Nanoelectronics Lecture Notes Highlights
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EE 315/ECE 451
N
ANOELECTRONICS
I
Derived from lecture notes by R. Munden 2010
8.1 D
ENSITY
OF
S
TATES
10/13/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
2
Imagine the hard walled box, and the energy states available:
# states in sphere of radius En:
Octant of sphere
D
O
S 3D S
YSTEM
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
3
Accounting for Spin. Potential and L
3
= 1 for density per unit volume:
8.1.1 D
ENSITY
OF
S
TATES
IN
L
OW
D
IMENSIONS
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
4
With spin and potential:
For One
Dimensional
Quantum Wire
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
5
8.1.1 D
ENSITY
OF
S
TATES
IN
L
OW
D
IMENSIONS
For 2D Quantum Well
For 0D Quantum Dots
Although real materials are 3D,
quantum confinement in small materials
can approximate low dimensional
structures, like quantum dots.
8.1.2 D
ENSITY
OF
S
TATES
IN
A
S
EMICONDUCTOR
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
6
In 3D materials:
We can use in semiconductors by substituting effective mass
for band structure and Ec for potential
In Silicon (with transverse and longitudinal effective mass)
and 6 fold symmetry of the conduction band:
8.2 C
LASSICAL
AND
Q
UANTUM
S
TATISTICS
Classical or Boltzman Distribution
(distinguishable particles – e.g.molecules):
Fermi-Dirac Distribution (indistinguishable,
exclusive particles – e.g. electrons):
Bose-Einstein Distribution (indistinguishable,
non-exclusive particles – e.g. photons and
phonons):
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
7
F
ERMI
D
ISTRIBUTION
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
8
“Ripples on the Fermi sea”
Occupied
Unoccupied
8.2.1 C
ARRIER
C
ONCENTRATION
IN
M
ATERIALS
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
9
3D confined box
8.2.2 T
HE
I
MPORTANCE
OF
F
ERMI
E
LECTRONS
11/1/2010
R.M
UNDEN
- F
AIRFIELD
U
NIV
. - EE315
10
E
LECTRON
S
TATES
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
11
8.2.3 E
QUILIBRIUM
C
ARRIER
C
ONCENTRATION
10/19/2015
J. D
ENENBERG
- F
AIRFIELD
U
NIV
. - EE315
12
8.3 M
AIN
P
OINTS
11/1/2010
R.M
UNDEN
- F
AIRFIELD
U
NIV
. - EE315
13
the concept of density of states in various spatial dimensions,
and the significance of the density of states;
how the density of states can be measured;
quantum and classical statistics for collections of large numbers
of particles, including the Boltzmann, Fermi-Dirac, and Bose-
Einstein distributions;
the role of density of states and quantum statistics in
determining the Fermi level;
applications of density of states and quantum statistics to
determine carrier concentration in materials, including in doped
semiconductors.
8.4 P
ROBLEMS
11/1/2010
R.M
UNDEN
- F
AIRFIELD
U
NIV
. - EE315
14
The image highlights key concepts from nanoelectronics lecture notes, covering topics such as density of states in different dimensions, classical and quantum statistics, Fermi distribution, and carrier concentration in materials. The visuals aid in understanding complex theoretical aspects of nanoelectronics discussed in the lectures by J. Denenberg from Fairfield University.
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Presentation Transcript
EE 315/ECE 451 NANOELECTRONICS I Derived from lecture notes by R. Munden 2010
8.1 DENSITYOF STATES 2 Imagine the hard walled box, and the energy states available: # states in sphere of radius En: Octant of sphere 10/13/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
DOS 3D SYSTEM 3 Accounting for Spin. Potential and L3 = 1 for density per unit volume: 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
8.1.1 DENSITYOF STATES IN LOW DIMENSIONS 4 For One Dimensional Quantum Wire With spin and potential: 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
8.1.1 DENSITYOF STATES IN LOW DIMENSIONS 5 For 2D Quantum Well Although real materials are 3D, quantum confinement in small materials can approximate low dimensional structures, like quantum dots. For 0D Quantum Dots 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
8.1.2 DENSITYOF STATES INA SEMICONDUCTOR 6 In 3D materials: We can use in semiconductors by substituting effective mass for band structure and Ec for potential In Silicon (with transverse and longitudinal effective mass) and 6 fold symmetry of the conduction band: 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
8.2 CLASSICALAND QUANTUM STATISTICS 7 Classical or Boltzman Distribution (distinguishable particles e.g.molecules): Fermi-Dirac Distribution (indistinguishable, exclusive particles e.g. electrons): Bose-Einstein Distribution (indistinguishable, non-exclusive particles e.g. photons and phonons): 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
FERMI DISTRIBUTION 8 Ripples on the Fermi sea Occupied Unoccupied 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
8.2.1 CARRIER 9 CONCENTRATIONIN MATERIALS 3D confined box 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
8.2.2 THE IMPORTANCEOF FERMI ELECTRONS 10 11/1/2010 R.MUNDEN - FAIRFIELD UNIV. - EE315
ELECTRON STATES 11 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
8.2.3 EQUILIBRIUM CARRIER CONCENTRATION 12 10/19/2015 J. DENENBERG- FAIRFIELD UNIV. - EE315
8.3 MAIN POINTS 13 the concept of density of states in various spatial dimensions, and the significance of the density of states; how the density of states can be measured; quantum and classical statistics for collections of large numbers of particles, including the Boltzmann, Fermi-Dirac, and Bose- Einstein distributions; the role of density of states and quantum statistics in determining the Fermi level; applications of density of states and quantum statistics to determine carrier concentration in materials, including in doped semiconductors. 11/1/2010 R.MUNDEN - FAIRFIELD UNIV. - EE315
8.4 PROBLEMS 14 11/1/2010 R.MUNDEN - FAIRFIELD UNIV. - EE315
