Supriyo Datta

Lessons from nanoelectronics

“ No trees were killed to send this message, however,

Note at the end of an e-message

a large number of electrons were terribly inconvenienced ”

2. What is “voltage” ?

1. How electrons are “inconvenienced?”

3. “Spin voltage” à New class of devices

https:/nanohub.org/groups/courses/fon1 ,2

Supriyo Datta

What is a transistor?

18

Resistance

R = VI

A controlled resistor

VG = 0

R = 108ohms

VG = 1 volt

R = 104ohms

n-MOS

VG = 0

VG = 1 volt

p-MOS . VG

How electrons are “inconvenienced”

Supriyo Datta

E

D(E)

How resistance is controlled

OFF ON n-MOS

ON OFF

17

. VG

µFermiEnergy

σ = q2 n τm

Drude formula

p-MOS

How electrons are “inconvenienced”

Supriyo Datta

Why electrons flow

Channel

µ E

D(E)

µ

Equilibrium

Current flows only in small energy window

Hard to understand if we say that electric field

drives electrons

µ E

q V

D(E)

16 How electrons are “inconvenienced”

Supriyo Datta

Conductance

D: Density of states t : transit time

D. qV2

= Iq

× t

PhD’s /year

# of PhD students

Time spent getting PhD =

G ≡I

V=

q2D

2t

Electrons /second

# of electrons in channel

Time spent in channel =

15

I ~ G(E) f1(E)− f2 (E)( )No energy loss in channel

How electrons are “inconvenienced”

Supriyo Datta

Ballistic Conductance

Channel Source

Drain

L W

tB = Lν

GB

W à 2 tD

→ h*M

G = q2 D2t

D ~ WL

M = 2,4,6,8, ……

GB ~ W

14

2 tD

= h

hq2

≈ 25 KΩ

ΔE ~ h2t

D = 1ΔE

~ 2th

M q2

h=GB

How electrons are “inconvenienced”

Supriyo Datta

The New Perspective

1+L

mfp

⎛⎝⎜

⎞⎠⎟

0.1 mm

10 µm

1 µ m

0.1 µm

10 nm

1 nm

0.1 nm

2015

1985

R =h

q2

1

M

hq2

≈ 25 KΩ

13

Atoms G = q2 D2t

1ρ≡ σ = q2 n τ

mDrude

formula

= ρW

LVI

≡ R

mfp: mean free path

L

https://nanohub.org/groups/courses/fon1, 2

Kubo formula

Supriyo Datta

Where is the Resistance?

12

µ1

µ2

qV

RB2

RB2

RBLmfp

R = RB 1+ Lmfp

⎛⎝⎜

⎞⎠⎟

What is “voltage?”

Standard view:

Follow the heat !

Ø  Joule Heating: I2R

Follow the voltage

Ø Voltage drop: IR

Supriyo Datta

Diffusion Equation

11

µ1

µ2

qV

RB2

RB2

RBLmfp

R = RB 1+ Lmfp

⎛⎝⎜

⎞⎠⎟

µ(x = 0) = µ1µ(x = L) = µ2

What is “voltage?”

J = − σqdµdx

µ+ (x = 0) = µ1µ− (x = L) = µ2

X µ+

µ-

Supriyo Datta

Ballistic Flow

10

µ1

µ2

qV

RB2

RB2

~ 0 R = RB 1+ Lmfp

⎛⎝⎜

⎞⎠⎟

What is “voltage?”

µ+

µ-

Lucknow NH-6 Allahabad NH-24B

Supriyo Datta

Localized Scatterer

9

µ1

µ2

qV

RB2

RB2

RB1−TT → R = RB

1T

What is “voltage?”

µ+

µ-

T Lucknow Allahabad NH-24B

Supriyo Datta

I2R is NOT localized

8

µ1

µ2

qV

RB2

RB2

RB1−TT

What is “voltage?”

µ+

µ-

T

T

1

0

µ+

µ1

↑ f (E)

1

0

EC

Even if R is localized

Supriyo Datta

Distributed Scatterers

7

µ1

µ2RB2

RB2

RBLmfp

“Spin voltage”

µ+

µ-

Topological Insulators

Bi2Te3

Channel

up

dn

Channel

up

dn

à µup

µdn ß

Supriyo Datta

Measuring Spin Voltage

6

µ1

µ2

µ+

µ-

à µup

µdn ß

µup − µdn = qI RB

(µP − µup ) g1 +(µP − µ dn ) g2 = 0

µP (+M )− µP (−M ) =

(µup − µ dn ) g1 − g2g1 + g2

FM

“Spin voltage”

µP

g1 g2

up

dn

Spin current ≠ 0

Supriyo Datta

Experiment

µP (+M )− µP (−M )

= qI RB PM y.M

THEORY Hong et al. PRB 2012

µup − µdn = qI RB

5

x

y

“Spin voltage”

Jonker et al. Nature Nano (2014)

Supriyo Datta

High S-O versus Magnetic

µup − µdn = qI RB

4 “Spin voltage”

Topo logicalInsulators : N = 0

p = M − NM + N

Channel

High S-O

Channel

Magnetic

M M

N N

Supriyo Datta

Pure Spin Conduction

3 “Spin voltage”

I I Is

Is

“ Conductance is Transmission “

Spin Conductance is NOT Necessarily Transmission

But

FMI X

Supriyo Datta

50

Spin Transport

25 25

0 100 100

Channel

θ

100

Channel I

= +

180 360 0

I

→ θspinor

+ =

vector

2

Σ1

Σ3

Σ4

Σ2

HΣ0 → Spin scattering

NEGF

Camsari et al. Sci. Rep. (2015)

Spin Circuits

Supriyo Datta

Spins & Magnets “Brain-inspired“ Magnetic Networks?

50 25 25 100

Channel I

= +

Solid-state “Stern-Gerlach”

1

Camsari et al. Sci. Rep. (2015)

Spin Circuits

Supriyo Datta Lessons from Nanoelectronics

nanohub.org/groups/courses/fon1 ,2

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. ’’

0

I ~ G(E) f1(E)− f2 (E)( )

Elastic Resistor: Good approx to nanodevice

§  Correct driving term

~ dfdx

~ dµdx

https://nanohub.org/groups/courses/fon1, 2

J = σ F ~ − dφ / dxUsual physical picture based on

Alternative physical picture