ARTICLE pubs.acs.org/JPCC
Fabrication of Carbon Nanoscrolls from Monolayer Graphene Controlled by P-Doped Silicon Nanowires: A MD Simulation Study Liangyong Chu, Qingzhong Xue,* Teng Zhang, and Cuicui Ling College of Science, China University of Petroleum, Qingdao, Shandong 266555, P. R. China ABSTRACT: It is demonstrated using molecular dynamics (MD) simulations that P-doped silicon nanowires (Si NWs) can activate graphenes self-scrolling onto Si NWs and thus produce new kinds of graphene nanoscroll (NS)/Si core/shell heterojunctions. The simulations show that graphene sheets can fully self-scroll onto Si NWs when the Si NW radius is larger than a threshold of about 5 Å, forming a stable core/shell structure. It is the van der Waals force that plays a primary role in the self-scrolling process. The configuration of the grapheneSi heterojunction depends significantly on the diameter of the Si NWs. The final NS becomes multiwalled with increasing graphene length when the diameter of the Si NWs is larger than a threshold of about 6 Å. The zigzag NS is proved to be the most stable, while the chiral NSs are unstable and tend to evolve into zigzag NS and a model is set up to interpret the tendency from the standpoint of bond. It is demonstrated that the graphene width has no influence on the self-scrolling process at all. Compared with the conventional fabricating method, the new self-assembling one occurs at room temperature and the thickness of the NSs can be controlled accurately. Besides, the unique structure of the graphene/Si core/shell heterojunctions will significantly enhance their applications in nanoelectronic devices, hydrogen storage, solar cells, chemical or biological sensors, and energy storage in supercapacitors or batteries.
1. INTRODUCTION With egregious electronic properties,1,2 predominant thermal,3,4 mechanical,5 and optical1,68 properties, graphene has attracted much attention since it was first discovered in 2004.9 Graphene nanoribbons have also been synthesized from graphene monolayers,10,11 and pertinent work has proved that the properties of graphene nanoribbons have much connection with their parameters such as the size and chirality.1216 Graphene nanoribbons with strong interlayer van der Waals (vdW) binding can interact with a variety of 3D structures, such as nanodroplet,17 carbon nanotubes (CNTs),18,19 and nanowires (NWs).20 Compared with the conventional nanodevices, the graphene ones show enhanced properties and even new features.21 Carbon nanoscrolls (CNS) have gained extensive attention due to their visible applications in hydrogen storage22 and energy storage in supercapacitors or batteries,23 as a result of their structural differences from CNTs such as the continuous variability of their diameter size and interlayer distance.24 Si NWs have attracted a lot of scientific interest as a result of their promising applications and being experimentally realized using the vaporliquidsolid method.25,26 Using these Si NWs, people have fabricated several nanostructures including field effect transistors,27 pn diodes,28,29 bipolar junction transistors,29 photodetectors,30 advanced anode for batteries,31 and sensors for chemical and biological substances.32,33 In these applications doping plays an important role.34 Currently, Si NWs can be doped using laser ablation,35 thermal evaporation of solid sources,36 and chemical vapor deposition methods.37 And several experimental groups have successfully achieved effective n- and p-type doping of Si r 2011 American Chemical Society
NWs,3840 and the microstructures have been proposed by pertinent theoretical studies.41 One-dimensional nanoscale heterojunctions have attracted enormous attention due to their wide range of applications in nanoelectronics, optoelectronics, plasmonics, medical diagnostics, catalysis, drug delivery, therapeutics, separations, and chemical sensing as a result of their unique electronic, optical, and magnetic properties, small size, and chemical reactivity.42,43 There are varieties of methods to fabricate the carbon radical onedimensional nanoscale heterojunctions. The synthesis of carbon radical core/shell heterojunctions usually involves either filling a CNT with some material, coating a CNT with some material, or coating a 1D material with a carbon shell.42 Most of the methods need rigorous conditions such as high temperature or exact instruments.4446 Herein, using