Reversible defect engineering in graphene grain boundaries

Research efforts in large area graphene synthesis have been focused on increasing grain size. Here, it is shown that, beyond 1 μm grain size, grain boundary engineering determines the electronic properties of the monolayer. It is established by chemical vapor deposition experiments and first-principle calculations that there is a thermodynamic correlation between the vapor phase chemistry and carbon potential at grain boundaries and triple junctions. As a result, boundary formation can be controlled, and well-formed boundaries can be intentionally made defective, reversibly. In 100 µm long channels this aspect is demonstrated by reversibly changing room temperature electronic mobilities from 1000 to 20,000 cm2 V−1 s−1. Water permeation experiments show that changes are localized to grain boundaries. Electron microscopy is further used to correlate the global vapor phase conditions and the boundary defect types. Such thermodynamic control is essential to enable consistent growth and control of two-dimensional layer properties over large areas.


Supplementary Note 1 Literature summary of reported carrier mobilities and the corresponding channel dimensions
The literature on graphene field effect devices is vast and dates back to 2004. There have been several reports of extraordinarily high charge mobilities in graphene. The reported values vary depending on type of graphene, substrate used, encapsulation provided, temperature of measurement, method of measurement and very importantly device dimensions. In Supplementary Figure 1, data from the literature has been summarized.
Values obtained in this work have also been included for comparison. It is easily seen that the combination of the range of mobility values demonstrated in this work and the channel size used for measurement is the best thus far. For a 100 μm channel size, the room temperature mobility of 20000 cm 2 V -1 s -1 is the largest value reported value yet, to the best of our knowledge. In the case of CVD grown graphene and other large area practical applications, charge mobility at room temperature and over large areas, and hence such larger channel dimensions, are of importance.
Supplementary Figure 1: Literature summary of room temperature electronic mobility in monolayer graphene and the device channel dimensions used for the measurements. 1,2,3,4,5,6,7,8 For a channel dimension of 100 µm -one of the largest used and one that is therefore representative of the large area characteristics of the monolayer-the range of mobilities measured and the largest mobility observed in this study are the best thus far.

Supplementary Note 2 Graphene grain boundary resistivity calculations
Since graphene grain boundaries are the most defective regions in graphene, they are  9 It can be seen that range reported here is larger than that anticipated from current literature trends. Image reproduced from IOP Science. Under Creative Commons. b Image of uncoalesced islands at 2.5 minutes. c Image of the uncoalesced islands just before complete coalescence at 4 minutes. The average grain size was estimated from counting the number of edges crossing the lines shown.
size of our samples was measured by analyzing SEM images just before coalescence. An image is shown in Supplementary Figure 2c. Line crossings were counted to determine the grain size. This was calculated to be 7.08 µm with a standard deviation of 0.88 µm. This is also in agreement with the water permeation measurements. Grain size depends on the conditions during its nucleation and growth up to 6 minutes. Since all the samples from S1-S4 had the same conditions, the average grain size remains approximately same. The range of sheet resistances observed in this work is shown in yellow in Supplementary Figure 2a.
In the literature 9 , the lowest sheet resistance measured across various grain sizes is taken as ? % . Taking ? % to be 159 Ω☐ -1 (lowest measured sheet resistance in sample S2), a grain boundary resistivity of 3.8 kΩ-μm is calculated for the sample S1. This grain boundary resistivity drops to 2.9 kΩ-μm and 1.7 kΩ-μm when the S1 is annealed at 68 kJ mol -1 and 72 kJ mol -1 respectively (Samples from group G2). The boundary resistivity in the reverse annealed sample S3 would be like S1.
In Supplementary Figure 2a, literature data shows that the sheet resistance does not vary significantly with the grain size after 1µm thereby implying that increasing grain size above 1 µm is of little value to improving the properties of the monolayer. However, the work done as part of this study show at grain sizes beyond 1 µm, grain boundaries become very important, as a large range of resistivities can be obtained depending on the degree of closure.
The range of sheet resistances measured in this study is superimposed on this plot.

