Inducing Aromaticity Patterns and Tuning the Electronic Transport of Graphene Nanoribbons via Edge Design S. Fias*, F.J. Martin-Martinez, G. Van Lier, F. De Proft, P. Geerlings General Chemistry (ALGC), Free University Brussels (VUB) Pleinlaan 2, 1050 Brussels, Belgium,
[email protected] ABSTRACT Tuning the band gap of graphene nanoribbons (GNR) by chemical edge functionalization is a promising approach towards future electronic devices based on graphene. The band gap is closely related to the aromaticity distribution and therefore tailoring the aromaticity patterns is a rational way for controlling the band gap. In our work, it is shown how to control the aromaticity distribution and the bandgap in both armchair and zigzag GNRs. We perform periodic density functional theory (DFT) calculations on the electronic structure and the aromaticity distribution, using delocalization and geometry analysis methods like the sixcenter index (SCI) and the mean bond length (MBL). These results are compared with nonequilibrium Green’s function (NEGF) transport property calculations. We also provide a complete description of the relation between band gap, transport properties, and aromaticity distribution along these materials, based on DFT results and Clar’s sextet theory. Keywords: aromaticity, graphene nanoribbons, Clar’s sextet theory, band gap, transport properties.
1 INTRODUCTION With the appearance of new chemical and lithography techniques, it is possible to tailor graphene nanoribbons (GNRs) with desired dimensions and shapes. The electronic confinement arising from cutting of graphene into ribbons gives raise to new electronic properties and applications. One of the main features of interest for the development of novel electronic applications based on GNRs is the energy band gap. A moderate band gap, around 1eV, is convenient, but the band gap is very sensitive to the width of the ribbon and the chemistry of the edges.[1-3] Moreover, the band gap is closely related to the aromaticity distribution in the GNR,[1] and therefore the study of aromaticity is an appropriate way to understand the electronic properties of GNRs. Although aromaticity is not a directly measurable property, and a multitude of criteria have been put forward to quantify this phenomenon, all of them are in agreement for describing Clar systems, like GNRs. In order to apply GNRs for electronic applications, control of the band gap is crucial. So if the aromaticity patterns can be rationalized, the associated band gap of the
GNR could be tuned. When modifying the width, the edge geometry and the functionalization of the edges, we control the electronic confinement and we tune the band gap towards the desired electronic applications. In the present study, we tackle the oxygen (O) and fluorine (F) terminated armchair GNRs, together with zigzag GNRs functionalized with additional hydrogen atoms, in order to suggest different ways of tuning the aromaticity patterns. The six-centre index (SCI), and the mean bond length (MBL) have been used for this purpose. The effect of the different types of edge functionalization on the aromaticity patterns, its effect on the energy band gap, and its dependence on the width are investigated to provide a complete picture of the fundamental rules that underlie the existence of aromaticity patterns in GNRs.
2
COMPUTATIONAL DETAILS
In the present work, the Gaussian 09 package[4] has been used to perform DFT Periodic Boundary Conditions (PBC) calculations on the GNRs. Optimised geometries, as well as the electronic structure were obtained with the 631G* basis set using the Heyd-Scuseria-Ernzerhof functional (HSE06). In all the calculations spin-restricted, singlet ground state wave functions have been considered. For the geometry analysis, we calculated the mean bond length (MBL), a ring-average parameter that quantifies the ring size of graphitic systems:
in which x is the C–C bond length. To quantify the delocalization in the six-membered rings of GNRs we calculated the six-center index (SCI) by integrating the six-electron exchange function over the six atomic domains of the ring[5] :
where P is the charge and bond order density matrix and S the overlap matrix of the basis functions. The Greek symbols refer to the basis functions, and Pi is a permutation operator that generates 5! terms by interchanging the basis function labels µ to . The final SCI value is relative to benzene, which represents a value of 100 in the SCI.
The electronic transport properties are calculated using the Non-Equilibrium Green’s Function (NEGF) formalism in conjunction with Density Functional Tight Binding (DFTB) implemented in the Atomistix ToolKit (ATK).[6] The notation of GNRs width uses the number of dimer lines across the ribbon width (Na). Similarly, zigzag GNRs are noted using the number of lines of hexagonal rings across the ribbon width (denoted as Nz).