MD simulations, we perform a simple method of synthesizing the heterojunction composite by visualized process of rolling up graphene activated by P-doped Si NWs. Compared with the conventional fabricating method, the new self-assembling one occurs at room temperature, and the thickness of the two components can be controlled accurately. For nanosized materials, owing to their large surface-tovolume ratio, interface properties become paramount. However, restricted by the complexity of the interface and the existing research methods, knowledge about the interface properties and the relevant mechanisms is quite limited. Received: April 2, 2011 Revised: June 26, 2011 Published: June 29, 2011 15217
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Previous work has demonstrated that graphenes can self-scroll onto CNTs and Si NWs guided by the interlayer vdW force.1820 The interface properties and mechanisms were investigated by analyzing the relevant binding energies. In this work, we demonstrate that P-doped Si NWs can activate the self-scrolling of planar graphene nanoribbons. The surface adsorption stress of the Si NWs, which comes from vdW force, is introduced to bend graphene nanoribbon to roll up and cover on the Si NWs’ surface. This is a one-dimensional core/shell nanoscale heterojunction composite synthesized by brand-new self-assembly method. We detect the mechanism and interface characteristics of the interface including how the parameters of the two components, such as the length, width, and chirality of graphene nanoribbons and diameter of Si NWs, affect the properties of the composite. When used as high-speed switching devices, optoelectronic devices, solar cells, and chemical or biological sensors, the new one-dimensional core/shell nanoscale heterojunction will show enhanced value due to the unique electron mobility of graphene nanoribbons and large surface-to-volume ratio. Besides, this new heterojunction may be a perfect choice for the fabrication of new generation solar cells owing to the high light transmittance of graphene.
2. SIMULATION METHODOLOGY SECTION MD simulations are implemented by the DISCOVER code in MATERIALS STUDIO software. The interatomic interactions are described by the force field of condensed-phased optimized molecular potential for atomistic simulation studies (COMPASS).47 This is the first ab initio force field that is parametrized and validated using condensed-phase properties in addition to various ab initio and empirical data, and it has been proven to be applicable in describing the mechanical properties of CNTs.48,49 Using the MD method, we have done a lot of research in the nanometer field,18,50 and the same method is used here. MD simulations were performed in periodic boundary conditions in the range of 260.000 260.000 37.600 Å3. In this study, we choose Si NWs doped 1% P to activate the self-scrolling process of graphene nanoribbons. Si NWs were doped with element by replacing a certain amount of surface Si atoms with P atoms symmetrically (e.g., for the Si NWs with 330 atoms, three of them were replaced.). The graphene was built by MS, and the unsaturated boundary effect of graphene was avoided by adding hydrogen atoms. Each CC bond length was 1.42 Å, and CH bond length was 1.14 Å. The hydrogen atoms had charges of +0.1268 e, and the carbon atoms connecting hydrogen atoms had charges of 0.1268 e; thus, the neutrally charged graphenes were constructed. As an initial configuration the Si NWs with the radii of 8 Å were put in the center of the supercell, the graphenes with the same width (32.424 Å) and length (120.207 Å) were aligned parallel to the Si NWs with about 5 Å separation. The model was put into an NVT ensemble simulation at 300 K. A time step of 1 fs is used, and data are collected every 1 ps. Then the full-precision trajectory was recorded, and the results were analyzed. 3. RESULTS AND DISCUSSION The bonding strength between the graphenes and the Si NWs is evaluated by the interaction energy of the composites. Generally, the interaction energy is estimated by the difference between the potential energy of the composites system and the potential energy for the Si NW molecules and the relevant graphenes as follows51 Einteraction ¼ Etotal ðEGN þ ENW Þ
ð1Þ
Figure 1. Snapshots of the graphene (32.424 Å 120.207 Å) self-scrolling onto the 8 Å radius Si NW cores in the simulation from 0 to 3500 ps.
