September 6, 2018 - by Simone Ulmer

Materials researchers analyse nanomaterials using a combination of experiments and computer simulations. Knowing the structure and electronic properties of nanomaterials is vital to their successful manufacture and application, because quantum mechanical effects play a considerable role in nanomaterials with only one or two dimensions. Compared with their three-dimensional relatives, such low-dimensional nanomaterials, therefore, have completely different and often surprising properties.

Hopeful graphene
There is a limit to how small one can build conventional electronic semiconductor components, such as transistors for controlling electrical voltages and currents. The uncontrollable quantum mechanical tunneling currents that come into play at orders of magnitude of just a few nanometers interfere with the way classical transistors work. Among the various low-dimensional nanomaterials, the carbon material graphene represents one of the great hopes in the search for new, smaller components, as it has high electron mobility and is just a single layer of atoms thick. However, graphene has no band gaps like those that exist between the conduction and valence bands in classical semiconductors, and graphene-based transistors, therefore, cannot be switched off.

This problem can be resolved with a method that allows the atomically precise production of graphene nanoribbons with a defined band gap. Such a method was presented in the journal Nature back in 2010 by Empa researchers working under Roman Fasel, Professor at the University of Bern and Head of the nanotech@surfaces laboratory at Empa, in collaboration with researchers from the Max Planck Institute for Polymer Research in Mainz and the Technical University of Dresden. The method has since been applied around the world and, according to the Empa researchers, it allows nanoribbons to be manufactured with a band gap that is suitable for use in transistors.

Because of the honeycomb arrangement of carbon atoms in a layer of graphene, it is possible to manufacture graphene nanoribbons with “zigzag” or “armchair” edges. “The edge structure has an important influence on the band gap and other electronic properties of the nanoribbons,” Fasel explains. However, the search for a “recipe” for nanoribbons with a pure zigzag edge — which are predicted to have promising magnetic properties — was, he says, a particularly laborious task. After years of research, a breakthrough finally came from Empa in 2016.

Atomically precise nanoribbons
By depositing a precursor molecule with specific properties on noble metals such as gold and silver, the researchers succeeded in manufacturing graphene nanoribbons with a high degree of structural precision. This precursor molecule shows the carbon atoms the way, so to speak, and thereby ensures their atomically precise arrangement so that the desired nanostructure can form. The researchers emphasise that, although the procedure has since been optimised for specific nanoribbons through a series of experiments, it would take a great deal of time to determine the optimum experimental parameters for each new type of nanoribbon. However, computer simulations could reduce this time considerably.

This is why Carlo A. Pignedoli and the team for atomistic simulations from Empa’s nanotech@surfaces lab are using CSCS supercomputer “Piz Daint” to simulate the on-surface chemical reactions that allow the nanoribbons to be constructed from specific precursor molecules, as well as the electronic structure of the desired nanoribbons. Conversely, the simulations can also be used to determine the optimum design of the precursor molecules for a given nanoribbon geometry.

“Atomistic simulations are a key part of this,” says Pignedoli. “On the one hand, simulations allow us to reproduce the chemical reactions on the surface and understand why a given precursor molecule is successful in producing a desired nanostructure or why it fails to do so. On the other hand, a comparison of the calculated and experimental electronic structures of a given nanomaterial is essential to understanding what properties we can expect from the corresponding material.”

New algorithm
The researchers calculate the electronic structure using the methods of density functional theory (DFT), which can predict the properties of systems containing thousands of interacting electrons based on specific approximations. One particularly laborious task involves describing the band gap correctly, which is done using the GW approximation. As Pignedoli explains, this takes a DFT-based calculation of the electronic ground state as its starting point and also takes into account the electron gas’s self-energy and polarisation, which are particularly relevant in the case of excitation.

To avoid coming up against the limits of feasibility due to the increasing number of atoms — and therefore electrons — to be included in the calculation, Jan Wilhelm from the research group of Jürg Hutter, Professor of Physical Chemistry at the University of Zurich, developed a special method for efficient GW calculation in collaboration with Pignedoli, a joint effort supported by the Swiss National Center of Competence in Research (NCCR) MARVEL. The method, which they recently published in the Journal of Physical Chemistry Letters, is capable of efficiently calculating the electronic states of thousands of atoms in nanostructures and molecules using modern supercomputers such as “Piz Daint” — for isolated molecules, for liquids and also for solids. The researchers implemented the new GW algorithm into the CP2K computer code, which determines the distribution of electrons in a material using density functional theory.

“Now, the aim is to use the new simulation method to find new graphene nanomaterials with specific electronic properties that are suitable for use in powerful transistors, for example,” says Pignedoli. Aside from graphene transistors, the scientists are also currently researching the potential of polycyclic hydrocarbons with a radical structure for applications in organic electronics, spintronics and optoelectronics.

Literature reference:

Cai J et al.: Atomically precise bottom-up fabrication of graphene nanoribbons, Nature (2010), DOI: doi.org/10.1038/nature09211

Ruffieux P et al.: On-surface synthesis of graphene nanoribbons with zigzag edge topology, Nature (2016), DOI: doi.org/10.1038/nature17151

Talirz L, Shinde P, Passerone D & Pignedoli CA: Synthesis of Atomically Precise Graphene-Based Nanostructures: A Simulation Point of View. In: Gourdon A. (eds) On-Surface Synthesis. Advances in Atom and Single Molecule Machines. Springer, Cham, DOI:
doi.org/10.1007/978-3-319-26600-8_12

Talirz L, et al.: On-Surface Synthesis of Atomically Precise Graphene Nanoribbons Adv. Mater. 28, 6222 (2016) DOI: doi.org/10.1002/adma.201505738

Llinas JP, et al.: Short-channel field-effect transistors with 9-atom and 13-atom wide graphene nanoribbons Nature Communications 8, 633 (2017) DOI: doi.org/10.1038/s41467-017-00734-x

Wilhelm J, Golze D, Talirz L, Hutter J & Pignedoli CA: Toward GW Calculations on Thousands of Atoms, The Journal of Physical Chemistry Letters 2018 9 (2), 306-312
DOI: doi.org/10.1021/acs.jpclett.7b02740