Micropatterned Strain Domain in Graphene on Cu Substrates: Correlation with Facet Structures

Metallic catalysts have emerged as prominent materials for graphene growth because the choice of the substrate significantly influences the properties of graphene. Among metallic catalysts, Cu is a highly promising catalytic substrate because it facilitates the growth of monolayer graphene. However, the growth process often induces strain and structural deformations that affect the electronic properties and device performance of graphene. In this study, we present the first observation of micropatterned strain domains in graphene grown on Cu substrates using chemical vapor deposition. Distinct strain‐induced shifts and broadening in the Raman peaks by employing Raman spectroscopy and atomic force microscopy are revealed, demonstrating the unique structural characteristics within the patterned domains. Furthermore, a strong correlation between the strain patterns in graphene and the facet structures of the underlying Cu surface is established. Our findings reveal intriguing variations in strain within the patterned domains and along the line boundaries, offering valuable insights into the intricate interactions between graphene and the Cu surface. These observed strain patterns and their spatial correlations with the Cu facet structures provide crucial guidance for designing graphene‐based devices with tailored strain engineering.


Introduction
Graphene, consisting a 2D lattice of carbon atoms in a single layer, demonstrates extraordinary properties that are significantly influenced by the choice of substrate during its synthesis.Metallic substrates have emerged as prominent catalysts in the quest for graphene growth, resulting in diverse structures depending on the metal species and surface attributes, [1][2][3][4][5][6][7] which can endow distinctive properties, that differ from the ideal characteristics of pristine graphene.
10] Cu catalysts offer various advantages such as cost-effectiveness and low carbon solubility, thereby facilitating the synthesis of monolayer graphene and making it a highly promising catalytic substrate.However, the progress of growing graphene on a Cu surface entails diverse structural changes from the nanoscale to the microscale owing to various factors in the CVD process.Typically, graphene growth requires high temperatures close to the melting point of Cu (≈1000 °C).After the growth process, the Cu substrate is rapidly cooled to room temperature, inducing compressive strain on graphene owing to the mismatch of the thermal expansion coefficients between the materials.[13][14][15][16][17][18][19] Moreover, certain regions of graphene develop wrinkles or ripples, which effectively release the strain caused by structural instability. [20,21]n the absence of wrinkles or ripples, specific regions on graphene retain various levels of strain, depending on the orientation of the Cu substrate. [22]These structures degrade electrical performance and introduce anisotropic charge transport in the devices. [23,24]As a result, various growth techniques [25][26][27][28][29] have been developed to eliminate these folded structures.Despite numerous studies on the relationship between the structural deformation and physical properties of graphene, reports on the comprehensive investigation of the overall performance of graphene grown on polycrystalline Cu are still limited.
In this study, for the first time, we visualized the presence of micropatterned strain domains within graphene, demonstrating their correlation with the Cu facet structure underlying the graphene layer.Raman spectroscopy was employed to analyze the distinct strain-induced shifts and broadening effects on the Raman peaks, providing crucial insights into the unique structural characteristics of both microscale and nanoscale strain variations in the patterned domains.Additionally, atomic force microscopy (AFM) was utilized to investigate the relationship between the Cu surface structure and its impact on graphene.

Synthesis and Characterization of Graphene
Graphene was synthesized via CVD using a polycrystalline Cu foil as the catalytic substrate.The schematic in Figure 1a shows the Cu foil placed in the center of the quartz reactor and annealed at 1000 °C under H 2 gas for 1 h.Subsequently, graphene was grown on a Cu substrate under a methane (CH 4 )/H 2 gas mixture for 30 min at a low-vacuum condition.Changes in the Cu surface, upon which graphene was grown, were observed after the reactor was rapidly cooled to room temperature.Figure 1b,c and Figure S1, Supporting Information, show the bright-and darkfield optical micrographs of the Cu surfaces before and after graphene growth.Prior to graphene growth, the Cu substrate showed a distinctive rolling mark pattern with small grains.Subsequent recrystallization at high temperature and growth steps [30] significantly increased the domain size and formation of faceted structures on the Cu surface underneath the graphene.The AFM topographic image revealed the existence of periodic facet structures, reaching a height of ≈100 nm, on the Cu surface underneath the graphene (Figure 1d).Graphene synthesized on the Cu surface by CVD typically produces anisotropic Cu step bunches owing to interfacial surface energy minimization and thermal expansion coefficient mismatch between graphene and the substrate. [11,19]