where Etotal is the energy of the composite including the graphene and NW, EGN is the energy of graphene without the NW, and ENW is the energy of NW without the graphene, respectively. In other words, the interaction energy can be calculated as the difference between the minimum energy and the energy at an infinite separation of the graphene and the NW. Self-Scrolling Process. The core/shell composite NWs produced by graphenes self-scrolling onto Si NWs are simulated by the MD method. Figure 1 shows the snapshots of the graphene self-scrolling onto the 8 Å radius Si NW core in the simulation from 0 to 3500 ps. At beginning the graphene was put parallel to Si NW with distance of about 5 Å. The graphene and the Si NW approach each other due to the strong attraction force. During the approaching process, the surface of the graphene which is closer to the Si NW side moves relatively faster because carbon atoms near the Si NW have stronger vdW force, as shown in Figure 1 at t = 200 ps, and then the graphene begins to wrap on the Si NW. After the nearest part of graphene surface wraps on the Si NW, the graphene begins to roll and gradually wraps the whole Si NW, as shown in Figure 1 at t = 2002910 ps. At t = 2910 ps, the graphene wraps onto Si NW totally, and the configuration of the core/shell composite NW keeps a relatively stable state until the simulation is completed. During the whole process, the Si NWs oscillate in short range, and the configuration of the Si NW changes so little that it looks the same as the initial state. Interfacial Interaction Analysis. In order to study the interface properties and the relevant mechanisms of graphene/Si NW composite, it is essential to get a better understanding of the interfacial force such as the strength and interaction distance (see Table 1). Herein, as shown in Figure 2, we take the graphene (32.424 Å 120.207 Å)/Si NW (8 Å radius) composite as an example to analyze the interfacial force. Here, the distance between graphene nanosheet and the Si NW surface is more than 2.5 Å, which is longer than the CSi bond length 1.86 Å. The interaction energy between the graphene and the Si NW is 466.129 kcal/mol, which after unit conversion is 1951.146 kJ/mol. In order to know the effect of Si atom position on the interaction energy between the graphene and the Si NW, we calculated the interaction energies between six different tubular Si structures and the same graphene nanoscrolls. As shown in Figure 2, all the C atoms of each tubular structure have the same distance from the central axis of the Si NW. From Figure 2 we can see that following the increase of interlayer distance between tubular Si structure and graphene nanosheet from 3.75 to 8.5 Å, the average interaction energy contribution per atom decreases as much as 2 orders of magnitude. The conclusion is also consistent with the fact that the limited interaction distance 15218
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Table 1. Information of the Interfacial Interaction Analysis of the Composite Structure Formed by Graphene Nanoribbon (32.424 Å 120.207 Å) and Si NW (8 Å Radius): Interaction Energy Contribution per Atom of Each Tubular Si Structure and the Interlayer Distance between Tubular Structure and Graphene Nanosheet tubular structures Si atoms included in the of the Si NW
tubular structures
interaction energy contribution of each interaction energy contribution tubular structure/kcal/mol
interlayer distance between tubular
per atom kcal/mol
structure and graphene nanosheet 8.5
1
6
0.2139
0.03565
2
28
3.3082
0.11815
7.75
3
52
25.4394
0.48922
6.75
4 5
56 28
37.7695 44.3228
0.67446 1.58296
6 4.5
6
160
355.2317
2.22020
3.75
Table 2. Doped P Atom Number of Different Radius Si NWs Varying from 4 to 10 Å
Figure 2. (a) Six different tubular Si structures that comprise the Si NW (8 Å radius) and the interlayer distance between tubular Si structure and graphene nanosheet. (b) Variation of the interaction energy contribution per Si atom of each tubular Si structure following the change of the interlayer distance between tubular Si structure and graphene nanosheet.
