Electronic%20and%20transport%20properties%20of%20graphene%20nanoribbons:%20influence%20of%20edge%20passivation%20and%20uniaxial%20strain

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Electronic and transport properties of graphene
nanoribbons influence of edge passivation and
uniaxial strain

• Benjamin O. Tayo
• Physics Department, Pittsburg State University
  Pittsburg, KS

WSU Physics Seminar Wichita, KS November 12, 2014
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Outline

• Part I Graphene Review (Tutorials)
• Introduction to graphene
• Structural properties of graphene
• Electronic properties
• Graphenes band structure and the band gap
  problem
• Part II Graphene nanoribbons
• Structural properties, edge passivation
• Electronic structure
• Effect of quantum confinement
• Effect of edges
• Effect of external strain
• Application charge transport
• Summary and conclusion

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Part I Graphene Review

• 1. Introduction, structural properties
• 2. Electronic structure
• Uniqueness of Graphenes band structure
• Band gap problem
• How to solve the band gap problem?

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Graphene

•  

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Graphene building block of other carbon
materials
Castro Neto et al. Peres, 2006a, Phys. World 19,
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• Graphene (top left) is a honeycomb lattice of
  carbon atoms.
• Graphite (top right) can be viewed as a stack of
  graphene layers.
• Carbon nanotubes are rolled-up cylinders of
  graphene (bottom left).
• Fullerenes C60 are molecules consisting of
  wrapped graphene by the introduction of pentagons
  on the hexagonal lattice.

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Graphene

• Isolation of graphene in 2004 by Manchester group
  headed by Andre Geim
• 2010 Nobel prize in physics awarded to Andre
  Geim and Konstantin Novoselov for groundbreaking
  experiments regarding the two-dimensional
  material graphene

Country Rankings in Graphene Publications to Date
(source Thomson Reuters ISI Web of Science
search dated 15 June 2012 using Topicgraphene
19,017 records)
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2D Graphite (Graphene) Unit Cells
Direct Lattice
Reciprocal Lattice BZ
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Energy Pi Bands of Graphene
R. Saito et. al, Physical Properties of Carbon
Nanotubes
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Graphene is a zero gap semiconductor
 
DOS plot http//large.stanford.edu/courses/2008/p
h373/laughlin2/
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Graphenes Low-energy Physics Dirac Fermions
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Experimental evidence of massless Dirac fermions
in graphene Cyclotron mass
A Area in k space enclosed by electrons
orbit n carrier concentration
Fitting the theoretical result with experimental
data yields vF 106
m/s, t 3.0 eV
Solid State Physics, Ashcroft and Mermin,
1976 The electronic properties of graphene, Rev.
Mod. Phys. Vol. 81, 2009
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The Band Gap problem in graphene

• Graphenes electrical charge carriers (electrons
  and holes) move through a solid with effectively
  zero mass and constant velocity, like photons.
• Graphene's intrinsically low scattering rate from
  defects implies the possibility of almost
  ballistic transport.
• The primary technical difficulty has been
  controlling the transport of electrical charge
  carriers through the sheet.

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How to solve the Band Gap Problem?

•  

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Part II Graphene Nanoribbons

• 1. Structural properties, edge passivation
• 2. Electronic structure
• Effect of quantum confinement
• Effect of edges
• Effect of external strain
• 3. Application charge transport

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Graphene Nanoribbons (GNRs)
 
 
W

• GNRs are elongated stripes of single layered
  graphene with a finite width
• Electronic properties depend on edge geometry and
  width
• Structurally very similar to carbon nanotubes

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AFM image of many graphene nanoribbons parallel
to each other
Cançado et al., Phys. Rev. Lett. 93, 047403 (2004)
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Graphene Nanoribbon structural parameters
N Number of dimer lines N-AGNR GNR with
armchair edges and N-dimer lines N-ZGNR GNR
with zig-zag edges and N-dimer lines N 3p, 3p1,
3p2, where p is a positive integer (family
pattern).
Benjamin O. Tayo, Mater. Focus 3, 248-254 (2014)
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Effect of edge passivation with Hydrogen

• Converged geometry of a H-passivated 7-AGNR
• Edge C-C bond lengths are shortened by 3 to 5
  compared to those in the middle of the ribbon
• Optimization was performed using DFT with the
  B3YPL XC potential and the 6-31 G(d) basis set,
  with the Gaussian 09 code