Micropatterned Strain Domains
Raman spectroscopy is a powerful and noninvasive technique for identifying and analyzing the quality of graphene and determining the number of layers. [31,32]In recent years, significant progress has been made in extracting valuable information regarding charge doping, [33][34][35] strain, [36][37][38][39][40] and edge effects [41][42][43][44] of graphene.Ryu and Stampfer et al. utilized the changes in the Raman shift and full width at half maximum (FWHM) of the G and 2D bands to explain the effects of strain and charge doping in graphene.This approach demonstrates high sensitivity to structural changes and electronic characteristics of graphene. [36,45]n our study, Raman spectroscopy is employed to investigate local strain variations in graphene grown on a Cu substrate.The prominent Raman features of graphene grown on a Cu substrate appeared at 1600 and 2700 cm À1 for the G and 2D bands, respectively, which arise from the in-plane vibration mode and double-resonance scattering. [32,46]The D band, originating from the breathing modes of the carbon atoms, [46] exhibits very low intensity at 1350 cm À1 (Figure S2, Supporting Information and Figure 2c).
The spatially resolved Raman maps, plotted using the G and 2D positions of graphene (Figure 2a,b) reveal two distinct micropatterned domains.To elucidate these intriguing observations, we classified these features in terms of: 1) a discernible pattern characterized by alternating bright and dark lines, and 2) the line boundaries (LBs), which delineate larger domain structures, such as domain 1 (D1), domain 2 (D2), and domain 3 (D3), encompassing multiple patterned domains.Figure 2c presents the average Raman spectra corresponding to each distinct feature indicated in the bright and dark lines in the micropattern as "a" and "b", respectively, and the LB represented as "c" in Figure 2a.
For the patterned domain structures (a and b), the FWHM of the 2D band is less than 35 cm À1 and low D band, representing a typical value for single-layer graphene with low defects. [47]he average positions of G and 2D bands in the bright-line domains (line a) were ≈1597 and 2709 cm À1 , respectively, whereas the positions in the dark-line domains (line b) were ≈1589 and 2697 cm À1 , respectively (Figure 2c).These peaks in both domains shifted significantly toward higher wavenumbers than those of unstrained graphene (G: ≈1581.9cm À1 , 2D: ≈2680.3cm À1 ). [47]Previous reports suggest that the strain effect in graphene is approximately twice the magnitude of the shift in the 2D peak compared to the G peak, while the doping effect results in a shift of ≈0.7. [35,36,48,49]This indicates that the graphene in this study was subjected to significant strain rather than a doping effect.Additionally, the FWHM of the G and 2D bands of graphene exhibit a similar patterned domain structure (Figure 2d and Figure S3, Supporting Information), suggesting that the difference between Raman spectra at a and b can be attributed to the strain effect induced by structural deformation.For the LB structure, the positions of the G and 2D bands are observed at 1583.5 and 2682.1 cm À1 , respectively, indicating lower compressive strain in graphene.However, the FWHM of both the G and 2D bands were significantly wider than those of the patterned domains.For precise analysis, the Raman map in Figure S4, Supporting Information, illustrates spectra with FWHM (2D) values categorized into three ranges: 1) below 15 cm À1 ; 2) covering values ranging between 15 and 35 cm À1 ; and 3) exceeding 35 cm À1 , which indicates that the majority of areas, including LB, demonstrate the formation of single-layer graphene.These findings imply the distinct physical characteristics of graphene in the patterned domains and LB region.
To elucidate the microscopic variation of compressive strain in graphene, we conducted a meticulous Raman analysis of the peak position (Figure 3a-d) and FWHM (Figure 3e-h) of the G and 2D bands of graphene at multiple points.In particular, we conducted a comprehensive comparison between the bright and dark lines in distinct domains, namely, D1, D2, and D3.The data points of the peak position within the patterned domains exhibited a scattered distribution along a line with a slope of 2.2, corresponding to the ratio of the strain-induced shifts of the G and 2D bands. [36,45]Notably, the peak positions in the bright and dark lines were separated, indicating an average strain difference of ≈0.05-0.08%assuming the biaxial nature of the strain.The position shifts of the G and 2D bands provide the presence of micropatterned strain domains.The spread of the strain within the bright and dark areas reached ≈0.23%, highlighting significant microscale strain variation across the graphene layer.On the other hand, the average FWHM of the G and 2D bands within the micropattern domains reached 12 and 29 cm À1 , respectively, indicating that single-layer graphene exists in all the domains (Figure S4 and S5, Supporting Information).
Figure 3d illustrates the peak position of the LB with an average strain of 0.05% and strain spread of ≈0.34%.Although the microscale strain variation remained higher than that observed in the patterned strain domains, the strain values suggest a substantial reduction in strain within the LB region.Additionally, the average FWHM of the G and 2D bands at the LB were 18 and 33 cm À1 , respectively, exceeding that of the patterned strain domains in Figure 3h.This observation indicates the presence of significant nanoscale strain variation [37] within the LB region, with a length scale smaller than the laser spot size.The data points of the FWHM, which were scattered along the line with a slope of 2.2, support the broadening of the FWHM of the G and 2D bands, due to the averaging effect of the strain variation within the laser spot.The overall distribution of the data points in Figure S5a,b, Supporting Information, reveals clear distinctions in the strain distribution of graphene between the patterned domain and LB region.
The spatial distribution of strain and doping in graphene on the Cu surface was analyzed using a vector decomposition method, [36,50] as illustrated in Figure 3i,j.Here, we assumed that graphene is p-doped under ambient air conditions, [51,52] and the carrier concentration (n) was determined based on values obtained from measurements conducted on gated graphene transistors. [53]The strain in graphene in this study varies from À0.5% to 0.1% within microscopic patterns, with graphene exhibiting less compressive strain in the LB structure.Graphene on Cu surface is charge-neutral or slightly p-doped, with carrier concentrations (n) typically below ≈5 Â 10 12 cm À2 , as expected from adsorbates in ambient air and the Cu substrate.The carrier concentration (n) in graphene varies within similar microscopic patterns of strain, suggesting a correlation between microscopic variations in strain and doping, likely influenced by factors such as the orientation of the Cu lattice. [54]It is noteworthy that the LB structure does not exhibit significant variations in doping, which can be interpreted as indicating that the graphene in the LB structure remains closely attached to the Cu surface, resulting in negligible differences in doping effects in the vicinity.