Supplementary Note 3 Growth setup and supersaturation calculations
Graphene growth was performed in a homemade CVD reactor equipped with gas purifiers, temperature, pressure and flow sensors. All the growth experiments were conducted at 1000°C in a horizontal tube furnace (Thermo-Fisher Lindberg BlueM) equipped with a 1 inch dimeter tube. Temperature was calibrated by using the melting point of Ge as a measure.
A piece of a single crystal Ge wafer, routinely used for device fabrication in our facility, was used for this purpose. Cu foil of 99.98 % purity was obtained from Sigma-Aldrich and the sample was pre-cleaned using acetone-iso propyl alcohol-DI-water clean sequence with 5 minute exposure in each medium. The foils were blow dried and loaded into the 1 inch quartz tube in quartz boats. Before every run, the loaded and closed quartz tube assembly, was leak tested using a He leak detector, to ensure specified leak rates below 4 x 10 -9 cubic centimeters per second of He. The reactor temperatures were raised to the value required for growth at 4 Torr pressure under a hydrogen flow of 400 standard cubic centimeter per minute (sccm).
The Cu foils were then annealed for 2 hours (unless otherwise stated) as mentioned in the main text before switching on methane flow into the reactor, from a vent line to a run line, to initiate graphene growth. The growth conditions are mentioned in the main text. The gas flow rates were first stabilized in the vent line before switching them into the run line to avoid turbulence.
Supplementary Figure 3: Thermodynamics details. Plot of supersaturation (DG) vs methane partial pressure ABC at a total pressure of 4 Torr and 1000°C temperature. Flow conditions are indicated in the table below. The supersaturations used in preparation of samples S1-4 and indicated in Figure 1 of the main text during various stages of nucleation, growth and annealing of graphene were obtained from the plot above. The gas flows and corresponding supersaturation are also provided.
For the methane decomposition reaction, CH C → C GH + 2 H J , ∆ M = 54 kJ mol -1 10 at 1000°C. The equilibrium rate constant K eq given by can be calculated to be 0.0057 at 1000°C. P is the partial pressure of the corresponding gas as indicated by the subscripts. The supersaturation calculated by using ∆ = Y OP Z ( : 3) and is plotted in Supplementary Figure 3 below. K represents the experimentally imposed \ ]^_ \^` ratio. Partial pressures were calculated by multiplying total reactor pressure by fractional flow rates.

Supplementary Note 4 Raman characterization of graphene films
Raman spectra was obtained using a 532 nm green laser with 1 µm spot size. The data overall graphene defect density value for a particular sample measured by Raman spectroscopy is obtained by averaging the values obtained in the mapped region. It is to be noted that the scales, blue to yellow, are not all the same. The maps show that the ID/IG ratio decreases from S1 to S2 and S3. Both, the large mobility difference between S2 and S3 (See Figure 2b of main text) and the trends in mobility are not captured by these Raman maps. .

Supplementary Note 5 Electrical measurements
Supplementary Figure ab is the channel resistance, is the device width, is the device length, % is the intrinsic carrier density, h+ is the gate dependent carrier density, ( is the gate voltage, ? is the source voltage, ( is the gate capacitance, zO{| and bM{} are the vertical and horizontal resistance according to Van Table 1 of the main manuscript. Rc is the contact resistance, no is the intrinsic carrier density, Id/Ig is the defect density value and std. err. is the standard deviation in the measurements. Row number 5, 14, 18 and 19 correspond to samples S1, S2, S3 and S4 respectively We measured at least 4 devices for statistical purposes. We have also repeated the growth for reliability tests. Supplementary Figure 6b shows the channel resistance vs gate bias for sample S2 for three different growth trials (see table 1 rows 26 -28). Supplementary Figure   6c shows the channel resistance vs gate bias for three samples whose mobilities are plotted in Figure 2a of the main text. These three samples were obtained by taking S1(VCG) and annealing them at the higher methane partial pressures indicated. The 82 kJ mol -1 is sample S2. The increase in mobility with supersaturation can be easily noted from the change in slope. It is also important to note that the unintentional doping density reduces as the mobility increases. This can be inferred from the shift in the zero gate bias towards zero voltage as well as increase in the zero bias resistance. Thus, the reduction in sheet resistance, Supplementary Figure 6d, is due to the rise in mobility and not due to doping. Rather, it is due to a reduction in defect density at the grain boundaries.

Supplementary Note 8 DFT computation details:
The reaction scheme used in DFT to model our CVD process is summarized in the 9 reactions below. The actual reaction during growth is the sum of Supplementary Equations (7) and (8) In contrast, the energy change by Dong et al. 11 is for

GE-H → GB + H (Supplementary Equation: 16
All first principles calculations in this work were performed using plane wave basis as implemented in Quantum Espresso 12 package. We use norm-conserving pseudopotentials 13 and generalized gradient approximation (GGA) 14 for the exchange-correlation functional.
The wavefunctions in our calculation were expanded using plane waves up to a cutoff energy of 70 Ry. We found this to be sufficient to ensure the numerical error of the results to be less where GE structure and some additional (nC) carbon atoms combine to form a GB structure.
The n1 hydrogen atoms that were passivating the GEs evolve as ½ n1 hydrogen molecules.
One can compute the change in Gibbs free energy of this reaction (GB formation energy from two GEs) as The free energy change for the Supplementary Equation 15 at 1000°C, calculated by the procedure just describe, as a function of methane partial pressure is plotted in Figure 4 of the main text.

