The Electrical, thermal, optical applications of Graphene

1. GRAPHENE
Thermal and Electrical
Properties
Presenter: Sandra Tembei
Course: MSE501 Material Properties and
Chemical changes
Course Coordinator: Prof. Ahmed Abd El-
Moneim
12th Dec. 2018

2. What is Graphene?
 2D Carbon sheet
 One atom thick
 Sheet thickness 0.035 to
0.07nm
 Carbon atoms Arranged in
a hexagonal honey-comb
lattice
 Graphite can be seen as
layers of Graphene

3. Graphene Properties
Type Property Graphene
MECHANICAL
Young’s Modulus (TPa) 0.5 – 1.05
Intrinsic Strength (GPa) 130
Poisson Ratio 0.186
Hardness (Mohr) >10
Mass Density (g/cm3) 2.2
Specific Surface Area (m2/g) 2630
ELECTICAL
Electron mobility at room temperature
(cm2/Vs)
2.5*105
Electrical Resistivity (Ωcm) 10-6
Relative current density wrt Cu 3 - 8 *106
Thermal Conductivity Wm/K 3000
Optical Transmittance 97.7%

4. Brief Background on
Graphite
 Interatomic bonds
within the planes are
very strong but much
weaker across planes
 Structure so different
in different directions,
thus, graphite is
strongly anisotropic,
being a conductor in
the direction of the
planes but an
insulator
perpendicular to them

5. Electrical Conductivity Of Graphene Explained
Sp2
2pz
ENERGY
Carbon when unbonded has it’s
6 electron occupying 3 energy
levels : 1s, 2s and 2p.
1s is closest to the nucleus with
low energy and so does not take
part in bonding. Electrons in 2s
and 2p subshells have higher
energy those in 2p being greater
than those in 2s
Carbon used the electrons in its
outer shell to form bond by
forming a hybrid sp2 or sp3
shell. In the case of and sp3
shell all electrons in the outer
shell are involved in bonding
like in the case of the Diamond.
In the Sp2 case, just 3 of the 4
are involved in the bonding and
1 electron is left free to move
freely across the lattice thus
making graphene electrically

6. Thermal Conductivity Of Graphene Explained
Atoms in Graphene Vibrate releasing Energy packets referred to at
Phonons

7.  Phonons exhibit
wave – Particle
duality just like
Electrons and
Photons since they
possess both
Energy and
momentum
 They are the
quantum units of
Crystal Lattice
vibrations
 Crystal are able to
Thermal Conductivity Of Graphene Explained
Fig: Phonon in action

8. Thermal Conductivity Of Graphene Explained
In crystals : N atoms in the primitive unit cell vibrating in the 3D
space ⇒ 3N degrees of freedom ⇒ finite number of normal
states ⇒ quantization of crystal vibrational energy
Atomic vibrations in a periodic periodic solid
standing elastic waves ≡ normal modes (ωS,
{ui}s )
If a classical harmonic System has a normal
oscillation mode at a frequency ω, the
corresponding quantum System will have
Eigen states with Energy
En = ħω(n+½) n = 0, 1, 2, 3, ….
ħ = h/2π , h = Plank’s Constant
Each excitation of this normal mode by a step up harmonic Oscillation
excitation Ladder (Increasing the quantum number n) is known as a
phonon.

9. Thermal Conductivity Of Graphene Explained
Just like with Photons, the is a finite number of Phonons
in the crystal Lattice at any given temperature define by
the Bose-Einstein equation
𝑛 𝜔, 𝑇 =
1
𝐸𝑥𝑝(ħω
𝐾 𝐵 𝑇 ) − 1
KB = Boltzmann's Constant
Heat capacity = dU/dT
𝑈 =
𝑁
2𝜋 −𝜋
𝑎
𝜋
𝑎
ħ𝜔(𝑘) 𝑛
𝜔
𝐾 𝐵 𝑇
𝑘 + 1
2 𝑑𝐾
Where:
K = Wave vector
U = total Heat Energy in the lattice

10. Thermal Conductivity Of Graphene Explained
• Graphene is a 2D Crystal therefore
compared to Diamond, its atoms have
a higher degree of freedom, thus
increasing it’s ability to generate more
phonons at a given Temperature
• Because of it’s large specific area
small mass density, and larger
number of phonons that transmit the
heat away, it is unable to store any
considerable amount of heat energy in
any unit cell of the crystal. This make
it’s heat capacity very low, thus
explaining it’s excellent thermal
conductivity
• Since the phonons also have wave
properties, at low temperatures they
are able to interfere contructively with
the waves of the electrons thus
increasing electron Mobility.