Correlation with Facets Structures of the Cu
The Cu surface was further characterized by AFM to reveal the relationship between the strain patterns in graphene and the underlying Cu surface.Figure 4a,b shows the AFM topographic image and Raman map plotted based on the G position obtained from the same region, respectively.The results revealed a spatial correlation between the facet structures of the Cu surface and patterned domains in graphene.Specifically, the Cu surface can be categorized into two distinct types of facet structures: line A exhibits unidirectional faceting with comparable lengths on both faces, whereas line B displays pyramidal faceting characterized by significant differences in the facet lengths.By juxtaposing the height profile and G peak position along each line, we observed a remarkable alignment between the length scale of the G position in the patterned domains and that of the facet structure on the Cu surface (Figure 4c,d).Notably, the points of low G position along lines A and B correspond to the facet planes, rather than the vertices.These regions are highlighted in green in line A and blue in line B.These results suggest that the formation of strained domains in graphene is strongly influenced by the facet structure of the Cu surface.One possible explanation for this observation could be attributed to the interaction between graphene and Cu, which is by the crystallographic orientation of different facets.During the high-temperature growth of graphene in the CVD process, large faceted Cu structures are generated beneath the graphene as a result of cooling via step bunching. [13]These steps exhibit unique orientations, dictated by surface energy anisotropy and surface dynamics of Cu. [13,19] As the system cools, graphene on each Cu facet with varying orientations may experience different degrees of compression due to the orientation-dependent interaction [19,55,56] or the influence of physisorption [57] between graphene and Cu.Consequently, varying levels of residual strain are observed in graphene on each facet.
As the configuration of Cu facets can vary due to factors such as growth temperature, [13,58] cooling rate, [59] and basal Cu orientation, [11,60] we anticipate that alterations in growth conditions and Cu orientation will have discernible effects on the size and intensity of these strain domains in graphene.Moreover, it is important to note that the strain values within these domains are not static under ambient conditions.Over time, exposure to air leads to the growth of copper oxide beneath the graphene, resulting in the release of the initial compressive strain in graphene. [51]This growth of copper oxide alters the morphology of the initial Cu facet structure, consequently impacting the micropatterned domains in graphene.
Here, we performed electrical characterization of graphene devices to investigate the potential correlation between residual strain in graphene and its electrical behavior (see Figure S6-8, Supporting Information).However, our investigation did not reveal clear indications of how strain, ripple, or wrinkle structures influence graphene because there were little differences in transport property in various directions of current flow.This phenomenon was ascribed to strain relief occurring during our wet-transfer process, with any discernible wrinkles not present within the tested device area.Additionally, the spatial strain mapping of graphene suggested that micropatterns of strain were not retained, and overall compressive strain was released following the transfer process.