Incomplete Clar
Clar
Kekulé
3 RESULTS AND DISCUSSION 3.1 Aromaticity pattern in armchair GNRs Armchair GNRs are not geometrically uniform, but they present distinct geometrical patterns. Such patterning appears also in the aromaticity distribution and depends on the width. Three different classes of patterns appear periodically every three steps as the width of the ribbon is increased. The three types of aromaticity patterns are [1]: • Kekulé: less aromatic rings (larger MBL), by more-aromatic ones (smaller MBL). • Clar: more aromatic rings (smaller MBL), by less aromatic ones (larger MBL). • Incomplete-Clar: having a sort of channel rings in the middle, with almost equal values (and MBL) for all rings.
surrounded surrounded of uniform aromaticity
These three different patterns can be interpreted in terms of Clar’s sextet theory, which assumes that electronic configurations with a maximal number of Clar rings are preferred over the other possibilities. We find that three possible arrangements of Clar rings are possible, depending on the position in which the first Clar ring is placed (Figure 1). In the case of the incomplete Clar GNRs, all three possibilities have the same number of Clar rings, resulting in a structure which is a mixture of the three, with a small bond differentiation. For the Clarr GNR, only one of the possible distributions presents maximal Clar coverage, giving raise to its aromaticity pattern. Finally, in the Kekulé GNR, two configurations have a maximal number of Clar rings, leading to an alternation of shorter and longer bonds in each ring, which ends up in a Kekulé arrangement. The periodicity in the arromaticity pattern is related to the pattern in the band gap. (Figure 2) The incomplete-Clar patterns have the smallest band gap, while the Kekulé arrangement have the largest one. The aromaticity values for the incomplete-Clar patterns are quite uniform in the middle part of the ribbon. This sort of channel in the middle might be the reason why its electronic structure is closer to a metallic behavior (smallest band gap). In contrast, in the case of Kekulé structures, electrons are mainly localized in the double bonds along the geometry, and thus the band gap is larger. Somewhere in between are the Clar structures, in which the electrons are delocalized in individual rings, which is a situation in between the two other extremes, resulting in a band gap in between the incomplete-Clar and Kekulé values.
Figure 1. The possible distributions of Clar rings for Na=1719. Representations leading to the final geometry are denoted with red lines. The final Clar ring configuration is related to the MBL (red to blue) and SCI (blue).
3.2 Edge functionalization of armchair GNRs 3.2.1.
Oxygen Functionalzation
Figure 2 shows the calculated band gap values (eV) of one-edge O-GNRs (light red), two-edge O-GNRs (dark red) and two-edge H-GNRs (blue). It is clearly noticeable how the width-dependant trend of the band gap is shifted in phase as we add oxygen to the edge.
Figure 2. Calculated band gap (eV) of one-edge O-GNRs (light red), two-edge O-GNRs (dark red) and two-edge HGNRs (blue), for Na = 4-22. The reason for this shift is that when carbonyl groups are added to an edge of the GNR, the only ‘reasonable’ resonance structures are those with C=O double bonds at the edge, disabling the possible localization of electron sextets and destroying the aromaticity of these rings. In
consequence, the distribution of the aromatic rings is equivalent to the H-GNR with one rows of carbon atoms erased (Na-1). This shifting of the aromatic pattern is also seen in the SCI values, where the aromaticity of the external rings almost decreases to zero (Figure 3).
H (2 edges)
O (1 edge)
Figure 3. SCI of O-GNRs with the top edge oxygenated (bottom) in comparison with H-GNRs (top). 3.2.2.
homogeneous and decreased aromaticity through the edge. Concerning incomplete-Clar GNRs, the values of the MBL and SCI for the different rings change with respect to the Hterminated ribbon. The central region that used to be homogeneous and less aromatic than the surrounding rings is now homogeneous but more aromatic. Therefore, although the overall pattern remains, the local values of the different rings are inverted with respect to the pattern of the H-terminated GNRs. The change in the pattern of incomplete-Clar and Kekulé classes of the F-GNRs can be explained using Clar’s sextet theory together with the mesomeric effect of the fluorine atoms. In contrast with the O atoms, F atoms do not disable the delocalisation of the electrons in the edgerings, but the mesomeric effect does allows one to write resonancestructures in which the aromaticity of the Clar rings close to the edge are broken (the shadowed rings in configurations 2 and 3 in Fig. 4). This leads to ‘noneffective’ Clar rings, leading to a different mixture of the clar configurations (Fig. 5).
Fluorene functionalization
When functionalizing the armchair GNRs with fluorine, no radical shift in the aromaticity pattern or the band gap is observed. The structures remain in the same class as the Hterminated ribbons, but the Clarr class now has the larger band gaps, while the band gap of Kekulé structures decreases when both sides are F-functionalised.[2] The aromaticity pattern of the Clar class is almost the same as the H-GNRs. In the Kelulé class, the pattern presents different aromaticity values at the edges, showing a
Figure 5. The possible distributions of Clar rings for Na = 14-16 F-GNRs. Non-effective Clar rings are shadowed in grey. The final Clar ring configuration is compared with the SCI.