11. Semi-conductivity of
Graphene
 Graphene is even
more conductive
than most metals
 It have no Band-gap
 For semi-conductor
applications, such as
Transistors, diodes
e.t.c, Graphene is
either n-doped or P-
doped to open up a
band gap.
Fig: Valence and Conduction
Band for Insulators

12. ENERGY BANDS

13. Energy Bands in Graphene
The valence and
conduction bands touch at
the Brillouin zone corners
thus making Graphene a
zero-bandgap
semiconductor.
Graphene
But due to high electron mobility in Graphene
(1000 times that of Silicon under the same
working conditions) Scientists have dared to
imagine using Graphene in the place of Silicon,
multiple electronic applications to achieve higher
performance (e.g higher processor speed in
computers) but the absence of a band gap in
Graphene posses a major huddle.

14. Why is a Band Gap Important?
It would be helpful to take a look at the p-n junction

15. Ambipolar Property of Graphene
Dirac
Point
This graph shows the variation of
resistance of graphene with electric
field. Resistance is highest at the
Dirac point.
This figure shows the variation of
resistivity with voltage applied
across graphene and corresponding
Fermi energy levels
So obviously, pristine graphene exhibits
strong ambipolar field effect indicating
the doping of electrostatic potential.

16. Effect of Chemical Doping on
Graphene
In the case of Chemical doping
we observe a shift in the Dirac
point relative to the Fermi level
as shown in this diagram
N-doped P-dopedPristin
e
For surface transfer (adsorbate -
induced)doping, doping is achieved
by electron exchange between a
semiconductor and dopants which
adsorb on the surface of a
semiconductor thus the
crystallography of the Graphene is
not altered.
Free standing Graphene would undergo
substitutional doping carbon atoms in
the honeycomb lattice of Graphene are
replaced by atoms with different number
of valence electrons such as nitrogen
and boron. This disrupts sp2
hybridization of carbon atoms hence
altering the crystal structure.

17. Effect of Chemical Doping on
GrapheneEnergy
HOMO
LUMO
Ef
HOMO
LUMO
Pristine Graphene
overla
p
Flow of
Charges
P-type dopantN-type
dopant

18. Effect of Chemical Doping on
Graphene
Doping graphene with p-block elements (i.e., nitrogen, boron, sulfur,
hydrogen, oxygen and fluorine) disrupts the planar structure and
introduces foreign elements which would alter its electronic properties
as shown:

19. Effect of Chemical Doping on the
thermal and Electrical properties of
Graphene
Graphene has been successfully doped with H, B, N, O, S F and
even Cl and their compounds for different reasons, e.g electronic
applications, gas sensing, catalysis e.t.c The Focus of this
presentation is the dopants that favour heating and electronic
application which would be B and N.

20.  Substitutional nitrogen doping
suppresses the DOS of Graphene near
the Fermi level and leads to band gap
opening.
 Carrier mobility and thus conductivity are
lowered below that of Pristine Graphene
 Nitrogen disrupts the aromatic rings in
Graphene so topology of the sheets is
changed thus posing hindrance to flow
of charges
Effect of Chemical Doping on the
thermal and Electrical properties of
Graphene
1. NITROGEN
Ef

21. • Graphene doped with 1.2 to 2.4
at% B shifts the Fermi level 0.65
eV below the Dirac point thus
indicating the p-type doping
behavior.
• B-doping improves electrical and
hence thermal conductivity to
levels higher than those pristine
Graphene or Nitrogen doped
Graphene
• Boron does not disrupt the
aromatic rings in Graphene so
topology of the sheets is
unchanged hence no hindrance to
flow of charges
Effect of Chemical Doping on the
thermal and Electrical properties of
Graphene
2. BORON (B)
0.65
eV

22. COMMENT
 In order to optimize high frequency
performance of Graphene two factors
need to be improved:
1. Increasing Mobility of charges
2. Decreasing net resistance by decreasing
the contact resistance between metal
and Graphene

23. The Concept of Plasmonic
Effect
Metal material with sea of Electron
surrounding positively charges
ions
Electrons in and atom are quantum
particles and their quantum states
defined by the following quantum
numbers
N = Energy Level
L = Orbital quantum number
Ml = Magnetic quantum number
Ms= Spin Quantum number
No two set of electrons in system can
have the same energy state.
The electron’s highest occupied
energy level at absolute zero is
call the Fermi energy, typically a
few eV. (Ef 7 eV for Cu)
Applying Ef = ½mu2
we can find that the electrons in
Cu move at 1.6 x106 m/s at 0 k

