1. Graphene doping with single atoms – a theoretical survey of energy surface  Elad Segev and Amir Natan* Department of Physical Electronics , Electrical Engineering school, Tel-Aviv University
Graphene is a single atomic layer material made of carbon. Graphene layers are held together with Van der Waals forces to form Graphite – a material that is known for centuries and can be found in every pencil. Graphene single layer was first isolated in 2004 by Novoselov & Geim and since then there are already many graphene based applications.
Graphene band structure
Figures taken from Neto et al. Rev. Mod. Phys. 81, 109 (2009)
Single atom doping for band gap engineering. The adsorption of atoms, at the graphene surface, can alter by covalent bonding the band structure of the material. The challenge is to move the fermi level and open a gap without altering too much the good properties of graphene. The effect of single fluorine (F) atom adsorption on graphene is modeled with Density Functional Theory (DFT). These results are part of an article in preparation by Amir Natan and Tamar Seideman.
Graphene (left) and Graphite (right) – taken from Neto et al. Rev. Mod. Phys. 81, 109 (2009)
Graphene unique band structure makes it a semi-metal or a zero gap semiconductor. The dependence of electron energy on momentum shows a linear dispersion instead of the parabolic dispersion that exists in most semiconductors. This gives graphene unique conductance properties and other interesting effects.
Electrons in graphene behave like relativistic fermions with m=0 and C=VF ! VF~=106 m/sec
Figure taken from: “Application of Graphene to High-Speed Transistors: Expectations and Challenges”, Yasushi IYECHIKA
Adsorption of F atom on graphene super-cell – (left) 4x4 super-cell with 32 carbon atoms per 1 F atom. (right) – 7x7 super-cell with 98 carbon atoms per 1F atom. black solid lines shows the band structure of the modified graphene, red dashed line , shows a shifted pristine graphene band structure. band gap opening and fermi level shift are clearly demonstrated.
Clustering patterns of 2 F atoms above graphene
Conclusions and future work
We have shown that the second F atom has better adsorption energy at sites near the first F atom – this hints that atoms will tend to cluster. Furthermore, the results suggest that the second atom prefers sites of the other carbon atom – if the first atom is above carbon A then the second atom is above carbon B and vice versa. This in contrast to fully fluorinated graphene (F-GR) where all F on the same side are on the same carbon type.
Future work
As LDA can have mistakes in the total energy we plan to repeat the calculations with other functionals such as HSE and also use some more exact calculations such as GW for the band structure. Furthermore – we plan to check larger super-cells.
While we are checking also the adsorption of a 3rd atom it becomes increasingly not practical to check all configurations as the number of possibilities is growing exponentially with the number of atoms. We would use ab-initio molecular dynamics (MD) to scan the energy surface. Another possibility is to use simpler models for the total energy in combination with MD.
Current work was performed on a free standing graphene. To check possible effects of substrate one has to include the substrate in the simulation (e.g. Silicon-carbide).
4x4 super cell
(a)
5x5 super cell
(b)
Total energy DFT-LDA calculations for 2 fluorine atoms adsorption on single graphene layer.
Location of the first F atom is shown with a black diamond, total energy of the system with the 2nd F atom is shown by the color of the circle: green circles are low energy (favorable) while red circles are high energy (less favorable), empty blue circles are points with missing calculations. The total range of energy difference is about 0.8 eV.
The calculations were preformed on 4x4 super cell (a) and 5x5 super cell (b). Some of the points completed by symmetry considerations. Both the 4x4 and 5x5 cases show that the second F atom prefers
to be on the other type of atom – if first atom is A then second is B .
This is in contrast to F-GR where all F in a given side are on same type carbon ( A or B )
Graphene on silicon-carbide
2 far F atoms above a 5x5 super cell of graphene .
2 near F atoms above a 5x5 super cell of graphene
3 F atoms above a 5x5 super-cell *