Detection of hydrogen using graphene
© Ehemann et al; licensee Springer. 2012
Received: 3 November 2011
Accepted: 23 March 2012
Published: 23 March 2012
Irradiation dynamics of a single graphene sheet bombarded by hydrogen atoms is studied in the incident energy range of 0.1 to 200 eV. Results for reflection, transmission, and adsorption probabilities, as well as effects of a single adsorbed atom to the electronic properties of graphene, are obtained by the quantum-classical Monte Carlo molecular dynamics within a self-consistent-charge-density functional tight binding formalism We compare these results with those, distinctly different, obtained by the classical molecular dynamics.
PACS: 61.80.Az, 61.48.Gh, 61.80.Jh, 34.50.Dy.
KeywordsGraphene DFTB Hydrogen detection HOMO-LUMO gap Molecular dynamics
The sp2 hybridized carbon allotrope, graphene, has recently shown particular promise in applications such as nanoscale electronics, hydrogen storage , and nanosensors. This is due to the material's outstanding thermal and electronic properties. The sensitivity of the electronic properties of a single graphene sheet to small defects in its 2-D crystal structure and chemical composition indicates a possibility of its application as a few-particle detector [2–4]. Graphene-based electronics in space vehicles might also be sensitive to the damages caused by cosmic radiation containing a wide spectrum of particles, a significant component of which would be light atoms from the solar wind. The significance of studies of graphene bombarded by hydrogenic atoms in understanding the damages of the CFC carbon tiles in the divertor of a fusion reactor (ITER) to the plasma irradiation has also been stressed recently [5, 6]. These defects include lattice defects, with possible creation of vacancies, as well as chemical changes induced by the hydrogen sticking to the lattice [7, 8]. The resultant changes in the electronic conductance due to changes in the electronic structure have also been studied [3, 9]. For example, work by Deretzis et al.  has shown that even single vacancy deformations in graphene nanoribbons can have measurable effects on the material's conduction properties. These applications all motivate our study of energetic particle impact with graphene.
In this paper, we study the perpendicular impact of hydrogen on a single graphene sheet over more than three decades of impact energies (0.1 to 200 eV) using methods of quantum-classical Monte Carlo molecular dynamics. Our approach is described in detail in the second section entitled 'Methods'. The irradiated target was an infinite graphene sheet obtained by applying 2-D periodic boundary conditions to a graphene cell of size 29.12 × 28.53 Å (336 C atoms). The graphene was prepared at a temperature of 300 K by a Nose-Hoover thermostat and left free during each collision event, which lasted 200 to 500 fs, depending on the impact energy. The irradiation was performed by more than 1,000 independent trajectories for each impact energy, with randomly chosen position of emission of an atom above the surface of the graphene cell. In this method, the total electronic energy of the system is solved quantum-mechanically at the beginning of each time step (on the order of a femtosecond), maintaining fixed atom positions; after incorporating the nucleus-nucleus interaction into the total electronic energy, forces on each atom are updated, and the atoms are moved classically within the time step. The electronic structure is solved here by the self-consistent-charge-density functional tight binding (SCC-DFTB) method [10–12]. To allow for the high-energy impact, we fit the original SCC-DFTB parameters  at close distances (< 0.2 Å) to the binary Ziegler-Biersack-Littmark (ZBL)  repulsive potentials.
Results for reflection and transmission probabilities, angular distributions, and adsorption probabilities at low energies (0.1 to 1 eV) are shown and analyzed in the first part of the 'Results and discussion' section, entitled 'Irradiation dynamics and effects on electronic structure'. Additionally, changes in the molecular orbital levels close to the Fermi energy, which influence the non-equilibrium ballistic electron transport properties (i.e., the electric conductance) of the system, are calculated and characterized by the changes, ∆E l-h , in the difference, E l-h , of the (discrete) lowest unoccupied molecular orbital and highest occupied molecular orbital energies in response to the hydrogen adsorption. These changes are indicative of possible changes in the graphene sheet conductance. They are, surprisingly, on the order of 1 eV and depend on the vibrational energy of the adsorbed hydrogen. Adsorption occurs only for the low-energy impacts (< 1 eV). This confirms some predictions in literature on the extreme sensitivity of the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap and transport properties of graphene and SWCNT to the adsorption of hydrogen and other atoms and molecules [15–19].