24. The Concept of Plasmonic
Effecto A Plasmon is a quasi particle i.e, a particle that can be described as a
collection of interacting particles this case electrons.
o Plasmons occur on the surface of a metal, they are quantized and
consist of a collective of oscillations of the free electrons gas.
The wave created in the surface Plasmon opposes the incident light’s
EM wave. The energy from this wave in the Plasmon dissipates the
energy of light. Since the energy of light is absorbed, the light cannot
penetrate the surface hence metals are opaque. The oscillating
electrons then re-emit the energy they absorbed as reflected light we
see coming from the metal. This is why metals are shiny reflective

25. The Concept of Plasmonic
Effect
Metallic nanoparticles can
be different colors
depending on their size.
This is because the
confinement of the surface
Plasmon to a small
surface, rather that a bulk
material changes the
possible wavelengths that
the surface plasmon in the
metal can have. Not all
wavelengths are available
in a small particle as they
would be in a bulk
For
NanoparticlesVariation of Plasmonic effect
with size

26. The Concept of Plasmonic
Effect
For
NanoparticlesVariation of Plasmonic effect
with size
Fig: UV-vis Spectra for Au nanoparticles
The absorbance of visible light changes as we change the size of the
nanoparticle. One can see a distinct peak in the nanoparticle’s spectrum, that
changes wavelengths as the particle size changes . Ad the particle gets
larger, the spectrum more and more continuous, similar to that of bulk gold.

27. The Concept of Plasmonic
EffectFor
NanoparticlesVariation of Plasmonic effect with shapes

28. The Concept of Plasmonic
EffectFor
NanoparticlesVariation of Plasmonic effect with elements
Gold nano-particles Silver nano-
The Plasmon energy id described classically as
𝝎 𝒑
𝟐
=
𝑵𝒆 𝟐
𝒎𝝐 𝒐
Where in: ωp = Plasmon resonance frequency (/s)
N = is the number density of electrons in the material (/m3)
e = electronic charge 1.602 x10-19 coulombs
m = electronic mass 9.11 x 10-31 Kg
ϵo= Permittivity of free space 8.854 x10 -12 Nm/C2
This explains why different materials nanoparticles that are different colors
even if they have the same size and shape

29. Why is Plasmonic Effect
relevant?
 One main reason for integrating 2D materials such as graphene
with Plasmonic metal nanomaterials is to enhance light absorption
through the Plasmonic effect of the metal component and then to
channel the absorbed light energy to the 2D material part for
technologically important light-involved applications, such as
photocatalysis, optical sensing, and optoelectronics.
 In addition, the Plasmonic electrical effects, including an
enhanced photo-generation rate, the plasmon-induced ‘‘hot
electrons’’, and improved conductivity of the hybrid
nanostructures, also play a significant role in enhancing the
photocatalytic reactions and the performance of photoelectric
devices.
 Recently, 2D MX2 type nanomaterials (M = W, Mo, Ta, Ti, Nb, Re,
etc.; X = Se, S, Te), i.e., transition metal dichalcogenides (TMDs),
have also gained significant attention due to their interesting
optical and electrical properties.

30. The thickness of Graphene and other 2D materials is too thin to absorb
sufficient light, which inevitably restricts their efficient applications, in
particular for some light-driven-related applications, such as photocatalytic
reactions, optical sensors, optoelectronics, and visual images.1,34–40
Specifically, their light absorption is only 2.3%
Why is Plasmonic Effect
relevant?
Fig. (a) The schematics of the Ag NP/graphene composite with the structure of Ag
film/graphene/Ag NPs, (b) the SEM image of Ag film/ graphene/Au NPs, and (c) the TEM image
of evaporated Ag NPs on top of graphene.

31. Graphene on Polymeric
materials
Fig. Graphs of (a) conductivity and (b) stress–strain curves of pristine PEDOT,
graphene/PEDOT, and graphene/PEDOT/graphene composite
Conducting Polymers:
• Polypryrol (PPy)
• Polyaniline (PANI)
• Polyacetylene (PAC)
• Poly(3,4Ethylenedioxythiophene) (PEDOT)
• Poly(3 AminoBenzeneSulfonic acid) (PABS)

32. THANK YOU!

33. Questions
1. a. What is Graphene
b. What is the molecular structure of Graphene? How are the atoms
bonded
c. What is the relationship between Graphene and graphite?
2. a. Would you classify Graphene as a metal, semimetal, semiconductor, or
insulator material and why?
b. Why is Graphene highly electrically conductive?
c. Why does Graphene have high mechanical strength?
3. What is the motivation for doping Graphene?
4. a. Describe Plasmonic effect
b. Given that electronic charge is 1.602 x10-19 coulombs, electronic mass
9.11 x 10-31 Kg and Permittivity of free space 8.854 x10 -12 Nm/C2 , what is to
be expected of the resonance frequency in 30 nm spherical Gold
nanoparticles with 5.90 x 1028m-3 electron density?