## 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

Supervisors

**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

the basis for the carbon based structures, from fullerene to graphite. Its bidimensionality

gives rise to unique structural and electronic properties. The sp2 hybridization of the

carbon atoms leads to a trigonal planar geometry, with sigma bonds between atoms that give

strength and robustness to the structure. The electronic structure is characterized by

the linear dispersion of the pi bands near the K point in the Brillouin zone, called Dirac

point, where the Fermi energy lies. The linear dispersion implies that electrons near the

Dirac point are described by a Dirac-like equation, hence they behave like relativistic

particles, yet at low velocities and energies. Moreover the charge carriers exhibit a high

mobility.

Due to its properties, there is a great interest on graphene based technological appli-

cation. An important aspect for this purpose is the response of graphene to an external

electric field, in particular if it is possible to tune the structure and the electronic proper-

ties. The aim of this work is to study the electromechanical properties and the electronic

response to an orthogonal electrostatic field of graphene with the specific focus on the pos-

sibility of controlling the local curvature of the graphene sheet by means external electric

fields. The interplay between electric field and curvature is related to the flexoelectricity,

namely the polarization response to a gradient of strain.

Several production methods have been developed and one promising is the grown on

a silicon carbide (SiC) substrate. The layer grown on SiC has some differences from

the free standing one. The graphene structure displays spontaneous ripples due to the

compression of the lattice parameter caused by the mismatch with the substrate. The

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

of the rippled structures on graphene, corresponding to a 4sqrt(3)x4sqrt(3)R30 supercell. Due

to the spontaneous rippling, epitaxial graphene on SiC is an ideal experimental system to

study the effect of electric field on curvature. However, up to now very a few experimental

studies of graphene embedded in electric fields were published, due to the experimental

difficulties.

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

real one, by means of Density Functional Theory (DFT) based computer calculations

and simulations. At variance with the experiment, in computer simulations the exposure

to an uniform and static electric field, even of high intensity, is possible with only minor

additional difficulties.

However, the model system reproducing the exact symmetry is quite large, especially

when one addresses it with ab initio methods, such as DFT. For this reason, massively

parallel computational resources and high performing codes were used for calculations,

and besides the 13x13 "real" model system, including also the substrate (several thou-

sands atoms), also the smaller 4sqrt(3)x4sqrt(3)3R30 one, approximately mimicking the real

rippling periodicity, was considered. In addition, the standard unit cell was also used as

test and for comparison.

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

compression and with a 2% compression, in order to reproduce the ripples present in the

graphene grown on SiC. For this cell also BN doped and N doped graphene structure

were simulated. The range of considered electric fields is very large, reaching the limits

of those that can currently be practically produced.

Results are reported for the change of electronic properties (band structure, charge

distribution and density of electronic states) and structure due to the electric fields.

Directly measurable observables, such as the local DOS measured by Scanning Tunneling

Microscopy (STM), were evaluated. The ionization limit is evaluated. The change of

flexoelectric properties and the possibility of manipulating curvature is quantitatively

estimated, for bare and substituted graphene. These results are of particular interest

for technological applications in energy storage and harvesting. In addition, the model

systems mimic the real experimental ones, and results could hopefully stimulate direct

measurements with which they could be straightforwardly compared.

the basis for the carbon based structures, from fullerene to graphite. Its bidimensionality

gives rise to unique structural and electronic properties. The sp2 hybridization of the

carbon atoms leads to a trigonal planar geometry, with sigma bonds between atoms that give

strength and robustness to the structure. The electronic structure is characterized by

the linear dispersion of the pi bands near the K point in the Brillouin zone, called Dirac

point, where the Fermi energy lies. The linear dispersion implies that electrons near the

Dirac point are described by a Dirac-like equation, hence they behave like relativistic

particles, yet at low velocities and energies. Moreover the charge carriers exhibit a high

mobility.

Due to its properties, there is a great interest on graphene based technological appli-

cation. An important aspect for this purpose is the response of graphene to an external

electric field, in particular if it is possible to tune the structure and the electronic proper-

ties. The aim of this work is to study the electromechanical properties and the electronic

response to an orthogonal electrostatic field of graphene with the specific focus on the pos-

sibility of controlling the local curvature of the graphene sheet by means external electric

fields. The interplay between electric field and curvature is related to the flexoelectricity,

namely the polarization response to a gradient of strain.

Several production methods have been developed and one promising is the grown on

a silicon carbide (SiC) substrate. The layer grown on SiC has some differences from

the free standing one. The graphene structure displays spontaneous ripples due to the

compression of the lattice parameter caused by the mismatch with the substrate. The

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

of the rippled structures on graphene, corresponding to a 4sqrt(3)x4sqrt(3)R30 supercell. Due

to the spontaneous rippling, epitaxial graphene on SiC is an ideal experimental system to

study the effect of electric field on curvature. However, up to now very a few experimental

studies of graphene embedded in electric fields were published, due to the experimental

difficulties.

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

real one, by means of Density Functional Theory (DFT) based computer calculations

and simulations. At variance with the experiment, in computer simulations the exposure

to an uniform and static electric field, even of high intensity, is possible with only minor

additional difficulties.

However, the model system reproducing the exact symmetry is quite large, especially

when one addresses it with ab initio methods, such as DFT. For this reason, massively

parallel computational resources and high performing codes were used for calculations,

and besides the 13x13 "real" model system, including also the substrate (several thou-

sands atoms), also the smaller 4sqrt(3)x4sqrt(3)3R30 one, approximately mimicking the real

rippling periodicity, was considered. In addition, the standard unit cell was also used as

test and for comparison.

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

compression and with a 2% compression, in order to reproduce the ripples present in the

graphene grown on SiC. For this cell also BN doped and N doped graphene structure

were simulated. The range of considered electric fields is very large, reaching the limits

of those that can currently be practically produced.

Results are reported for the change of electronic properties (band structure, charge

distribution and density of electronic states) and structure due to the electric fields.

Directly measurable observables, such as the local DOS measured by Scanning Tunneling

Microscopy (STM), were evaluated. The ionization limit is evaluated. The change of

flexoelectric properties and the possibility of manipulating curvature is quantitatively

estimated, for bare and substituted graphene. These results are of particular interest

for technological applications in energy storage and harvesting. In addition, the model

systems mimic the real experimental ones, and results could hopefully stimulate direct

measurements with which they could be straightforwardly compared.

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