Electronic properties of nanosize GNRs: the role of the anchoring groups

L. Álvarez de Cienfuegos*, S. Rodríguez-Bolívar†, F.M. Gómez Campos†, T. García†,

J.A. López-Villanueva†, J.E. Carceller†, A. Martín-Lasanta*, J.M. Cuerva*

Department of Organic Chemistry* and Department of Electronic and Computer Technology†

Faculty of Sciences, Campus Fuentenueva, University of Granada

Granada, Spain lac@ugr.es; rbolivar@ugr.es

E. Buñuel, Diego J. Cárdenas Department of Organic Chemistry C-I

UAM, Cantoblanco, E-28049 Madrid, Spain

Abstract—In this work we have studied the electronic behavior of organic molecules that could be considered as basic blocks of graphene nanoribbons. We have focused on the role that plays the molecule-metal contact. Thus, the influence of the number and positions of those contacts is analyzed. To carry out the calculation we have used the Density Functional Theory and Non-Equilibrium Green Functions Approach.

Keywords-component; molecular electronics, graphene nanoribbons, transmission, conductivity, eigenchannels

I. INTRODUCTION Molecular electronics is an exciting new nanotechnology

field which deals with the study and application of molecular building blocks for the fabrication of electronic devices.

In this context the knowledge about the nature and the strength of the electrode-molecule contact emerges as one of the key points for the future development of efficient and reliable organic-based nanodevices.

The consequences of joining a molecule with more than one linker group to the metallic electrode could be an increase in the conductivity of the whole system and a better mechanical stability, reducing the conformational changes and possible disconnections of the metallic electrode. This last fact would prevent instabilities in the current due to thermal or mechanical stress, and thus would make a more reliable system. However, although the importance of the interaction between the molecule and the electrode is great, there are scarce available data about the conductivity or the electronic properties of molecules which have more than one connection per metallic electrode.

Nowadays, it is possible the use of numerical frameworks to perform theoretical calculations to gain information about the behavior of these systems. Among them, codes based on Density Functional Theory (DFT) and Non-Equilibrium Green Functions (NEGF) [1,2], allow the simulation of multi-atoms

devices, including a complete description of the electrodes and the molecule electronic structure of all the atoms. These theoretical studies constitute an excellent and complementary work with respect to the experimental data that in some cases are quite difficult to obtain. Nevertheless, the best approach of work in this field is to the study these systems both ways, theoretically and experimentally. In our case, this is what we are planning to do, and complementary to these theoretical studies, the synthesis of these compounds is going to be carried out. For this reason, this theoretical study has been developed to impose the most realistic assumptions possible to facilitate future experimental validation of the predictions.

In this work we have studied the different behaviors that present these systems with different number of anchoring groups. As we are comparing the systems between them, we have kept constant the theoretical parameters during all the calculus. In this way our conclusions are extracted based on the relative values. In fact, beyond limitations derived from this approach [3-9], it can be useful, at least qualitatively, to understand the experimental results [10,11].

II. DESCRIPTION OF THE SYSTEM As stated before, in this work we present a study of the

influence of the number of anchoring groups in the electronic properties of we can consider the most basic organic structures derived of a graphene sheet: benzene and anthracene based molecular devices. Regarding the anthracene molecule, we have considered different types of connection to the metallic electrodes derivatives. Thus, we can study their different behavior between them and also compare the mono-linked anthracene derivatives with the benzene molecule.

Fig. 1 shows the nomenclature used thought out this paper.

Figure 1. Nomenclature of the different molecules studied in this work.

It is worth noting that customized graphene-like π-extended nanoribbons (graphene nanoribbons, GNRs) can be now synthesized as potential components for electronic nanodevices by a bottom-up approach. This approach ensures the homogeneity of the size and shape of such molecules, and consequently, their electronic properties.

