Electronic and optical properties of graphene- and graphane ... - MIFP

Electronic and optical properties of
graphene- and graphane-like
SiC layers
Paola Gori, ISM, CNR, Rome, Italy
Olivia Pulci, Margherita Marsili, Università di Tor
Vergata, Rome, Italy
Friedhelm Bechstedt, IFTO, Friedrich-Schiller-
Universitat, Jena, Germany
ESF Workshop on Polaritonics, March 20-23, 2012 - Marino (Rome), Italy

Outline
• Graphene and graphane-like SiC based 2D sheets: structure
• Electronic properties: face-dependent behaviour
• Optical properties: polarizability, bound excitons
• Conclusions and outlook

c
Theoretical tools: ab-initio methods
v
hn
DFT GW
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v
MBPT
ground state Band structure, I, A
c
EXC
hn W
wcv
v
BSE
Optical properties

c
Theoretical tools: ab-initio methods
v
hn
DFT GW
c
v
MBPT
c
EXC
hn W
wcv
v
BSE
1) 2) 3)

Quasiparticle equation
�
� iGW
G: single particle Green’s function
�1
W � � V
W: screened Coulomb interaction
Lars Hedin 1965

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Optical properties: Bethe Salpeter
equation
v
hn
DFT GW
c
v
MBPT
c
EXC
hn W
wcv
v
BSE
1) 2) 3)

hn
GW BSE
Bethe Salpeter equation
c
v
Absorption spectra
A photon excites an electron from an occupied
state to a conduction state
e
h
4
4 4
P � PIQP
� PIQP
Bethe Salpeter Equation (BSE)
Kernel:
�
e-h exchange
�
v �
W
4
�
4
P
bound excitons

SiC nanotubes
SiC-based nanostructures
Sun et al., JACS 124, 14464 (2002)
SiC nanowires
Pan et al., Adv. Mater. 12, 1186 (2000)
Applications for hydrogen storage,
nanoelectronics, microelectromechanical
systems

Graphene and graphane-like 2D SiC layers
Silicongraphene Silicongraphane
Flat honeycomb structure (sp 2 +p z )
C-Si bond length = 1.79 Å
intermediate between
graphene (C-C = 1.42 Å) and silicene
(Si-Si = 2.28 Å)
Buckling (�z) = 0.58 Å
(sp 3 hybridization)
C-Si bond = 1.9 Å
intermediate between
graphane (C-C = 1.54 Å) and
silicane (Si-Si = 2.36 Å)

2D SiC:H from a SiC surface?
Is it possible to obtain 2D SiC:H form a slab of hydrogenated
C-terminated 3C-SiC(111)?
[E tot(SiC:H 5bil_slab) + E tot(2D-SiC:H)]-[E tot(SiC:H 6bil_slab) + E tot(H 2)]
= -0.15 eV,
E tot(SiC:H 5(6)bil_slab) = total energy of a 5(6)-bilayer 1x1 SiC(111) slab
E tot(H2) = total energy of an hydrogen molecule
� An hydrogenated slab of 3C-SiC(111) in presence of
hydrogen can give rise to a stable 2D hydrogenated sheet
of SiC

Quasiparticle band structures
SiC SiC:H

Quasiparticle band gaps
2D sheet
GW direct
gap (eV)
SiC 3.7 (K)
SiC:H 5.3 (G)
C:H 5.4 (G)
Si:H 3.6 (G)

SiC:H band edge density of states
The fundamental gap of SiC:H approaches the value found for graphane:
near the gap the DOS is dominated by C and H(C) states.

SiC:H - Electrostatic potential

SiC:H - Electrostatic potential
Two vacuum levels appear as a consequence of the sheet polarity.
A dipole discontinuity �V=1.7 eV occurs, related to the electron
transfer Qe between Si and C.
According to Gauss law,
4�
Qe
�V � �
� A
where � s=2.03, A 0=8.48 Å 2 , �=0.58 Å.
This gives Q=0.25, smaller than expected for ionic bonding
�significant covalent bonding contribution.
Possible application of 2D SiC:H as electron/hole filter in
LED or solar cells
s
0
P. Gori, O. Pulci et al., APL 100, 043110 (2012)

Other systems with orientation-dependent
ionization energy
a-sexithiophene/Ag(111)
Duhm et al., Nature Mat. 7, 326 (2008)
Standing 6T molecules
Lying 6T molecules
Ionization
potential
varied of
0.6 eV

Optical properties (RPA)
SiC SiC:H

Bound excitons in 2D SiC, SiC:H

2D SiC: first exciton in k-space
Holes in the last valence band,
Electron in the first conduction band

2D SiC: third exciton in k-space
Holes in the last valence band,
Electron in the first conduction band

2D SiC:H: first exciton in k-space
Holes in the two last valence bands,
Electron in the first conduction band

2D SiC:H: third exciton in k-space
Holes in the last valence band,
Electron in the first conduction band

Bound excitons in 2D hydrogenated C, Si, Ge
Ge:H
Si:H
C:H

Excitons in 2D systems
• Exciton size and/or binding energies are heavily influenced by
confinement
• In particular, screening is hindered and binding energies are
consequently very large
• Rough estimate of the binding energy and excitonic radius for
the lowest bound exciton through a simplified model similar to a
2D hydrogenic model of the excitons

With the two limits:
2D Screened Coulomb potential
For vanishing sheet thickness, the screened Coulomb potential is r = in-plane radius
W
e
2
�
�
�r� � � �H
�
�
�
� � �
�
�
�
0 N0
�
4a 2D
� � 2�a
2D
� � 2�a
2D
��
r
�
�
H 0 = Struve function
N 0 = Neumann function
2D electronic polarizability:
� �
2
e
W �r � � � for 2�a2 D �� r 2D hydrogen atom
r
2
e � � r � �
� � � � �
2
2�a
2D
� � 4�a
2D
� �
�r� ln�
� � 0.
5772 for 2�a
�� r
W D
r
��
a
2D
�
L ���0 �1��
4�
L = distance between sheets
Log e-h attraction

Log e-h attraction
2D Screened Coulomb potential
2D hydrogen atom

Log e-h attraction
2D Screened Coulomb potential
2D-C:H
2D-Si:H
2D-Ge:H
2D-SiC
2D-SiC:H
2D hydrogen atom

Bound excitons in 2D systems
SiC, Si:H, Ge:H
Large oscillator strength � Short radiative lifetime � No possibility of BEC
C:H, SiC:H
Vanishing dipole matrix element � Not so small radiative lifetime � BEC?
SiC, Si:H, Ge:H
Large oscillator strength
AND � Possible significant RT exciton-polariton effects
Large exciton binding energy

Conclusions and outlook
• 2D-based SiC and SiC:H: interesting properties + possibilities of integration
with Si technology
• Side-dependent electronic behaviour in SiC:H � applicability for
hole/electrons filters
• Strongly bound excitons both in SiC and in SiC:H. Similarities with 2D-C:H, Si:H,
Ge:H
• Laboratory for studies of fundamental physics, e.g. bosonic effects at room
temperature
• Possible applications for polaritons lasers