18 Bandstructure 3 - Fundamentals of Nanoelectronics...

Fundamentals of
Fundamentals of
Nanoelectronics
Nanoelectronics
Prof. Supriyo Datta
ECE 453
Purdue University
Network for Computational Nanotechnology
10.06.2004
Lecture 18: Bandstructure 3
Ref. Chapter 5.1 & 5.2

Review
00:03
• Last time we talked about the principle of
bandstructure which allows one to calculate the
energy levels of a periodic structure. In
particular we talked about a dimerized solid
which has two atoms per unit cell.
• The dispersion relation looks like:
• Today we want to expand this idea to a
higher dimension: 2D.
• In particular we’ll use the principle of
bandstructure to describe the energy
levels of graphene…
1 1’ 2 2’ 3 3’ N N’
"
a
{}{} ⇒ =
ikna
n
e
0
ϕ
{ } ( )
[ ]{ }
0 0
k h E =
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
N N
E
φ
# #
2
1
2
1
Every row looks
the same
E
k
1
N

Graphene: Atomic
Orbitals
05:55
• GRAPHENE
• The importance of this material comes in