In the second part of the 'Results and discussion' section entitled 'Comparison with classical molecular dynamics', we perform classical molecular dynamics (CMD) calculations with two state-of-the-art bond order hydrocarbon potentials, reactive empirical bond-order (REBO)  and adaptive intermolecular reactive empirical bond order (AIREBO) . We use the corrected set of the classical potentials  to allow high impact energies and compare the classical MD probabilities with our quantum-classical results. Although CMD with these potentials is significantly faster than SCC-DFTB, allowing for longer timescales, larger systems, and greater energy ranges to be studied, it turns out that the classical potentials are of limited applicability for the studied system and dynamics. We hope that this data motivates improvements to these potentials since their speed is very attractive for radiation damage-type problems. Our conclusions are given in the final section.
To simulate effects of irradiation on graphene, one can apply direct molecular dynamics methods in which electronic structure is treated explicitly using quantum mechanics, while the motion of the nuclei is described by the means of the classical dynamics. This allows one to accurately describe bond breaking and formation as well as the interatomic potentials. Such an approach is, however, computationally very expensive, which greatly limits the system sizes, timescales, and choice of quantum mechanics-based methods. To mimic the dynamics observed by experiment, we apply a Monte Carlo approach to the trajectories, i.e., using a large number of trajectories, randomly varying 'impact parameters' to obtain acceptable statistics of the collision events. Even using this approach, we must use a less expensive and more approximate quantum-mechanical approach. Here, we use the SCC-DFTB method, an approximate density functional theory (DFT) method in which only valence electron interactions are considered. Although a full DFT treatment would be ideal, this is currently too expensive computationally, even for a handful of trajectories. In SCC-DFTB, the total electronic densities and energies are expressed by solution of the Schrodinger equation in the Kohn-Sham form, using predetermined Hamiltonian and overlap integrals as well as repulsive splines fit to reference systems (so-called Slater-Koster parameters). The tight binding methods applied to the large (solid-state) systems have a long history. Here, we use a self-consistent charge version developed by Bremen Group (Bremen, Germany) [10–12]. SCC is a second-order correction term in the DFTB total energy involving interactions between localized fluctuations of the electron density; it uses an iterative procedure to converge on the new electron density at each time step. In this SCC-DFTB method, spin polarization is neglected. We employed a Fermi-Dirac smearing with electronic temperature Tel = 1,000 K, which has a similar effect to averaging over many electronic states near the Fermi level.
Notably, there are two bonding regions in the H-graphene potential. For incidence directly upon a lattice carbon, the potential minimum occurs at approximately 1.1 Å, while incidence upon a C-C bond center shows a shallower potential with minimum close to 1.0 Å. Indeed, there are many potential wells in the 3-D multibody potential that are responsible for capturing impinging hydrogen atoms; these will later be shown to have an effect on the electronic structure of resultant H-graphene surfaces. There are repulsive barriers at the bond center and hexagon center of heights 17 and 2.5 eV, respectively. Notably, hydrogen encounters no barrier before entering the potential well when incident directly on a lattice carbon.