3.3 Edge functionalization of zigzag GNRs
Figure 4. F-mesomeric effect at the edges of the three possible Clar representations for armchair F-GNRs. Aromatic rings affected by the mechanism are shadowed in grey. The final structures are encircled with dashed lines.
Zigzag GNRs present uniform geometries where all hexagonal rings are almost equivalent with equal size and aromaticity. This uniform aromaticity distribution also explains the zero band gap in these GNRs. The reason for the uniformity can be found using Clar’s sextet theory, where the three possible configurations have the same number of Clar rings giving a uniform structure[3]. Functionalizing one out of three positions at the edge with additional hydrogens will avoid the presence of a Clar sextet in the functionalized ring end thus break the uniformity and open up the band gap.
un
Figure 8 shows the I-V curves of GZ-8 for different functinalizations (additional hydrogen, AH; Oxygen, O and Carbon deletion, CD). GZ-8 itself is a metallic conductor, having a linear I-V curve. On the other hand, the functionalized GZ-8 GNRs (AH, CD and O) behave like semiconductors. Systems with a Clar type aromaticity pattern start conducting at a lower bias than systems with a Kekulé type pattern, as expected from the values of their band gaps. This allows the ad hoc design of semiconductors based on zigzag GNRs with different ‘on-voltages’, as needed for a desired application.
Figure 6. The three possible distributions of Clar rings in GZ-8 GNR functionalized with additional hydrogen. Penalized Clar rings are in red. The final structure is highlighted in a green box (on the right). Figure 6 shows the unit cell for a GNR (Nz=8) functionalized with additional hydrogen atoms (AH). There are two different arrangements for the one out of three AH functionalization. In these two arrangements, the three different Clar’s sextet configurations are affected differently. In the first arrangement (Fig. 6a) the additional hydrogen atoms coincide with the location of Clar sextets in two of these configurations. Therefore these configurations are penalized and contribute less to the final structure. The final structure corresponds mainly with the pattern with the maximal number of Clar rings. When the functionalization is done in the second arrangement (Fig. 6b), only one of the three configurations is penalized, and the combination of the two remaining configurations gives a Kekulé structure. Figure 7 shows the band gap of all AH functionalized zigzag GNRs with Nz from 4 to 9. The values describe a zigzag-shaped curve as we increase the width of the ribbon, switching between a Clar and Kekulé patterns. All the values in the upper part of the graph coincide with Kekulé structures, while the values below correspond to the Clar GNRs. It is clear that Kekulé-patterned GNRs always present higher band gap values.
Figure 7. Band gap of the zigzag AH-GNRs under study.
Figure 8. The I-V curves of all the investigated GZ-8 GNR.
4
CONCLUSIONS
Edge functionalisation is one of the most suitable ways for controlling the band gap of GNRs towards their application in electronic devices. Due to the close relation between the band gap and the aromaticity distribution in these nanomaterials, understanding the aromaticity patterns is essential to perform a rational control of the band gap. In the present study we show how different edge functionalisation implies different aromaticity patterns, in both armchair and zigzag GNRs, that results in different band gap values. Even more, we provided a general model, based on Clar’s sextet theory, on how edge effects affect the aromaticity distribution, and therefore how is it possible to control the aromaticity patterns, band gap and transport properties using different functional groups.
REFERENCES [1] F. J. Martín-Martínez, S. Fias, G. Van Lier, F. De Proft and P. Geerlings, Chem. Eur. J., 18, 6183-6194, 2012. [2] F. J. Martín-Martínez, S. Fias, G. Van Lier, F. De Proft and P. Geerlings, P. Phys. Chem. Chem. Phys., 15, 12637-12647, 2013. [3] F. J. Martín-Martínez, S. Fias, B. Hajgató, G. Van Lier, F. De Proft and P. Geerlings, J. Phys. Chem. C, 117, 26371–26384, 2013. [4] M. J. T. Frisch et al. , Gaussian, Inc., Wallingford CT, Revision A.1 edn., 2009. [5] P. Bultinck, R. Ponec and S. Van Damme, J. Phys Org Chem, 18, 706-718, 2005. [6] Atomistix ToolKit version 12.8.2, QuantumWise A/S (www.quantumwise.com).
