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Figure 1: Equilibrium and transition state geometries for oxygen on graphene. The left configuration corresponds to the equilibrium structure (labeled ‘E’ in Fig. 2) and the right configuration to the transition state (Labeled ‘T’ in Fig. 2).

Using Density Functional Theory, we measured changes in the energy barrier of diffusion for oxygen on graphene after adding or removing charge from the system. We found that the diffusion barrier was influenced greatly by the change in charge; specifically, electron doping lowered the barrier substantially. This knowledge can facilitate the production of chemically functionalized graphene nano-electronics.

Gate Voltage Control of Oxygen Diffusion on Graphene

Since its discovery in 2004, graphene has generated a great deal of interest in physics and materials science. Graphene, which is an atomically thick layer of graphite, has a unique 2-dimensional geometry. Due to its unique symmetry, graphene is 100x stronger per gram than steel[1], has extremely high electron mobility (up to 15,000 cm2 V-1 s-1 in ambient conditions[2]) and has extraordinary thermal conductivity (twice that of diamond). Due to Carbon’s affinity for tetrahedral bonding, its surface is amenable to making other interesting 2D crystals such as graphene fluoride, graphene oxide, and graphane[3,4]. Its potential applications in transistors, transparent conductors, molecular sensors, and more are so far reaching that its discoverers, Andre Geim and Konstantin Novoselov, were awarded the 2010 Nobel Prize in physics.

Since graphene is exclusively a surface, it is highly susceptible to interactions with other atoms. Our research focuses on the attachment and diffusion of different atomic species to the surface of graphene using Density Functional Theory (DFT) algorithms running on the computing facilities at Penn State. We became particularly interested in the effect of doping on adatom diffusivity due to graphene’s ability to be ‘doped’ with electrons or holes on the fly with the application of a gate voltage. This allows charge to be added or removed from the graphene in a fully reversible fashion and without direct chemical modification. For this project, we focused on the diffusion of oxygen on graphene, due to its interesting adsorbed geometry (see Figure 1) and its role in catalysis and graphene oxide production.

Using Density Functional Theory, we calculated the energetics of diffusion for oxygen on a graphene surface containing different levels of charge. Since the simulation takes place in a periodic cell, a jellium background is added to the cell counteract the added charge and avoid a divergent potential. As seen in Figure 2, the barrier is reduced substantially when the graphene is electron doped. At a charge concentration of one electron per 50 carbon atoms (-7.64x1013 cm-2), the energy barrier is 80% lower than for neutral graphene. This leads to a diffusivity increase of at least nine orders of magnitude[5].

Configuration Energetics
Figure 2: The energetics for the configurations along the diffusion path. Different curves correspond to different doping levels on the graphene plane as noted in the legend. The adsorption barrier is ~0.73 eV and 0.15 eV for the neutral case and the 7.64x1013cm-2.

Studying the difference in electron density between the charged (-7.64x1013cm-2 in this case) and neutral systems as well as analyzing the relevant partial densities of states uncovered the reason behind this drastic effect. As shown in Figure 3, the charge is mostly distributed homogeneously across the graphene plane (on one of the carbon sublattices) in the equilibrium and transition states. Although there is a large oscillation of the charge near the oxygen adatom, a Mulliken analysis shows that the total charge on O deviates less than 2% between the charged and uncharged cells. This rules an unphysical scenario in which the oxygen would absorb most of the charge added to the system. Figure 4 shows the underlying cause for our observed energy barrier change as elucidated by the partial densities of states. The left plots show the equilibrium state configuration for both the neutral (a) and charged (b) configurations. Since oxygen settles in a ‘bridge’ configuration between two carbon atoms, the states just above the fermi level show the anti-bonding mixing states between the pz orbitals of the oxygen and neighboring carbon atoms. Upon charging, these states become partially filled, weakening the CO bonds in the system. On the right plots, ( (b) & (d) ) we see a different effect due to the gometry of the transition state. Since the oxygen is directly above a carbon atom in this case, a bonding state is created between the pz orbital of the oxygen and the pz orbitals of the three carbon atoms neighboring the carbon bonded to the oxygen. This bonding peak actually appears just above the fermi level when the system is neutral. Upon charging, these states become partially filled (and even develop a magnetic moment), which strengthen the bond at the transition state.

Charge Density
Figure 3: Charge density difference between the 7.64x1013cm-2 electron doped neutral cells. Of note is the homogeneous distribution charge along the graphene plane, focused on one graphene sublattice.

DOS
Figure 4: The total density of states as well as the partial densities of states corresponding to the px and pz oxyeben orbitals as a function of energy measured from the Fermi level. Panels a) and c) show the equilibrium state for the neutral plane and the electron doped (-7.64 × 1013cm-2) plane respectively. Panels b) and d) correspond to the neutral and electron doped (-7.64 × 1013cm-2 ) transition states respectively. The partial densities are rescaled for clarity.

This discovery can further facilitate the production of chemically functionalized graphene nano-electronics. Specifically, this will allow further control of how adatoms are ordered on graphene, which can yield complete circuits built from ‘nano-roads’[6] of graphene embedded in an insulating matrix of graphane, graphene oxide, or fluorinated graphene. This type of circuit could eliminate many bottlenecks seen in the semiconductor industry today, such as contact resistance and quantum tunnelling issues which arise as CPU feature sizes continue to shrink.

References
[1] Lee, C. et al. (2008). "Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene". Science 321 (5887): 385
[2] Geim, A. K. and Novoselov, K. S. (2007). "The rise of graphene". Nature Materials 6 (3): 183–191.
[3] J.?O. Sofo, A.?S. Chaudhari, and G.?D. Barber, ”Graphane: a two-dimensional hydrocarbon”. Phys. Rev. B 75, 153401 (2007).
[4] D. C. Elias,R. R. Nair, et al. ”Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane”. Science 30 January 2009: 323 (5914), 610-613.
[5] A. M. Suarez, L. R. Radovic, E. Bar-Ziv and J. O. Sofo, "Gate Voltage Control of Oxygen Diffusion on Graphene". to appear in Phys. Rev. Lett. (2011)
[6] Singh, A. K.; Yakobson, B. I. “Electronics and magnetism of patterned graphene nanoroads”. Nano Lett. 2009, 9, 1540–1543.

Acknowledgements
Data was acquired and summary written by Alejandro Suarez. This work is funded by the Donors of the American Chemical Society Petroleum Research Fund as well as by the US-Israel Binational Science Foundation grant 2006238 in collaboration with Prof. Ezra Bar-Ziv at the Ben-Gurion University of the Negev. Supercomputing facilities used were funded in part by the Materials Simulation Center, a Penn-State MRSEC/MRI facility, and through instrumentation funded by the National Science Foundation (grant OCI-0821527).

Publications

2011 · All
A. M. Suarez, L. R. Radovic, E. Bar-Ziv and J. O. Sofo, "Gate Voltage Control of Oxygen Diffusion on Graphene," Phys. Rev. Lett. 106, 146802 (2011) Abstract/Comments
L. R. Radovic, A. M. Suarez, F. Vallejos-Burgos and J. O. Sofo, "Oxygen Migration on the Graphene Surface. 2. Thermochemistry of Basal-Plane Diffusion (Hopping)," Carbon 49, 4226 – 4238 (2011)
J. O. Sofo : Gate Voltage Control of Oxygen Diffusion on Graphene