WHAT IS GRAPHENE?
Graphene is a flat monolayer of carbon
atoms packed into two-dimensional honeycomb structure.
Graphene is expected to replace silicon-based electronic
devices. Graphene-based devices are predicted to be
substantially faster, thinner and more efficient.
NOBEL PRIZE 2010
Nobel Prize in Physics for 2010 was awarded
to Sir Andre Geim and Sir Kostia Novoselov
“for ground-breaking experiments
regarding the two-dimensional material graphene”
PROPERTIES OF GRAPHENE
2D Honeycomb Structure
Electronic dispersion of graphene
Electrons in graphene behave like massless
relativistic (Dirac) particles
Semiconductor Band Width
No current can flow when an electrical field is put across a
semiconductor because electrons cannot flow from the
valence band (red) to the conductive band (blue).
Electrons need energy to pass from the valence band to
the conductive band. This energy is provided by photons.
The closer the two bands (smaller the band width) the
less energy is required to excite the electrons to the
Energy of photons:
P=ħk where k is a wave vector
Graphene Band Width
When graphene is put in an electric field there is no band
width a current can flow as electrons can move from the
valence band to the conductive band without the need for
extra energy i.e. from a photon.
Energy of Photons:
E=VfP where Vf is 106 ms-1
Energy of photons in both cases are proportional
relationships. EαP but with different constant values.
Pauli Principle: Because of the
opposite spin states fermions cannot
share the same energy level/state.
The highest energy level occupied by
a fermion is known as the Fermi level.
You should know that electrons demonstrate properties of both
particles and waves also…
Wave Function, ψ
ψ Describes the quantum state of a particle and how it behaves, in the case of graphene, we’re look
ψ is complex – has real and imaginary parts
|ψ|2, is real, |ψ|2 = ψ x ψ*
|ψ|2 corresponds to the probability density of finding a particle in a given place in a given time
The probability of finding a
particle between two x values:
Quantum tunnelling is a phenomenon wher
In classical physics the electron will rebound
In quantum mechanics the electron has a sm
In quantum electrodynamics such as if the b
Structure of Graphene
Graphene is a lattice that can go on to infini
Unit cell shows it’s the symmetrical at this p
Because of this you get a brillouin zone
S = +1
S = -1