About ten per decade incident kinetic energies ranging from 0.1 to 200 eV are considered for the impinging hydrogen atom. While cumulative bombardment is not investigated, 1,008 single impact simulations are performed for each incident energy; this is achieved using 1,008 processors, one for each trajectory, on the Kraken Cray XT5 supercomputer (National Institute of Computational Sciences, University of Tennessee, Knoxville, TN, USA). The target graphene surface described in the 'Background' is situated in the z = 0 plane and periodically extended in the xy coordinate plane. To simulate the bombardment in a real-world environment, the sample is thermostated (via Nose-Hoover scheme) to 300 K before bombardment and left to evolve freely during approximately 0.1 to 1 ps (depending on incident energy) simulation time. The impinging hydrogen atom is released from a random (x, y) position in the z = 10 Å plane, with velocity perpendicular to the graphene sheet.
Results and discussion
Irradiation dynamics and effects on electronic structure
By examining the position within the hexagon where incident atoms are reflected, transmitted, or adsorbed, one can infer the form of the many-body potential at nonsymmetrical parts of the lattice. Figure 4 shows the hexagon-localized reflection, transmission, and adsorption for several energies. Lattice positions represented in Figure 4 are the turning points for reflection, closest approach positions for transmission, and final x-y positions for adsorption. Adsorbed atoms are clustered around the carbon atoms, often showing some lateral vibration.
Reflection is distributed evenly around the perimeter of the hexagon, indicating that incident atoms are deflected away from the hexagon center due to the relatively low force experienced here. Also due to the weak interaction at the hexagon center, it is the most probable location for transmission to occur. Thus, atoms incident upon or deflected toward this position are both able to penetrate. These results agree with those from a previous study , which found that reflection occurs at all points in the hexagon, and transmission is most probable near the hexagon center.
Here, 1/Nmax normalizes the distribution, and the differential solid angle d Ω becomes 2π sin θ dθ due to the azimultal symmetry of the problem. N(θ ± Δθ/2) is the number of atoms scattered into a bin of width Δθ centered at polar angle θ.
Small changes in the x- or y-components of an atom's linear momentum are much more visible for low incident energies, where these changes can be comparable to the initial momentum. In the SCC-DFTB simulations, atoms with such low incident energy tend to reflect when not adsorbed, and the reflected angular distribution shows much more scattering. Transmitting hydrogen atoms in these simulations tend to have higher incident energies, so the small x- or y-forces don't produce a significant angular displacement of their momenta. While atoms incident at 5 and 10 eV have a wider distribution than at the higher energies, they tend to penetrate only near the center, where the H-C interactions are weakest.
The dominance of adsorption in SCC-DFTB simulations at impact energies below 1 eV provides enough statistical weight for an investigation of the effects of H-adsorption on the E l-h quantity of the affected graphene. However, roughly a third of the incident atoms are found to bond to the surface after initially being reflected at a large angle relative to their initial momenta. These 'wandering' hydrogen atoms, primarily seen at 0.5 eV incidence, generally drift above the graphene surface at a distance of about 3 Å for 2 to 5 fs before falling toward a lattice carbon and adsorbing. Roughly 10% of these 'wanderers' do not bond to a carbon within the simulation time. Therefore, while they are counted as adsorbed in Figure 3, they are ignored in the henceforth analysis to reduce uncertainties.
The graphene band gap is often computed using a band structure or density of states calculation. However, the graphene system studied here is subject to thermal motion as well as bombardment, and the impinging particle should not be included in Brillouin zone integration. As discussed earlier, we simply define a quantity E l-h by subtracting the energy of the highest occupied orbital from that of the lowest unoccupied orbital. The 1,000-K electronic temperature used creates a 'smearing' of the orbital occupations near the Fermi level. We use occupations of 1.8 for h (analogous to the HOMO) and 0.2 for l (analogous to the LUMO). This allows us to accomplish significant statistics while accounting for the different sites of adsorption and variety of vibrational states in which atom is adsorbed. The system is a 336-atom supercell, equivalent to an 18 × 18 × 1 k-point grid.
One can see that the standard deviation, representative of the distribution's width, is higher for low averaging times. Additionally, atoms incident with higher kinetic energy are adsorbed with greater vibrational energy, so they display a wider distribution of z-positions. As shown in Figure 7, the wider distributions that come with this higher vibrational energy produce a smaller change in the E l-h on average.
