can now estimate the two free parameters A and γ setting the magnitude of ρFP and ρRIP by fitting the 12 curves 73 of Fig 5. 6e This leads to A = 3·1017 kΩ/(eV cm2 ), in reasonable agreement with Refs ([111],[34]), and γ = 6∼ 10−6 Vs/(mK)2 Interestingly, this extracted value of γ matches well the experimental... perpendicular (⊥) or parallel (∥) to the NRAs (Fig 5. 6a and 5. 6b) We analyzed the corresponding transport data by assuming a resistivity ρ of the form: ρ(n, T) = ρ0 (n) + αT + ρS (n,T), where ρ0 (n) is the T-independent residual resistivity, αT is the acoustic phonon (AP) induced resistivity (α= 0.1 Ω/K), and ρS (n,T) the 72 superlinear part of the resistivity In Fig 5. 6e, we directly compare ρS (n,T) for the... sample set S1 at n = 2.0 ×1012 /cm2 (d) Estimate of the NRA impact on CVD SLG R and µ at n = 2 ×1012 /cm2 (e) ∆ρ(T) obtained from a second set of devices S2 for different charge densities ranging from 2.0 ×1012 /cm2 to 3.4 ×1012 /cm2 To explicitly measure the influence of NRAs on CVD SLGs resistivity, we have fabricated GFETs where the orientation of the electrodes is such that the current is either... demonstrates that NRAs contribute also in CVD SLG importantly to the T-dependence of ρ Assuming a simple resistor-in-series and resistor-in-parallel model, we estimate the impact of NRAs on key figures of merit such as µ and R2 In Fig 5. 6d, The solid red and black curves represent the RT mobility µ against liquid Helium T mobility µ0 for CVD SLG in both ⊥ (solid red) and ∥ (solid black) NRAs configurations,... (in the nanoripples) and electron RIP-scattering events (between the nanoripples) independent of the NRAs orientation With this we write ρS⊥ = f·ρFP + (1-f)·ρRIP and ρS∥ = (f/ρFP + (1f)/ρRIP )−1 , where f is the ratio of the typical ripple width w and the mean inter-ripple spacing a Besides, we assume ρFP is of the form γT 2 /ne [13, 113, 114] and ρRIP can be written as (A/n)(g1 /(Exp(E1 /(kB T))-1) . K 200 K 250 K 100 K 50 K 5 K 100 K 50 K 5 K 300 K 200 K 350 K -2 -1 0 1 2 3 4 -2 -1 0 1 2 3 -3 T (K) 50 150 250 350 50 150 250 2.8 (10 cm ) 12 -2 1 2 3 100 0 200 300 400 ρ (Ω) s 0.4 0 .5 1.4 1.6 1.8 1.4 1.2 1.0 0.2 0.8 3.8. 0.8 µm 2 2 2 50 0 0 5 1 3 2 4 ρ ( Ω) k V - V (V) BG D Graphene 1.2 mm a d Figure 5. 2: (a) SEM image of submonolayer graphene on Cu foil. (b) Optical image of high BL coverage CVD graphene on 300. [44, 50 ]. In order to improve the electrical properties of CVD graphene grown on copper (Cu-CVD graphene) , recent efforts have focussed on increasing the grain size of such polycrystalline graphene