of vdW force is 9.5 Å. Considering the interaction distance, we know that the interface formed by the first NS layer and the outer surface of Si NW plays a primary role on the interfacial properties of the composite. For the forming of the second NS layer, considering the fact that the distance between NS layer and Si layer is bigger than 6.5 Å, the primary activated force comes from the first NS layer; this is similar to the graphene nanoribbons self-scrolling onto the CNTs forming the core/shell structure.18 Different from the CNTs, the radius of the NS is variable when activated by the second NS layer, so the forming of the second NS layer will have an influence on the interfacial properties of the composite as shown in the latter paragraph. Size Effect. (1). Radius Size Effect. To calculate the radius size effect on adhesion, we simulated the same graphene (49.204 Å 63.179 Å)
radius of Si NWs/Å
Si atoms
doped P atoms
doped percentage/%
4
123
1
0.813
5
208
2
0.962
6
294
3
1.020
7
374
4
1.069
8
494
5
1.012
10
820
8
0.976
scrolling onto different radius NWs varying from 4 to 10 Å. The NWs were approximately doped with 1% P element by replacing a certain amount of surface Si atoms with P atoms symmetrically as shown in Table 2. It is obvious that the 4 Å radius Si NW cannot induce the graphene self-scrolling onto it; the graphene layer only produced a certain degree of bending, and this is probably because the interlayer force is not strong enough to activate the graphene to form NS structure with relatively small radius. All the Si NWs left can induce the graphenes self-scrolling onto them, and the graphene just coils the 8 Å radius Si NW around as shown in Figure 3a. When the NWs radii vary from 5 to 8 Å, the interaction energies increase linearly as a result of the rapid increasing of the SiC interfacial area. When the radius of the NWs is beyond 8 Å, the interfacial area keeps constant and the contribution of the additional core Si atoms becomes so negligible that the interaction increases slightly as shown in Figure 3b. Considering the fact that the elastic energy cost for bending the graphene sheet is the main competing effect, we calculate the elastic energy to prove that the vdW interactions are strong enough. Taking the model of Si NW radius 8 Å as an example, the elastic energy is 119.968 kcal/mol, smaller than the vdw interaction energy which is 646.988 kcal/mol. Particularly, we note that the 5 Å radius knot structure is different from the others, and it is not unique as it occurs in former works. Niladri Patra and co-workers17 demonstrated that water nanodroplets can activate and guide the folding of planar graphene nanostructures, and they found that with proper nanodraplets size, the ribbon folds around the droplet into a knot structure. Previous work51 about CNTs collapsing and self-scrolling onto Cu NWs also found a similar structure, when CNTs (35, 35) interacted with the 10 Å diameter Cu NWs. To demonstrate that the final structure is relevant to the radius of the NWs and the appearance of the knot structure is not accidental, we change the length of the graphene nanoribbons to repeat the selfscrolling process with various NWs radii as shown in Figure 4. 15219
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Figure 3. (a) Final structures of the composites formed by the same graphene nanoribbon (49.204 Å 63.179 Å) and Si NWs with various radii from 4 to 10 Å. (b) Variation of the interaction energies following the increase of the Si NWs radii varying from 4 to 10 Å.
Figure 4. Graphene nanoribbon (32.424 Å 120.207 Å) self-scrolling onto Si NWs with various radii from 5 to 10 Å.
Herein, we can see that when the radius of the NWs is 5 Å, the final structure becomes single-walled while others become multiwalled. When the first carbon shell finishes self-scrolling, the left graphene nanoribbon begins the process mainly activated by the first carbon shell. However, the vdW force of the first carbon shell gain from the Si NW is not strong enough, so the first shell opens and finally the single-walled knot structure forms. Following the increase of the NW radius, we get multiwalled structures when the first interlayer vdW force is strong enough to keep the first layer adhesive as shown in Figure 4. (2). Graphene Nanoribbon Length Effect. Considering the fact that different Si NW radii lead to dissimilar structures, we calculate them separately. Here are the two models: Model 1. We choose the Si NWs (5 Å radius and 47.158 Å length) to active the graphene nanoribbons with various lengths (21.567, 32.226, 44.862, 62.638, 71.295, 100.921 Å) while keeping the width 34.663 Å constant. The structures and the relevant interaction energies are as given in Figure 5.
