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Supriyo Datta http://nanohub.org/groups/lnebook
FUNDAMENTALS OF NANOELECTRONICS
A. Basic Concepts 1. The new perspective
2. Energy band model
3. What and where is the voltage?
4. Heat & electricity:
Second law & information
Semiclassical Model
B. Quantum Transport
1. Schrodinger Equation
2. Contact-ing Schrodinger
3. More Examples
4. Spin Transport
Quantum Model
Epilogue
EdX: Oct.8 – Dec.8, 2015 EdX: Oct.8 – Dec.8, 2015 EdX: Oct.8 – Dec.8, 2015 Self-paced on nanoHUB-U along with Part A
Supriyo Datta http://nanohub.org/groups/lnebook
Transport Physics
Schrodinger
Quantum Transport
+
Newton Semiclassical Transport
+
out in
Supriyo Datta http://nanohub.org/groups/lnebook
Contact-ing Schrodinger
Schrodinger +
NEGF Equations
Current Operator
Keldysh 1965
and others ..
Supriyo Datta http://nanohub.org/groups/lnebook
Schrodinger to NEGF
GR
Datta Cambridge
1995 2005
Diagram technique for non-equilibrium
processes
Keldysh 1965
Supriyo Datta http://nanohub.org/groups/lnebook
NEGF: Our Perspective
Before 1990
Essential physics
Unimportant detail
Our Perspective
Essential Physics
Additional detail Additional
------------------
After ---------
Supriyo Datta http://nanohub.org/groups/lnebook
Signal propagation
R L
C
Switch Light Bulb Velocity of light
Velocity of electrons
Supriyo Datta http://nanohub.org/groups/lnebook
Where is the Resistance?
Standard view:
Follow the heat !
Joule Heating: I2R
Follow the voltage
Voltage drop: IR
1
T
1-T
0
µ1
µ2
Supriyo Datta http://nanohub.org/groups/lnebook
NEGF Treatment U
f=1 f=0
X
US
Supriyo Datta http://nanohub.org/groups/lnebook
“Vertical” Flow
E1
E2
E3
Inelastic processes
Absorbs heat
f=1 f=0
Dissipates heat
Supriyo Datta http://nanohub.org/groups/lnebook
Alternative view
NEGF viewed as esoteric tool accessible to those well-versed in many-body perturbation theory (MBPT)
MBPT One-electron theory
One-electron theory,
with “care”
“ Courses detailing these (NEGF) approaches usually spend half the time on the formalism, finding the poles of the various Green’s functions, and figuring out analytic continuations and so on. ..”
Supriyo Datta http://nanohub.org/groups/lnebook
NEGF Equations
MBPT One-electron theory
One-electron theory
with “care”
Techniques have evolved
May need non-perturbative
techniques
Relevant to many problems in
nanoelectronics
Supriyo Datta http://nanohub.org/groups/lnebook
50
Spin Transport
25 25
0 100 100
Channel
100
Channel I
= +
I
spinor + =
vector
Spin circuits
Supriyo Datta http://nanohub.org/groups/lnebook
Moving on ..
Magnet dynamics
Detailed numerical examples
Quantum Mechanics Statistical Mechanics
Many-body Theory Second Quantization
Supriyo Datta http://nanohub.org/groups/lnebook
NEGF: One-electron picture
Should be part of grad / undergrad
curriculum
MBPT One-electron
theory
Prerequisite: Calculus,
Differential Equations
Part B requires Matrix Algebra
Helps bring clarity to discussion
Supriyo Datta http://nanohub.org/groups/lnebook
NEGF: One-electron picture
MBPT One-electron
theory
Many subtle issues clouded by formalism,
for example, in spintronics
Helps bring clarity to discussion
Supriyo Datta http://nanohub.org/groups/lnebook
NEGF: One-electron picture
From Feynman Lectures, 2-1 “ .. people.. say there is nothing which
is not contained in the equations .. if I understand them mathematically,
I will understand the physics ..
Only it doesn’t work that way.
A physical understanding is completely unmathematical, imprecise and inexact .. but absolutely necessary for a physicist. ’’
Helps bring clarity to discussion
Supriyo Datta http://nanohub.org/groups/lnebook
FUNDAMENTALS OF NANOELECTRONICS
Text: Lessons From Nanoelectronics: A New Perspective on Transport
World Scientific (2012) II Edition 2016
A. Basic Concepts 1. The new perspective
2. Energy band model
3. What and where is the voltage?
4. Heat & electricity:
Second law & information
EdX: Oct.8 – Dec.8, 2015 EdX: Oct.8 – Dec.8, 2015 EdX: Oct.8 – Dec.8, 2015 Self-paced on nanoHUB-U
along with Part A B. Quantum Transport
1. Schrodinger Equation
2. Contact-ing Schrodinger
3. More Examples
4. Spin Transport Prerequisite: Calculus,
Differential Equations
Part B requires Matrix Algebra