As can be see in Fig. 1, sulfur is used as the linker with the metal electrode of Au(111). It has been described that the stability for this kind of junction (S-Au) is several order of magnitude higher than for other anchoring groups. The anthracene molecule almost perfectly matches with the surface of this metal since the distance between the hydrogen atoms in position 1 and 8 in anthracene is 5 Å, which is closed to the distance between equivalent positions in Au(111): 4.995 Å. In fact, the reason to discard the specie with 2 aromatic rings in this study was its imperfect matching to the gold electrodes.

Fig. 2 shows the system under simulation: the molecule between the 2 gold electrodes in a sandwich-type junction. In the calculations we have included both, the electrode and the molecule atoms. Although it is a time-consuming procedure, we have considered the whole system due to that our objective was to analyze the role of the contact in detail. Furthermore, this configuration simulates the often used approach of scanning probe microscopy to measure molecular conductivity.

Once the system was defined, we made use of the SIESTA and Atomistix simulation packages [12,13], based on Density Functional Theory (DFT) and Non-Equilibrium Green Function (NEGF) approaches [2].

The calculation procedure was the next one: first we made a relaxation of the whole system in order to obtain the equilibrium positions of every atom. This was done with SIESTA. Second, we calculated the transmission through our system using Atomistix.

Figure 2. Scheme of the system .

Finally, in this framework the current has been calculated by

( ) ( ) ( )0

dEI = f E +eV f E G Ee

∞

−⎡ ⎤⎣ ⎦∫ (1)

where f(E) is the Fermi-Dirac probability function, e is the absolute charge of the electron, V is the applied voltage,

( ) ( )2e²i, j

i, j

G E = T Eh ∑ (2)

h is the Planck constant and Ti,j is the transmission between eigenchannel i and eigenchannel j.

III. SIMULATION RESULTS Fig. 3 shows the intensity versus voltage curves calculated

for the different optimized nanodevices. We have presented a voltage window of 2.0 V due to the restrictions of the theoretical approach and with the confidence that electronic devices based on organic molecules work with lower values of voltage.

From the figure 3, it is clear that 24S and 24SH2 show a similar behavior, and indeed, the current doubles that of the molecule 1. This indicates that there is not an appreciable loss of current in the bigger molecules, which on the other hand, bind stronger with the surface. The results also show that nanoribbons constituted by 1D molecular wires linked by insolating alkyl side chains (24SH2) can be as efficient as fully conjugated 2D nanoribbons (24S), which are often unstable.

The I vs V curves are almost symmetric, reflecting the bidirectionality of the system. The exception is device 23S which is asymmetrically linked. It is also remarkable that molecule 1 has, in general, less capability to transport current than molecule 2. However an exception occurs with molecule 22SD. The geometrical configuration of the last one, with the linkers placed in diagonal, has an evident impact in its conductivity.

S

S

S

S

S

S S

S

S S

S

S

S

S

S

24S

23S 22SL 22SD

24SH2

S

S

1

Figure 3. Intensity versus Voltage for the different devices.

More interesting conclusions can be obtained if we compare results of molecules 22SL, 23S and 1S. For positive voltages molecules 22SL and 23S provides almost the same current, something greater than molecule 1. This indicates that essentially, the linear linkers of 23S define the path along which the current flows. However, because this molecule is type 2, it provides a better conductivity than molecule 1. For reverse polarizations the behavior is different. In that situation the intensity through 23S is also greater than 22SL, what means an implication of the diagonal linker in the current characteristics.

Therefore, from Fig. 3 we conclude that although the molecule core has intrinsic capabilities for electron transport, the electronic behavior is highly determined by the number and positions of the linker groups.

Equations (1) and (2) express the relation between the intensity and the transmission. In order to gain a deeper insight in the physics of our systems we have also calculated the transmission spectra of the different devices. Figure 4 shows the results when the applied voltage, V, is 0 V. There are clear differences between tetra-linked (24S and 24SH2 devices) and bi-linked (1, 22SL and 22SD) devices. In the first group it can be observed transmission coefficients greater than 1 in the voltage window studied. This fact is the consequence of the existence of more than one orthogonal eigenchannel for that energy in that device, and this implies that more than one electron with similar energies passes through the device with the consequent increase in the current.