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Herein, we can see that when the NW radius is 5 Å, only singlewalled structures occur even if we make the graphene nanoribbon long enough. When the length is less than 44.862 Å, the interaction energies increase linearly, as a result of the increase of the SiC interfacial area as shown in Figure 5ac. Afterward, the interaction energy decreases slightly owing to the change of the interlayer distance as marked in Figure 8d. When the graphene nanoribbon is longer than 72 Å, the additional part has nearly no contribution to the interaction energy because the distance is larger than 9.5 Å. Model 2. Here we choose the Si NW (8 Å radius and 35.404 Å length) to active the graphene nanoribbons with various lengths (35.439, 49.805, 65.202, 84.879, 100.937, 120.608 Å) while keeping the width 34.659 Å constant. The structures and the relevant interaction energies are as given in Figure 6. Herein we can see that for 8 Å radius Si NWs when the graphene nanoribbon is long enough, the final structures become multiwalled owing to the fact that the SiC interlayer vdW force becomes stronger, and as a result, the first graphene layer keeps adhesion in the process. The interaction energy exhibits similar variation with the former 5 Å radius when the length of graphene nanoribbons is less than the threshold. However, following the increase of the layer, the interaction energies decrease visibly. To detect the factors that lead to the drop of the interaction energies, choosing parts d and f as examples, we obtain the atomic concentration profiles for C and Si separately as shown in Figure 7. Figure 7b,c shows the concentration profiles of the combinations separately. For part b, the d1 and d2 denote the distances between two peaks, respectively. The intuitionistic definition is shown in Figure 7a, and the distance d1 is 3 Å, d2 is 2.5 Å. For part d, the distance d1 is 3 Å, d2 is 3 Å, and d3 is 3.5 Å. Obviously, the adhesion of the second graphene layer leads to the expansion of the SiC interlayer distance given that the first graphene layer provides the main driving force for the second layer’s scrolling. As we have demonstrated, the expansion of the SiC interlayer distance will significantly decrease the interaction energies. (3). Graphene Nanoribbon Width Effect. In this simulation, we change graphene width to research the width effect on the interaction energy between graphenes and Si NWs. Figure 8a illustrates the interaction between Si NWs and graphenes with various widths. The Si NW with 7 Å radius and 54.307 Å length is doped with 1% P element. The graphenes have the same length, and their widths vary from 16.937 to 50.408 Å. After simulation, the graphenes scroll onto Si NWs partially to almost totally. The interaction energies between Si NW and various widths graphenes are plotted in Figure 8b, and the interaction energies increase linearly with the increasing widths. Since the contact area will increase with increasing graphene width, we plot the interaction energies per width changing with graphene width, as shown in Figure 8c, and the interaction energies per width almost keep constant. From Figure 8b,c, we can observe that the graphene width has no influence on the process of the graphene self-scrolling onto Si NWs at all. (4). Graphene Nanoribbon Chirality Effect. As we know, the chirality of graphene has a significant effect on the properties of graphene, while the chirality of graphene can vary its type from metallic to semiconductor. To investigate the effect of chirality on the mechanical properties of the composite system, we perform the Si NWs doped P interacting with graphenes of different chiralities and similar parameters. Figure 9a shows the graphene sheets with different chiralities before simulations and the core/ shell composite nanostructures formed after the MD simulations. 15220
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Figure 5. (af) Final structures formed by 5 Å Si NWs and graphene nanoribbons of various lengths (21.567, 32.226, 44.862, 62.638, 71.295, 100.921 Å) and same width 34.663 Å. (g) Variation of interaction energies following the increase of the graphene nanoribbon length.
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Figure 7. (a) Final structure formed by 8 Å Si NW and graphene nanoribbon (34.659 Å 84.879 Å). (b) Si and C atoms concentration profile of (a). (c) Final structure formed by 8 Å Si NW and graphene nanoribbon (34.659 Å 120.608 Å). (d) Si and C atoms concentration profile of (c).
