Doping, Functionalization, and Permeability of Graphene: Insights from First-Principles Studies
Authors: Tsetseris Leonidas , Wang Bin , Pantelides Sokrates T 
Published: February 2020

Even though graphene is exceptional with respect to several physical properties,1 its employment in electronic devices often requires the modification of the material. For example, development of graphene-based transistors necessitates the controlled increase of the number of charge carriers.2 Other applications may employ graphene chemical derivatives with enhanced functionalities. Here we use density-functional theory (DFT) calculations to propose key processes that could dope3-5 or functionalize graphene.6 Furthermore, we demonstrate that graphene may be selectively permeable to certain atomic species.7

Previous studies have shown2 that nitrogen and boron atoms trapped at graphene mono-vacancies turn the material to n- and p-type, respectively. Actually, in the case of nitrogen, DFT studies5 have identified a multitude of configurations that are created when nitrogen precursors react with graphene vacancies or nano-ribbon edges. These N-induced structures can dope the material with either electrons or holes.5

Despite being the most plausible doping scenario, the replacement of a single carbon atom by a N or B dopant has shortcomings. In particular, mono-vacancies are mobile and tend to cluster into double- or multi-vacancies. Moreover, the number of suitable precursors for deposition of boron dopants is rather limited. Based on DFT calculations we have shown4 that efficient doping of graphene can be achieved when other group-III and group-V elements occupy stable double-vacancies. These dopant configurations dope graphene with holes without causing other significant changes in the electronic properties of the host system. Future studies can explore whether impurities trapped at larger vacancies may also act as dopants for graphene. In addition, atoms trapped at double- or multi-vacancies could play a similar role in other honeycomb-based two-dimensional systems.
An alternative way to inject carriers in graphene relates to the so-called molecular doping approach, wherein molecular adsorbates act as dopants. There are two key conditions that affect the efficiency of molecular doping: dopants ought to have significant adsorption binding energies on graphene; their adsorption should not modify the electronic profile of graphene drastically to avoid enhanced scattering of carriers. Our DFT studies3 have shown that ammonium groups fulfill the above conditions and are thus ideal molecular dopants for graphene. They physisorb on graphene with a large binding energy of more than 1 eV and they shift the Fermi level inside the valence band without changing the electronic density of states significantly, at least in the vicinity of EF.
Finally, an important aspect for the use of graphene in some applications is its well-known impermeability. We have examined this property for a number of prototype atomic impurities, namely hydrogen, oxygen, nitrogen, and boron atoms. Based on calculated DFT barriers, we find that the permeation of the first three types of atoms through a graphene is not activated, even at high temperatures. Surprisingly, however, the same process for a boron atom has an activation energy of only 1.3 eV, suggesting that graphene is selectively permeable for certain atomic species. This selectivity could have important ramifications for the evolution of impurities in graphene-based devices.
The work was supported by the McMinn Endowment at Vanderbilt University and Grant HDTRA 1-10-10016. The calculations used the EGEE and HellasGrid infrastructures.

References

[1] A. K. Geim, Science 324, 1530 (2009).[2] S. T. Pantelides et al., MRS Bull. 37, 1187 (2012).[3] L. Tsetseris and S. T. Pantelides, Phys. Rev. B 85, 155446 (2012).
[4] L. Tsetseris, B. Wang, and S. T. Pantelides, Phys. Rev. B 89, 035411 (2014).[5] B. Wang, L. Tsetseris, and S. T. Pantelides, J. Mater. Chem. A 1, 14927 (2013).
[6] L. Tsetseris and S. T. Pantelides, J. Mater. Sci. 47, 7571 (2012).
[7] L. Tsetseris and S. T. Pantelides, Carbon 67, 58 (2014).