ECE 802-604: Nanoelectronics

1
ECE 802-604Nanoelectronics

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

2
Lecture 15, 17 Oct 13
In Chapters 02 and 03 in Datta How to correctly
measure I GV Add scattering to
Landauer-Buttiker Buttiker approach for dealing
with incoherent scatterers 2.6 occupied states
as scatterers 3.1 scattering/S matrix
3
1 Deg, M 1
mR
mL
X
X
O
probe
m
m
4
Outline of the solution
Goal V IR, solve for R What is V mA
mB What is I I I1 I2
5
(No Transcript)
6
Lec 14
where
Ielectron
7
Lec 14 Further benefit from I3 I4 0 with
Unitarity and symmetry, found m
8
Lec 14 Used 3 conditions
1/ I3 I4 0
2/
3/
9
Datta Sec. 2.6
10
1 Deg, M 1
mR
mL
X
X
O
probe
m
mA
mB
m
11
(No Transcript)
12
NT(E)
13
Where from
14
Where from
15
Where from
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
above mB
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
Datta Sec. 3.1
33
What is a scattering S matrix?
34
Introduce an S-matrix to describe both probe and
occupied state scattering while maintaining
Landuaer-Buttiker approach of treating all
terminals alike
35
(No Transcript)
36
Datta, Sec. 3.1
Two propagating modes into one propagating
mode expect scattering due to occupied states
Game plan for each Si j element determine
is it a reflection or a transmission?
37
Start with a more familiar example from a paper
by Engquist
The single in/out channel for the incoherent
scatterer gives an experimentally wrong
resistance. The Buttiker two-channel probe
description turned out to be correct.
38
Example find the S-matrix for the diagram shown.
39
Example find the S-matrix for the diagram shown.
40
Example find the S-matrix for the diagram shown.
41
Example find the scattering matrix S for the
Engquist diagram
42
Example find the scattering matrix S for the
Engquist diagram
aout
bin
gin
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
Datta Sec. 3.1
47
Example find the S-matrix for the diagram shown.
48
(No Transcript)
49
(No Transcript)
50
(No Transcript)