LB Network
In the previous sections, we presented evidence of LB crossing between the domains and discussed their Raman characteristics.This LB formed a mesh network with deformed hexagons in certain regions, as shown in Figure 5a.An angle θ represents the angle subtended by the two LBs.The angle distribution in Figure 5b was obtained from the data in Figure 5a and Figure S9, Supporting Information.Notably, the angle distribution exhibited a prominent peak at ≈120°, which is correlated with the crystal structure of graphene.Similar network structures were observed in exfoliated graphene on SiO 2 [61] or boron nitride, [62] and in CVD graphene on nickel [63] or silicon carbide. [64]hese observations can be attributed to the relaxation of the biaxial compressive strain in graphene owing to the thermal expansion mismatch between graphene and the substrate, indicating that the domain boundaries are a common occurrence in graphene.Thus, the hexagonal symmetry of graphene plays a crucial role in the formation of the domain boundary network because it determines the preferred direction for strain-energy release.
][67] The formation of wrinkles in graphene was attributed to buckling, wherein buckling ridges are generated owing to the structural instability caused by the compressive strain.These ridges can reach heights of several nanometers depending on the thermal conditions and the substrate.Interestingly, LBs were only detected in the Raman measurements in this study, and no evidence of the LBs was observed in the AFM (Figure S10, Supporting Information).This observation suggests the strong adhesion of graphene to the Cu surface along the LBs.Moreover, despite the absence of the D peak, the increased FWHM of the Raman peak and their position shifts indicate the presence of a significant nanoscale strain variation within the LB region.Thus, the LBs in our study can show the release of interfacial compressive stress without deadhesion to the Cu substrate.

Conclusion
This study investigated the strain patterns present in graphene grown on a Cu substrate and explored their correlation with the facet structure of the Cu surface.Raman spectroscopy and AFM were employed to analyze the strain variations at the microscopic level, revealing the existence of micropatterned strain domains and their spatial relationships with the facet structures of the Cu surface.The LBs formed a mesh network with deformed hexagons.The Raman spectra exhibited distinct peak position shifts and FWHM broadening in the patterned domains, suggesting significant strain effects.AFM characterization further confirmed the correlation between the strain patterns in the graphene and the underlying Cu surface, including the regions with wrinkle-free graphene.These findings provide valuable insights into the interaction between graphene and the Cu substrates, offering potential opportunities for tailored strain engineering in graphene-based devices.