Comparison with classical molecular dynamics
In the classical molecular dynamics approach, the physical accuracy of the simulation is determined mainly by the quality of the interatomic potentials. Like its predecessor, the REBO potential, AIREBO is a member of the classical bond-order family of potentials [20, 21] of the Tersoff-Brenner type, which provides a good description of the covalent bonds for nonpolar systems. The REBO potential is short ranged (< 2 Å) and, therefore, considerably less costly to use in computation but might not be suitable for collisions where long-range interactions are important, or for describing the coupling of adjacent graphene planes. REBO is also known for its poor treatment of conjugated couplings . The AIREBO contains improved descriptions of the torsional and long-range van der Waals interactions (< 11 Å) as well as improved bonding interactions. The ability to use a classical (if reactive) molecular dynamics approach for the bombardment problem is highly desirable since these approaches are orders of magnitude computationally cheaper than even SCC-DFTB.
Understanding the effects of irradiation is paramount in developing graphene-based nanosensors and nanoelectronics. Thus, in this work, simulations of single-layer graphene bombarded by hydrogen atoms for a wide range of incident energies were carried out using quantum-classical molecular dynamics based on the self-consistent-charge-density functional tight binding method for treatment of the electron dynamics, combined with classical dynamics of the nuclei. The effects of this bombardment on the graphene sheet and the scattered particle distributions were analyzed in terms of reflection, transmission, and adsorption probabilities and angular distributions. Particularly significant effects of adsorption on the graphene E l-h quantity, analogous to the HOMO-LUMO gap in clusters, were investigated, predicting a notable change of the graphene electrical conductivity for even one H-atom chemisorbed. Adsorption was found to be the dominant process below 1 eV, with transmission dominating above 20 eV and reflection dominating at the intermediate energies. Reflection was found to have a more significant scattering effect than transmission.
A comparison between results of the SCC-DFTB simulations and classical MD simulations employing the AIREBO potential was made, showing a significant difference in the calculated probabilities and chemistry, mainly caused by differences in the multibody potentials. The AIREBO H-graphene potential overestimates (in comparison to SCC-DFTB) the interaction at the hexagon center (π-orbital) and C-C bond center (σ-orbital) lattice positions. A comparison of REBO and AIREBO showed that the overestimate is a result of the Lennard-Jones terms in AIREBO. The effect of this added repulsiveness permeated all of the dynamics, producing wider scattering, a much smaller adsorption probability, and nonzero sputtering yields. Refitting of these terms may significantly improve the accuracy of AIREBO.
Changes in the graphene E l-h quantity, qualitatively associated to the H-L gap and electric conductance of graphene, were found to depend on incident atom energy. Using an averaging time of 32 fs, in addition to averaging over all adsorbed trajectories, the adsorption effect on the E l-h differed by roughly 10 meV between incident energies. By virtue of higher vibrational energy, larger incident kinetic energies are found to have a smaller effect on the band gap, as shown in Figure 9. Further characterization of the E l-h changes and/or adsorbed vibrational modes could support the application of graphene in a hypersensitive slow single-particle detector in agreement with the sensitivity to a single biomolecule being coupled to a graphene sheet . This hypersensitivity of the E l-h quantity to hydrogen adsorption indicates that the functionality of graphene-based nanoelectronics could be adversely affected by the irradiation by light, chemically reactive species.
We acknowledge the support of the Offices of Fusion Energy Sciences (US DOE) (PSK) and the ORNL LDRD program (PSK and JD) as well as the ORISE SULI program (RCE). We acknowledge the support of the TG NSF program for the use of the NICS computer facilities (Kraken). JJ acknowledges the support by the SC/TN-EPSCoR grant. Research by PRCK was supported by the Scientific User Facilities Division, U.S. Department of Energy.
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