## Tesi etd-09032014-093349 |

Thesis type

Tesi di laurea magistrale

Author

CAVALLUCCI, TOMMASO

URN

etd-09032014-093349

Title

Density Functional Theory simulations of the electromechanical properties of naturally corrugated epitaxial graphene

Struttura

FISICA

Corso di studi

FISICA

Commissione

**relatore**Tozzini, Valentina

Parole chiave

- graphene
- electric field
- curvature
- flexoelectricity
- electromechanical
- polarizability
- DFT
- silicon carbide

Data inizio appello

24/09/2014;

Consultabilità

completa

Riassunto analitico

Graphene is a monolayer of carbon atoms arranged in a honeycomb lattice, and it is<br>the basis for the carbon based structures, from fullerene to graphite. Its bidimensionality<br>gives rise to unique structural and electronic properties. The sp2 hybridization of the<br>carbon atoms leads to a trigonal planar geometry, with sigma bonds between atoms that give<br>strength and robustness to the structure. The electronic structure is characterized by<br>the linear dispersion of the pi bands near the K point in the Brillouin zone, called Dirac<br>point, where the Fermi energy lies. The linear dispersion implies that electrons near the<br>Dirac point are described by a Dirac-like equation, hence they behave like relativistic<br>particles, yet at low velocities and energies. Moreover the charge carriers exhibit a high<br>mobility.<br>Due to its properties, there is a great interest on graphene based technological appli-<br>cation. An important aspect for this purpose is the response of graphene to an external<br>electric field, in particular if it is possible to tune the structure and the electronic proper-<br>ties. The aim of this work is to study the electromechanical properties and the electronic<br>response to an orthogonal electrostatic field of graphene with the specific focus on the pos-<br>sibility of controlling the local curvature of the graphene sheet by means external electric<br>fields. The interplay between electric field and curvature is related to the flexoelectricity,<br>namely the polarization response to a gradient of strain.<br>Several production methods have been developed and one promising is the grown on<br>a silicon carbide (SiC) substrate. The layer grown on SiC has some differences from<br>the free standing one. The graphene structure displays spontaneous ripples due to the<br>compression of the lattice parameter caused by the mismatch with the substrate. The<br>SiC-graphene interface shown a double periodicity: the first is the exact periodicity corresponding to a supercell of 13x13 compared to the unit cell, the second is the periodicity<br>of the rippled structures on graphene, corresponding to a 4sqrt(3)x4sqrt(3)R30 supercell. Due<br>to the spontaneous rippling, epitaxial graphene on SiC is an ideal experimental system to<br>study the effect of electric field on curvature. However, up to now very a few experimental<br>studies of graphene embedded in electric fields were published, due to the experimental<br>difficulties.<br>The aim of this Thesis work is the theoretical study of the electronic and structural properties of a graphene system exposed to electric field, as far as possible similar to the<br>real one, by means of Density Functional Theory (DFT) based computer calculations<br>and simulations. At variance with the experiment, in computer simulations the exposure<br>to an uniform and static electric field, even of high intensity, is possible with only minor<br>additional difficulties.<br>However, the model system reproducing the exact symmetry is quite large, especially<br>when one addresses it with ab initio methods, such as DFT. For this reason, massively<br>parallel computational resources and high performing codes were used for calculations,<br>and besides the 13x13 "real" model system, including also the substrate (several thou-<br>sands atoms), also the smaller 4sqrt(3)x4sqrt(3)3R30 one, approximately mimicking the real<br>rippling periodicity, was considered. In addition, the standard unit cell was also used as<br>test and for comparison.<br>Model systems were simulated at null electric field and with fields of increasing intensity and different direction. The 4sqrt(3)x4sqrt(3)R30 graphene cell was simulated at zero<br>compression and with a 2% compression, in order to reproduce the ripples present in the<br>graphene grown on SiC. For this cell also BN doped and N doped graphene structure<br>were simulated. The range of considered electric fields is very large, reaching the limits<br>of those that can currently be practically produced.<br>Results are reported for the change of electronic properties (band structure, charge<br>distribution and density of electronic states) and structure due to the electric fields.<br>Directly measurable observables, such as the local DOS measured by Scanning Tunneling<br>Microscopy (STM), were evaluated. The ionization limit is evaluated. The change of<br>flexoelectric properties and the possibility of manipulating curvature is quantitatively<br>estimated, for bare and substituted graphene. These results are of particular interest<br>for technological applications in energy storage and harvesting. In addition, the model<br>systems mimic the real experimental ones, and results could hopefully stimulate direct<br>measurements with which they could be straightforwardly compared.

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