From Figure 9a we can observe that different CNSs are formed by rolling up different chiral graphenes and the formed CNSs exhibit the single-wall CNT (SWNT) structure with different chiralities. To clarify the influence of the chirality on adhesion of this core/ shell composite structure, we calculate the interaction energies between the P doped Si NWs and the graphenes with different chiralities shown in Figure 9b. Herein, we find that following the increase of the chiral angle, the interaction energies of the core/shell nanostructures decrease visibly. To detect the mechanism of the chiral effect on interaction energy, we detect the topological unit of the chairl graphene as shown in Figure 10a. In Figure 10a, the chairl angle is θ, and the angles R, β, and γ depend on the chairl angle. We define L as the projection of CC bond along the rolling direction. L ¼ 2ðcos R þ sin β þ cos γÞ R ¼ θ þ 30°, β ¼ θ, γ ¼ 30° θ L ¼ 2ðcos R þ sin β þ cos γÞ ¼ 2½cosð30° þ θÞ þ sin θ þ cosð30° θÞ ¼ 2½cos 30°cos θ sin 30°sin θ þ sin θ þ cos 30°cos θ þ sin 30°sin θ ¼ 4cosðθ 30°Þ
Figure 6. (af) Final structures formed by 8 Å Si NWs and graphene nanoribbons of various lengths (35.439, 49.805, 65.202, 84.879, 100.937, 120.608 Å) and same width 34.659 Å. (b) Variation of interaction energies following the increase of the length of the graphene nanoribbons.
With the angles we can calculate the project vertical to the radical orientation of all six CC bonding as shown in Table 3 and Figure 10b. It is obvious that the L magnitude represents the obstacle that needs to be overcome in the self-scrolling process. When activated by the same Si NWs, graphenes with different chiralities having different L will lead to the change of the NS radius, and as a result, the interaction energies change. As a result, the armchair scrolls are the most stable configuration. 15221
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Figure 8. (a) Final structures formed by the same Si NW (7 Å radius and 54.307 Å length) and graphene nanoribbons of various widths from 16.937 to 50.408 Å. (b) Variation of interaction energies following the increase of the width of the graphene nanoribbons. (c) Interaction energies per width following the increase of the width of the graphene nanoribbons.
Figure 9. (a) Various chiral graphene nanoribbons (chiral angle varying from 0° to 30°) and final structures formed by the same Si NW and graphene nanoribbons of various chiralities. (b) Variation of interaction energies between 1% P doped Si NWs and different chiral graphene nanoribbons with similar parameters.
Besides, during our simulation we find another interesting phenomenon that all the other chiral scrolls tend to convert into
armchair. We take the 20° chairl NS as the example shown in Figure 11; the red C atoms are symbolized to illustrate the 15222
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Figure 10. (a) Topological unit of the chiral graphene nanoribbon. (b) Change of L following the change of the chirality.
Table 3. Project Vertical to the Radical Orientation of All Six CC Bonding armchair R/° 30
5°
10°
15°
20°
25°
zigzag
35
40
45
50
55
60
β/°
0
5
10
15
20
25
30
γ/°
30
25
20
15
10
5
0
3.9848
4.0000
L
3.4641
3.6252
3.7588
3.8637
3.9392
conversion. Considering the topology units of the different chiral graphene nanoribbons, the conversion is acceptable. The armchairl graphene nanoribbons conquer the least elastic energies in the self-scrolling process, and as a result, the radius of the NS becomes smaller after the conversion which leds to bigger interaction energies and more stable structure. This is the rough description of the mechanism of the chiral-induced conversion. So we can conclude that the armchair ones are the most stable configuration while chiral scrolls are unstable and tend to evolve into armchairs. Moreover, a similar phenomenon is also found in other NS structures. Eric Perim et al.52 demonstrated that the armchair boron nitride nanoscrolls (BNNSs) are the most stable configuration while chiral scrolls are unstable and tend to evolve into zigzag or armchair configurations depending on their initial geometries. Herein, when can see that the two works confirm each other well, in the mean time they also provide us a better understanding of the chiral effect on graphenes.