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Passivation with other atoms or groups
A. Simbeck et al., Phys. Rev. B 88, 035413 (2013)

• Different atoms or functional groups provide
  different levels of perturbations to the
  nanoribbon.
• Electronic properties depend on edge passivation

X. Peng, and S, Velasquez, Appl. Phys. Letts.,
98, 023112, (2011).
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Electronic structure effect of quantum
confinement
 
 
 
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Effect of strain and H-passivation model
Hamiltonian
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Model Hamiltonian
At k 0, Hamiltonian is
Y.W. Son, M. L. Cohen, and S. G. Louie, Phys.
Rev. Lett. 97, 216803 (2006). Benjamin O. Tayo,
Mater. Focus 3, 248-254 (2014).
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Tight-Binding Parameters

• Hopping integrals are calculated using analytic
  expressions for TB matrix elements between C
  atoms
• For edge carbon atoms, additional strain due to H
  passivation has to be taken into account

D. Porezag, et al., Phys. Rev. B 51, 12947
(1995).
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(a) Band Gap of Unstrained H-passivated GNR
M. Han et al.,Energy Band-Gap Engineering of
Graphene Nanoribbons, PRL 98, 206805 (2007).
 
Benjamin O. Tayo, Mater. Focus 3, 248-254 (2014).

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(b) Effective mass of Unstrained H-passivated GNR
TB approx.
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(c) Band Gap and Effective mass of strained
H-passivated GNR
X. Peng S. Velasquez, Strain modulated band
gap of edge passivated armchair GNRs, APL 98,
023112 (2011).
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(a) Asymmetry of Band Gap variation with strain
 
B. Tayo, Mater. Focus 3, 248-254 (2014).
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Application Charge transport in AGNR

• Carrier scattering by longitudinal acoustic
  phonons plays a significant role in charge
  transport in intrinsic semiconductors.

 
C stretching modulus E1 Deformation
potential constant
J. Bardeen and W. Shockley, Phys. Rev. 80, 72
(1950). F. B. Beleznay, F. Bogr, and J. Ladik, J.
Chem. Phys. 119, 5690 (2003).
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Application Charge transport in AGNR

• The advantage of gapless graphene is its high
  carrier mobility.

• When a non-zero gap is engineered by patterning
  graphene into nanoribbons, the mobility has been
  shown to decrease dramatically

• The hardness to achieve high mobility and large
  on/off ratio simultaneously limits the
  development of graphene electronics.

• Suitable choice of strain and edge passivation
  could be used to open the band gap while
  maintaining a low effective mass.

X. R. Wang, Y. J. Ouyang, X. L. Li, H. L. Wang,
J. Guo, and H. J. Dai, Phys. Rev. Lett. 100,
206803 (2008). J. Wang, R. Zhao, M. Yang, Z. Liu,
and Z. Liu, Chem. Phys. 138, 084701 (2013).
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Future of Graphene Electronics
Walt A. de Heer Researchers should stop trying
to use graphene like silicon, and instead use its
unique electron transport properties to design
new types of electronic devices that could allow
ultra-fast computing
Exceptional ballistic transport in epitaxial
graphene Nanoribbons, J. Baringhaus, M. Ruan, F.
Edler, A. Tejeda, M. Sicot, A. Taleb-Ibrahimi, A.
Li, Z. Jiang, E. H. Conrad, C. Berger, C.
Tegenkamp, and Walt A. de Heer, Nature Physics
10, 182, (2014).
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Summary

• Edge passivation and strain can both be
  described within the TB approx. by simply
  renormalizing the C-C hopping integral.

• Studied relationship between carrier mass and
  band gap energy for strained H-passivated AGNRs
  belonging to different families N 3p, 3p1,
  3p2

• For unstrained H-passivated AGNRs, the effective
  mass exhibits a linear dependence on band gap
  energy for small energy gaps or large ribbon
  width.

• However for ribbons with small width or larger
  band gaps, the effective mass dependence on
  energy gap is parabolic.

• In the presence of strain, both band gap and
  effective mass displays a nearly zigzag periodic
  pattern, indicating that the effective mass
  remains proportionate to the band gap even in the
  presence of applied strain.

• Finally, we discussed the implications of
  non-zero band gap on carrier mobility

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Acknowledgement

• Pittsburg State University summer faculty
  fellowship

• Supercomputer core time from NERSC _at_ LBNL

• Use of Gaussian 09 software for DFT calculations

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THANK YOU FOR YOUR ATTENTION