Experimental Section
Synthesis of Graphene: Graphene synthesis was performed using a CVD system, utilizing polycrystalline Cu foils (99.9%) with a thickness of 35 μm as the substrate.The Cu foil was placed in a quartz reactor and subjected to a temperature of 1000 °C for 1 h, with a constant flow of 25 sccm H 2 gas at a pressure of 1.5 mTorr.After stabilizing at 1000 °C, the Cu foil underwent a 30 min annealing process under the same conditions.For graphene synthesis, a gas mixture consisting of 10 sccm CH 4 and 25 sccm H 2 was introduced into the reactor for 30 min while maintaining a pressure of 1.3 mTorr.Subsequently, the reactor was rapidly cooled to room temperature (25 °C) with the assistance of H 2 flow Characterization of Cu Surface Morphology underneath Graphene: To obtain tomography images, AFM was conducted using a Park Systems XE-100 microscope, operating in noncontact mode, with a resolution of 256 Â 256.The graphene on the Cu foil was characterized using Microconfocal Raman spectroscopy with a Raman touch from Nanophoton instrument, utilizing a 532 nm laser with a power of 1 mW.The Raman spectra of graphene on Cu were acquired with a Â100 objective lens from Nikon with a numerical aperture of 0.9, and the laser was precisely focused to generate a spot size of less than 500 nm with a scanning step of 200 nm.
Transfer of CVD Graphene on SiO 2 Substrate: For transferring of CVD graphene onto a SiO 2 substrate, we utilized the wet transfer method, which is a widely adopted technique for transferring graphene to the desired substrate.Polymethyl methacrylate (PMMA, 495, A5, Kayaku Advanced Materials) was spin-coated on Cu foil to support the graphene during the etching process.The PMMA-supported graphene sample was floated on a 10% weight solution of ammonium persulfate (Sigma--Aldrich, #215 589) for ≈7 h to ensure complete etching of the Cu foil.
Fabrication of the CVD Graphene Device: Fabrication of the CVD graphene device involved utilizing E-beam lithography for patterning the graphene and electrodes.The entire graphene area, excluding the channel, was totally removed through an O 2 plasma process.Then, Ti/Au (3 nm/60 nm) was deposited using E-beam evaporation to create the contacts and pads.
Characterization of Electrical Property on Graphene Device: To confirm the relation between the graphene structure and the electrical property of the device, electrical measurements were performed using a Keithley 4200 A-SCS.To decrease the effects of the moisture or gases in the atmosphere on graphene device, measurements were conducted in a vacuum probe station at a pressure of ≈10 À2 torr.Additionally, the sweep speed of the gate voltage was adjusted to check the hysteresis of the source-drain current, which could be related to adsorption/desorption of chemical species on the graphene surface.

Figure 1 .
Figure 1.a) Schematic of the changes in the Cu surface morphology before and after graphene growth by CVD.b) Bright-field and c) dark-field optical micrographs of the graphene grown on Cu surfaces.d) AFM topographic image of the corrugated Cu surface in the white dashed box.

Figure 2 .
Figure 2. Spatially resolved Raman maps plotted using the a) G and b) 2D positions.Scan size: 12.7 Â 25 μm.c) The average Raman spectra of graphene on Cu were collected at the points denoted as "a" and "b", representing the bright and dark lines domains, respectively.The point "c" was obtained from the dotted-green line within the LB in (a) and (b).d) A table represents the peak positions and the FWHM of the Raman spectra.

Figure 3 .
Figure 3. Correlation between the 2D band and G band of graphene, extracted from D1, D2, D3, and LB of Raman maps in Figure 2 and Figure S2-4, Supporting Information.Scatter plots present the distribution of a-d) G and 2D positions and e-h) Γ 2D and Γ G recorded from three domains and LB on graphene.The red, cyan, and brown points represent Raman spectra obtained from dark regions in each domain on graphene, respectively.The black, orange, and yellow points correspond to Raman spectra taken from bright regions in each domain on graphene, respectively.Solid lines in black and magenta indicate ε = 0 and n = 0, respectively.The magenta points where they intersect correspond to pristine in (a)-(d), indicating undoped and unstrained graphene.Areal distribution images of i) strain and j) doping profiles of graphene on the Cu foil.

Figure 4 .
Figure 4. a) An AFM topographic image and b) a Raman map plotted by the G position of graphene on the same Cu surface.AFM line profiles and Raman maps plotted based on the G position were recorded along c) line A and d) line B, respectively.