Supplementary Note 9 Effect of supersaturation on graphene grain size
For the results shown in figure 5 of the main manuscript, graphene monolayers were nucleated and grown at different ΔGs to obtain different grain sizes. The set of experiments were conducted to quickly prove that the degradation happens at grain boundaries and triple junctions. Supplementary Figures 8a and b show that increasing supersaturation from 36 and 82 kJ mol -1 during nucleation, would decrease grain size in the coalesced monolayer. This in turn would increase the grain boundary length per unit area. The fact that sheet resistance degradation increases with a decrease in grain size shows that the responsible defects are associated with the grain boundaries.
Supplementary Figure 8: Effect of supersaturation a 36 kJ mol -1 and b 82 kJ mol -1 at nucleation on grain size

Supplementary Note 10 Ge etch experiments:
The defect structures in graphene were made visible using a technique reported by Suran et al. 17 . A drop of water is placed on a graphene monolayer transferred on to a Ge film. Water percolating through defects in the graphene layer oxidizes and dissolves the Ge below. The etch profile thus created is a replica of the microstructure of graphene layer. A sample time Supplementary Figure 9: Etch sequence comparison: a Revealing defects in a graphene monolayer by studying the etching of an underlying Ge film: The optical microscope snapshot images of Graphene-on-Ge surface is shown after exposure to water with time in minutes is shown in each image. Preferential permeation of water is seen as the color of certain regions start to change from green to red. The line features seen in this time sequence of VCG represent grain boundaries in the Cu layer used for deposition. They show that in VCG graphene grown on top of the Cu grain boundaries are seriously defective as discussed in the main paper. b The Ge etch experiments were conducted on four graphene coated films. The micron markers are all 20 μm. The etch sequence comparison for the 2 hours annealed Cu foil is shown for the four samples S1, S2, S3 and S4 taken at 3 minutes, 24 minutes, 62 minutes and 100 minutes respectively. The etch sequence observed in each of the samples are presented row-wise. The etch in the case of S1 was stopped at 62 minutes because the Ge film was almost etched, and the differences ceased to be prominent. The etch was predominantly happening in the sample S1 along the Cu grain boundaries making them more visible than the rest of the regions. In S2 and S3, the etch rate was lower and was predominantly happening at the graphene grain boundaries sequence of the etching that reveals the graphene microstructure is shown in Supplementary   Figure 9.

Supplementary Note 11 AFM scans of etch pits
The

Supplementary Note 13 Angular Misorientation of grains by TEM
The angular misorientation between the grains shown in main article was calculated using made by Yazyev et al. 15,19,20 were used to determine the hexagon to Stone-Wales defect site ratio.
A representative image of the calculated number of 5-7 structures to the standard hexagons are shown in Supplementary Figure 13a. At least two rows of hexagons were first established to identify the grains and the angle between them. This has been marked by the white lines in Supplementary Figure 13b below. Once the two rows were identified, the region in between was assumed to constitute the grain boundary. It is made up of hexagons and pentagons and heptagons whose numbers were determined to be 13, 8 and 8 respectively.
Supplementary Figure 13: TEM image analysis. a Grain boundary image using HRTEM. b The angular misorientation of the grains were determined and observed to be symmetric with respect to the boundary defects. The hexagonal graphene lattice and the defect structures between the grain is identified. The ratio of the hexagon to 5-7 structures was calculated as detailed above.

Supplementary Note 14 Misorientation defect density calculations
The angular misorientation of grains G1 and G3 with respect to the grain boundary (dotted line), denoted by q1 and q2, is shown in Supplementary Figure 13b. The total misorientation q = q1 + q2 is 13.8 degrees and it is almost a symmetric boundary. From Yazyev and Louie 19 the grain boundary energy, is seen to be less than 0.50 eV/Å for a symmetric 14° misorientation.
Taking the formation energy of hexagon lattice as reference, the formation energy of Stone-Wales defect is reported to be about 7.5 eV 19 . As shown in Supplementary Figure 14, using the C=C bond length of 1.42 Å, the Stone-Wales heptagon-pentagon pair (vertex to vertex) length can be calculated to be (Cb/2*(1 + Ö5) + Cb / (2 * tan ( π/2 / 7 ) ) 5.3 Å and that of hexagon-hexagon pair to be 3*Cb or 4.26 Å. Given these numbers, if " " is the number of Stone-Wales defects and " " is the number of hexagon pairs, the energy per unit length of the grain boundary can be calculated using the left side of Supplementary Equation (22).
When, this is equated to the number 0.5 eV/ Å, the boundary energy 19 , the ratio ( / ) can be calculated to be 0.46. The number at the boundaries observed by us is greater than 1. The triple junction which is close to the imaged boundary could also influence the defect density. However, what this simple calculation nevertheless shows is that defect densities at boundaries and especially closer to triple junctions would be much larger than those theoretically anticipated. They, in turn, could have a significant impact on the properties of the monolayer.
Supplementary Figure 14: Defect structures. Calculated length for a Stone-Wales defect site and b hexagonhexagon pair.