ECE 802-604: Nanoelectronics

1
ECE 802-604Nanoelectronics

• Prof. Virginia Ayres
• Electrical Computer Engineering
• Michigan State University
• ayresv_at_msu.edu

2
Lecture 26, 02 Dec 13
Carbon Nanotubes and Graphene CNT/Graphene
electronic properties sp2 electronic
structure 2DEG E-k relationship/graph for
graphene and transport 1DEG E-k
relationship/graph for CNTs and
transport Examples Molecular Electronics
R. Saito, G. Dresselhaus and M.S.
Dresselhaus Physical Properties of Carbon
Nanotubes
3
CNT Unit cell in green
Ch n a1 m a2 Ch avn2 m2 mn dt
Ch/p cos q a1 Ch
a1 Ch T t1 a1 t2 a2 t1 (2m
n)/ dR t2 - (2n m) /dR dR the
greatest common divisor of 2m n and 2n m T
v 3(m2 n2nm)/dR v 3Ch/dR N T X Ch
a1 x a2 2(m2 n2nm)/dR
4
Example is Ch for the armchair CNT at right
angles to Ch for the zigzag CNT?
5
Example is Ch for the armchair CNT at right
angles to Ch for the zigzag CNT? Answer No. Its
at an angle. HW evaluate the angle.
6
If this is the specified unit vector system, then
armchair Ch is at the chiral angle and zigzag Ch
in a1 direction .
a1
7
Example for the paper cutout, is Ch for the
armchair CNT at right angles to Ch for the zigzag
CNT?
8
Example for the paper cutout, is Ch for the
armchair CNT at right angles to Ch for the zigzag
CNT? Answer. No. Answer doesnt change.
9
Example for the paper cutout, number and create
the largest possible zigzag CNT
10
Example for the paper cutout, number and create
the largest possible zigzag CNT Answer (5,0).
HW evaluate T and cut out the proper Unit cell
length.
11
Example for the paper cutout, number and create
the largest possible armchair CNT
12
Example for the paper cutout, number and create
the largest possible armchair CNT Answer (3,3).
HW evaluate T and cut out the proper Unit cell
length.
13
Example Unit vectors a1 and a2 are not pointing
in the same directions in (a) and (b). What is
the goal of each arrangement?
ARMCHAIR
ZIGZAG
14
Example Unit vectors a1 and a2 are not pointing
in the same directions in (a) and (b). What is
the goal of each arrangement? Answer
ARMCHAIR
ZIGZAG
15
Lec 24 Graphene the 6 equivalent K-points ?
Bottom of the conduction band the 6 equivalent
K-points ? metallic
E
ky
kx
This factor slices the graphene Eg2D
16
Lec 24 At a K- point metallic
Condition
Armchair (n,n) are always metallic
17
Lec 24 At a K- point metallic
Condition
Example Prove this condition. First identify
the Unit vector system being used.
18
Answer First identify the Unit vector system
being used.
ARMCHAIR
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
Ch n a1 m a2 Ch avn2 m2
mn cos q a1 Ch a1 Ch
For HW
25
For HW Find K1 in this system. Show K1 2p
/ Ch
26
Lec 06
27
Lec 24 What you can do with an E-k diagram
Answer
28
1DEG CNT
Conduction energy levels
29
Lec 24 Consider an (n, n) armchair CNT. This is
where the periodic boundary condition on kX comes
from in
That leaves just kY as open, MD calls it just k.
30
Linearize graphene dependence around the K-point
31
Lecture 26, 02 Dec 13
Molecular Electronics Why not polyacetylene? or
any conjugated ene? Examples of
possibilities Actual performance Electronic (p)
structure brief review Mechanical (s) structure
brief review New bond alteration
structure Electronic result of bond alteration
structure Qualitative
32
CNTs Electronic structure
Armchair (n,n)
Zigzag (3n,0)
Armchair (?3n,0)
33
CNTs Electronic device
34
Graphene Electronic structure
35
Graphene Electronic device
36
Polyacetylene Electronic structure
37
Polyacetylene Electronic device
38
Polyphenylene Electronic structure
39
Polyphenylene Electronic device
40
(No Transcript)
41
(No Transcript)
42
If it looked the same in 2008 as in 1992, there
are some problems that people are still trying to
solve!
43

• Expected performance Polyphenylene and
  Polyactetylene
• Quasi-ballistic like graphene and SWCNTs

• Actual performance Polyphenylene and
  Polyactetylene
• Slow
• Variable

44
Factors that affect transport

• Availability of electrons AND empty states to
  take them
• Scattering
• Particle-like Lf lt Lm lt L
• Wavelike (ballistic) L lt Lm lt Lf
• Electrons in a 2D or 1D structure are wavelike
  and therefore should have limited scattering
• Transport mechanism
• Diffusion
• Tunnelling
• Ballistic (Plasmon)
• Charge transfer
• Soliton (Polaron)
• Exciton
• Hopping
• Injection (Contacts)

45
Lecture 27, 03 Dec 13
Molecular Electronics Why not polyacetylene? or
any conjugated ene? Examples of
possibilities Actual performance Electronic (p)
structure brief review Mechanical (s) structure
brief review New bond alteration
structure Electronic result of bond alteration
structure Qualitative Quantitative Solitons
(polarons) Su-Schreiffer-Heeger (SSH) model
46
Division of structural and electronic properties
in sp2 makes both good
-CC-
Structure s-bonds
Electronic p-bonds
47
Structure s-bonds
Electronic p-bonds
p -conduction band e- ECE, PHY -anti-bonding
e- CHM
Electronic Delocalized p e-
p -valence band e- ECE, PHY -bonding e- CHM
48
Division of structural and electronic properties
in sp2 makes both good
-CC-
Structure s-bonds
MECHANICAL
Electronic p-bonds
ELECTRICAL
49
Lecture 26, 02 Dec 13
Molecular Electronics Why not polyacetylene? or
any conjugated ene? Examples of
possibilities Actual performance Electronic (p)
structure brief review Mechanical (s) structure
brief review New bond alteration
structure Electronic result of bond alteration
structure Qualitative Quantitative Solitons
(polarons) Su-Schreiffer-Heeger (SSH) model
50
Review Polyacetylene HAA types
c
c
H
H
51
New Bond alteration polyacetylene HAA typesNo
formula changes due to long single and short
double bonds
A
B
-a
a
52
Review Polyacetylene HAB types
a
a
H
H
H
H
A
c
c
c
c
c
c
c
B
H
H
H
-a/2
a/2
53
New Bond alteration polyacetylene HAB types
-a
a
A
B
B
54
Also Two identical bond alterations
55
This is handled by a perturbation approach.
less
more
56
(No Transcript)