4. CONCLUSION In conclusion, we demonstrate that P-doped Si NWs can activate the self-scrolling of graphene nanoribbons around the P-doped Si NWs and then form one-dimensional core/shell nanoscale heterojunction composite. The interfacial properties and the relevant mechanisms of the core/shell heterojunction are studied including the length, width, and chirality of graphene nanoribbons and diameter of Si NWs. It is found that the van der vdW force plays an important role in the formation of the C/Si core/shell composite nanostructures. The simulations show that graphene sheets can fully self-scroll onto Si NWs when the Si NW radius is larger than a threshold of about 5 Å, forming a stable core/shell stucture. The final NS becomes multiwalled with increasing graphene nanoribbon length when the diameter of the Si NWs is larger than a threshold of about 6 Å. The armchair-NS is proved to be the most stable while chiral NSs are unstable and tend to evolve into armchairs, and a model is set up to interpret the tendency from the standpoint of bond. It is demonstrated that the graphene width has no influence on the self-scrolling process at all. Using this method all kinds of new
Figure 11. (a) Si NW and 20° chiral graphene nanoribbon before dynamics. (b) Final structure of the composition formed by Si NW and 20° chiral graphene nanoribbon.
core/shell C/Si heterojunctions, including PN, PP, NN C/ Si heterojunctions, can be fabricated. Due to the unique electronic properties of graphene nanoribbons and large surface-to-volume ratio, the new types of C/Si heterojunctions may be used as highspeed switching devices, optoelectronic devices, solar cells, chemical and biological sensors, and so on.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work is supported by the Natural Science Foundation of China (10974258), the Program for New Century Excellent Talents in Universities (NCET-08-0844), the Natural Science Foundation of Shandong province (ZR2010AL009), and the Fundamental Research Funds for the Central Universities (10CX05001A). ’ REFERENCES (1) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6 (3), 183–191. (2) Novoselov, K. S.; Jiang, Z.; Zhang, Y.; Morozov, S. V.; Stormer, H. L.; Zeitler, U.; Maan, J. C.; Boebinger, G. S.; Kim, P.; Geim, A. K. Science 2007, 315 (5817), 1379–1379. (3) Hu, J. N.; Ruan, X. L.; Chen, Y. P. Nano Lett. 2009, 9 (7), 2730–2735. (4) Ghosh, S.; Calizo, I.; Teweldebrhan, D.; Pokatilov, E. P.; Nika, D. L.; Balandin, A. A.; Bao, W.; Miao, F.; Lau, C. N. Appl. Phys. Lett. 2008, 92 (15), 1519111–3. (5) Lee, C. G.; Wei, X. D.; Kysar, J. W.; Hone, J. Science 2008, 321 (5887), 385–388. (6) Son, Y. W.; Cohen, M. L.; Louie, S. G. Nature 2006, 444 (7117), 347–349. (7) Prezzi, D.; Varsano, D.; Ruini, A.; Marini, A.; Molinari, E. Phys. Rev. B 2008, 77 (4), 0414041–4. (8) Gorjizadeh, N.; Farajian, A. A.; Esfarjani, K.; Kawazoe, Y. Phys. Rev. B 2008, 78 (15), 1554271–6. (9) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306 (5696), 666–669. (10) Jiao, L.; Zhang, L.; Wang, X.; Diankov, G.; Dai, H. Nature 2009, 458 (7240), 877–880. (11) Kosynkin, D. V.; Higginbotham, A. L.; Sinitskii, A.; Lomeda, J. R.; Dimiev, A.; Price, B. K.; Tour, J. M. Nature 2009, 458 (7240), 872–876. (12) Son, Y. W.; Cohen, M. L.; Louie, S. G. Phys. Rev. Lett. 2006, 97 (21), 216803-1–4. € (13) Melinda, Y. H.; Ozyilmaz, B.; Zhang, Y.; Philip., K. Phys. Rev. Lett. 2007, 98 (20), 206805-1–4. 15223
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