epilogue - nanohub.org

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


Transport Physics

Schrodinger

Quantum Transport

+

Newton Semiclassical Transport

+

out in


Contact-ing Schrodinger

Schrodinger +

NEGF Equations

Current Operator

Keldysh 1965

and others ..


Schrodinger to NEGF

GR

Datta Cambridge

1995 2005

Diagram technique for non-equilibrium

processes

Keldysh 1965


NEGF: Our Perspective

Before 1990

Essential physics

Unimportant detail

Our Perspective

Essential Physics

Additional detail Additional

------------------

After ---------


Signal propagation

R L

C

Switch Light Bulb Velocity of light

Velocity of electrons


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


NEGF Treatment U

f=1 f=0

X

US


“Vertical” Flow

E1

E2

E3

Inelastic processes

Absorbs heat

f=1 f=0

Dissipates heat


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. ..”


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


50

Spin Transport

25 25

0 100 100

Channel

100

Channel I

= +

I

spinor + =

vector

Spin circuits


Moving on ..

Magnet dynamics

Detailed numerical examples

Quantum Mechanics Statistical Mechanics

Many-body Theory Second Quantization


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



MBPT One-electron

theory

Many subtle issues clouded by formalism,

for example, in spintronics




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. ’’



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

epilogue - nanohub.org

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