GRAPHENE -THE NEW WONDER MATERIAL

WHAT IS GRAPHENE?

Graphene is a flat monolayer of carbon atoms packed into two-dimensional honeycomb structure.

Graphene is expected to replace silicon-based electronicdevices. 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

• Highly Conductive• Very Strong• 2D Honeycomb Structure• Extremely Thin

Electronic dispersion of graphene

ELECTRONIC PROPERTIES

Electrons in graphene behave like massless relativistic (Dirac) particles

ordinarysemiconductor

graphene

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 conductive band. Energy of photons:E=ħωP=ħk where k is a wave vectorω=CkTherefore… E=CP

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 Similarity:Energy of photons in both cases are proportional relationships. EαP but with different constant values.

Fermi Levels

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.

A-Level Physics!Wave-particle duality

Electromagnetism

Photons Waves

Photoelectric effect

Double slit interference

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 looking at the quantum behaviour of the electrons

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:

∫𝑥 1

𝑥 2

|ψ |2𝑑𝑥

Quantum Tunnelling

Quantum tunnelling is a phenomenon where a particle passes through a barrier that classically cannot.In classical physics the electron will rebound off the barrierIn quantum mechanics the electron has a small chance to tunnel through the barrierIn quantum electrodynamics such as if the barrier is graphene the electron will always tunnel through.

Structure of Graphene

Graphene is a lattice that can go on to infinityUnit cell shows it’s the symmetrical at this point and everywhereBecause of this you get a brillouin zone

A

B

Py

PX

KK’

K’

K’K

K

S = +1

S = -1

X

Brillouin Zone

ΨA =

ΨB =

A

B

P

A

B

P ΨA =

ΨB =

R

V0

d

T

x0 D

E

V0

Stage 1 Stage 2 Stage 3

Why Do Electrons in Graphene Behave Differently?

Boundary Conditions