9/17/09
ECE 495N, Fall09
GRIS 280 MWF 1130A-1220P
Fundamentals of Nanoelectronics
HW#3: Due Monday Sept. 28 in class.
Problem 1: We wish to calculate the current, I through a single discrete energy level
and the average number of electrons, N using the m
11/12/09
1
ECE 495N, Fall09 GRIS 280, MWF 1130A 1220P
HW#7: Due Friday Nov.20 in class.
Problem 1: Obtain the following expression for the conductivity (at low temperatures)
=
GL
=
W
q2
h
L
+L
4 s ns
(1)
in terms of the electron density n s using the conc
12/3/09
1
ECE 495N, Fall09 GRIS 280, MWF 1130A 1220P
HW#9: Due Wednesday Dec.9 in class. This is the last HW for the semester.
Pauli spin matrices:
01
x
=
0
,
10
y
=
(2x2) Identity matrix:
1
i
,
+i 0
=
z
0
0
10
I=
1
01
1. What are the eigenvalues of the (
12/10/09
1
ECE 495N, Fall09 Fundamentals of Nanoelectronics
Final examination: Wednesday 12/16/09, 7-9 pm in CIVL 1144.
Cumulative, closed book. Equations listed below will be provided.
Pauli spin matrices:
01
x
=
10
0
,
y
=
i
+i 0
Eigenvectors of
(2x2) I
8/28/09
ECE 495N, Fall09
GRIS 280 MWF 1130A-1220P
Fundamentals of Nanoelectronics
HW#2: Due Friday Sept.18 in class.
Page numbers refer to the recommended reference
S.Datta, Quantum Transport: Atom to Transistor, Cambridge (2005)
ISBN 0-521-63145-9.
Pleas
10/21/09
ECE 495N, Fall09 GRIS 280, MWF 1130A 1220P
HW#6: Due Friday Oct.30 in class.
Assuming periodic boundary conditions, find
the density of states
D(E ) =
(E
( k )
(E
( k )
k
and the mode density M ( E ) =
k
v x (k )
L
for a two-dimensional conductor
11/20/09
1
ECE 495N, Fall09 GRIS 280, MWF 1130A 1220P
HW#8: Due Friday Dec.4 in class.
Basic equations of
1
coherent transport
+
1 ], 2
1. 1 = i [ 1
= i[ 2
2]
2
+
2
H
]
1
2
1
,
2. G( E ) = [ EI
H
3. A( E ) = i[G
G + ] = G 1G + + G 2G +
Density of states /
1
ECE 495N EXAM II
Friday, Nov. 6, 2009 (in class) GRIS 280, 1130A-1220P
CLOSED BOOK: The following equations will be provided in the exam.
[H ] exp(ik .(d
h( k ) =
nm
m
dn )
Bandstructure
m
D( E ) =
(E
(E
( k )
Density of states
( k )
k
M(E) =
k
+
GB =
f
1
ECE 495N EXAM I
Friday, Oct.2, 2009
GRIS 280, 1130A-1220P
CLOSED BOOK :
The following equations will be provided in the exam.
I=
2q
+
1
+
with
and
+
N = 2( for spin )
U = UL + U0 (N
Fermi functions :
f1 ( E ) =
Law of equilibrium : P =
[ f (E)
12
dE D(
10/9/09
ECE 495N, Fall09 GRIS 280, MWF 1130A 1220P
HW#4: Due Friday Oct.16 in class.
Problem 1: Consider the (2x2) matrix
cos
sin e i
A=
sin e+ i cos
Show that the following
cos ( / 2) e i / 2
sin ( / 2) e i / 2
and
V1
V2
+ i / 2
+ i / 2
sin ( /