It is also interesting that the shape of transmission for 24SH2 is almost the same than that of 1, but more than twice greater. This indicates that in 24SH2 there are two different eigenchannels that are almost independent as a consequence of the nature of its central aromatic ring. Precisely the dependence that exists between them is the reason that makes its transmission more than twice greater.

Figure 4. Transmission spectrum for the different devices.

Molecule 23S also deserves a comment. In spite of the 3 linkers, its transmission never is more than the unity in the range of voltage showed in the figure. It underlines that the presence of multiple eigenchannels is related with the number of pairs of linker atoms connecting both electrodes and not with the global number.

In bi-linked devices only one eigenchannel is operative in the voltage window, being the maximum of transmission related with the presence of the corresponding MPSH, and show a current intensity close to benzenedithiol-based device 1. This result points out that the efficiency of the molecular conduction is related with the position of the HOMO level and not with the HOMO-LUMO gap (1: 3.32 eV, 22SL: 1.77 eV, 22SD: 1.85 eV) or the poly-aromatic nature of the organic conductor. In fact, we think that device 22SD is even less efficient than 1, probably due to an interference phenomena.

The presented results confirm that molecular conductivity is related with the number and transparency of open eigenchannels, and these eigenchannels (and the probability of electron flow) are very sensitive to the connection of the molecule to the metallic electrodes.

We have analyzed in more detail molecules 24SH2 and 24S. We have carried out the corresponding decomposition of the transmission spectra of devices 24S and 24SH2 in eigenchannels and plotted them in Figs. 5 and 6. These figures confirm the contribution of two different channels for both devices. Figure 6 also validates the above commented disconnection in molecule 24SH2, and the resemblance of the shape of those eigenchannels transmission with the one of device 1. However the behavior of 24S is different: the preeminence of one eigenchannel seems clear.

We have also checked that the maxima of such channels at low energies correspond with the self-energies of the Molecular Projected Self-consistent Hamiltonian (MPSH) of the naphthalene-based organic conductor. The relevance of the π-conjugated system of the organic molecule was also confirmed by the shape of the LDOS and the transmission spectrum at these energies.

-2 -1 0 1 2

-100

-50

0

50

100

Inte

nsity

(μA

)

Voltage (V)

24S 22SL

24SH2 22SD

23S 1S

-2,0 -1,5 -1,0 -0,5 0,0 0,5 1,0 1,5 2,00,0

0,5

1,0

1,5

2,0

Tran

smm

isio

n

Energy (eV)

24S

24SH2

23S

22SL

22SD

1

Figure 5. Eigenchannel and total transmission spectrum for 24S.

Figure 6. Eigenchannel and total transmission spectrum for 24SH2.

IV. CONCLUSIONS In this paper we have analyzed the role that the number and

positions of the anchoring groups play in the conductivity of the graphene nanoribbons. We have studied benzene and anthracene-based molecules. From our results we conclude that although the molecule core has intrinsic capabilities for electron transport, the electronic behavior is highly determined by the number and position of the linker groups. In this sense we have obtained that the presence of multiple eigenchannels is related with the number of pairs of linker atoms connecting both electrodes and not with the global number.

ACKNOWLEDGEMENTS We thank to the Regional Government of Andalusia for

finantial support (P06-FQM-01726) and to the “Centro de SuperComputación de la Universidad de Granada” and the Centro de Computación Científica-UAM for computation time. AML thanks MICINN for her FPU fellowship and LAdC thanks UGR for his research contract.

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-2 -1 0 1 2

0,0

0,5

1,0

1,5

2,0 Total EigenChannel 1 EigenChannel 2 EigenChannel 3

Tran

smis

sion

Energy (eV)

24SH2

-2 -1 0 1 20,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

Tran

smis

sion

Energy (eV)

Total EigenChannel 1 EigenChannel 2 EigenChannel 3

24S