Tunnel Transistor Mechanism Based on Density of States

Tunnel Transistor Mechanism Based on

Density of States Switching

Nov. 3-4, 2011

Eli Yablonovitch, Berkeley EECS Dept.

Our Sponsors:

A Science & Technology Center

The New Switch has to Satisfy Three Specifications:

1. Steepness (or sensitivity)

switches with only a few milli-volts

60mV/decade 1mV/decade

2. On/Off ratio. 106 : 1

3. Current Density or Conductance Density

(for miniaturization)

old spec at 1Volt: 1 mAmp/micron

our spec: 1 milli-mho/micron

A 1 micron device should conduct at 1K in the on-state.

A Science & Technology Center

• Modulate the Tunneling Barrier

• Density of States Switch

2 Ways to Obtain Steepness

The sub-threshold slope for tunneling depends

on the steepness of the band-edges:

The Zener Diode:

EFc

EFv

Bias Voltage

Cu

rren

t

EF

ba

nd

to

ba

nd

tu

nn

elin

g

Bias Voltage

Sharp Step

Cu

rren

t

The Esaki Diode:

The Backward Diode as a Switch:

EFc

EFv

Bias Voltage

Cu

rren

t

Sharp Step

The Backward Diode:

These have been routinely

made in Ge homo-junctions,

since the 1960's.

Conduction

band

Valence

band

Switching

Principle:

Conduction

band

Valence

band

Switching

Principle:

What could go wrong?

1. quantum-mechanical level repulsion:

Ener

gy L

evel

Gate Voltage

levels never line up!

What could go wrong?

2. The levels broaden due to the contacts:

conflicting requirements:

a. low contact resistance

b. sharp level

contact

b

Z

2

T4k

E2qT

hcontact conductance =

linewidth = (2/) EZ Tcontact

What could go wrong?

2. The levels broaden due to the contacts:

A compromise must be

accepted:

Tk

γ

8

2q

b

2

hGcontact conductance

Conductance

quantum

Penalty

for steep

response

1. Solve quantum-mechanical level repulsion problem:

En

erg

y L

evel

Gate Voltage

Ensure that contact broadening >

device,,

1T fZiZif EEM

device,,

1T fZiZif EEM

tunnel

matrix

element

1. Solve quantum-mechanical level repulsion problem:

Tcontact Tdevice

Requirement:

contact tunnel transmission is better than device tunnel transmission:

Tcontact >Tdevice

The device tunneling probablity

should neither be to big nor too small!

Tcontact

What else could go wrong? 3. The contact broadening is bad enough,

the also levels broaden due to the phonons

and due to Coulomb Blockade

and they possibly develop side-bands

also called: band tails

also called: phonon assisted tunneling

It is embarrassing to the scientific world that we know

so little about this.

Both: theory is weak, and

experimental data are almost non-existent.

This science has to be a major goal of the Center

It is embarrassing to the scientific world that we know

so little about this.

Both: theory is weak, and

experimental data are almost non-existent.

This science has to be a major goal of the Center

What else could go wrong? 3. The contact broadening is bad enough,

the also levels broaden due to the phonons

and due to Coulomb Blockade

and they possibly develop side-bands

also called: band tails

also called: phonon assisted tunneling

EC

OFF

material 2 (AlGaSb)

oxi

de

gate metal

qu

antu

m w

ell 1

(In

As)

EF

EV

EF

EC

ON

EF

EF

EV

oxi

de

gate metal

qu

antu

m w

ell 1

(In

As)

material 2 (AlGaSb)

EC

SHARPLY OFF

material 2 (AlGaSb)

oxi

de

gate metal

qu

antu

m w

ell 1

(In

As)

EF

EV

EF

CDEP

CQW

COX

z

A Density of States Switch is

explicitly affected by dimensionality:

I p

I

p

n

I p

n

I

p

I

p

n

I p

n

n

I

p

I

p

n

I p

1d:1d

1d:1d

0d:1d

0d:0d

2d:2d

2d:2d

n n

n

1d:2d

3d:3d 2d:3d

I

Z P

N

I P

N

Z LZ,i

I

VG

2OLVI

I

VG

N

I

P

Z

I

VG

N

I

P Z

X VG

OLVI 1

N

I

P

Z

I

VG

I

P

N

Z

I

VG

ConstantI

Y I

P

N

Z

Z I

P

X

N

I

VG

2/3OLVI

I

VG

OLVI

N

I

P

Z

I

VG

ConstantI

0 2 4 6 8 100

5

10

15

20

0 10 20 30 40 500

5

10

15

20

G

VOL(mV) (a)

Conduct

ance

(µS

)

G

VOL(mV) (b)

Conduct

ance

(µS

)

=2.34 meV

EZ=50 meV

Tdevice=2.16%

LX=32 nm

LZ=8.672 nm

m*=0.1

0 10 20 30 40 500

0.2

0.4

0.6

0 2 4 6 8 100

0.2

0.4

0.6

G/µm

VOL(mV) (a)

Con

duct

ance

Den

sity

(m

S/µ

m)

G/µm

VOL(mV) (b)

Conduct

ance

Den

sity

(m

S/µ

m)

40

=2.34 meV

EZ=50 meV

Tdevice=2.16%

LX=32 nm

LZ=8.672 nm

m*=0.1

Case Picture Current Conductance, G Maximum G for pert.

theory to be valid

Maximum G

for end contacts

1d-1d N/A N/A

3d-3d N/A

N/A

2d-2dedge

N/A

N/A

0d-1d N/A

N/A

2d-3d N/A

N/A

1d-2d N/A

N/A

0d-0d

2d-2dface

1d-1dedge

T4k

qV

h

2q

3π

Vqm2L

b

deviceOL

2OL

*

X T

T4k

qE

2q

b

deviceZ T

h

T4k

qE

4q

2

qV

2π

Am

b

deviceZOL

2 T

h

T4k

qE

4qVqm

π

L

b

deviceZOL

*X T

h

T4k

qE

4q

bcontact

deviceiZ,

T

T

T4k

qEE

π

qmA

b

devicefZ,iZ,32 T

deviceOL

2OL

*

XV

h

2q

3π

Vqm2LT

deviceZE2q

Th

deviceZOL

2E

4q

2

qV

2π

AmT

h

deviceZOL

*X E4q

Vqmπ

LT

h

contact

deviceiZ,E

4q

T

T

devicefZ,iZ,32EE

π

qmAT

device

OL

fZ,iZ,22 qV

mEE

π

Lq2 T

T4k

q

qV

mEE

π

Lq2

b

device

OL

fZ,iZ,22 T

Tk

γπ

h

2q

b

22

22

b

232

π

2mA

T4k

1γ

2

π

h

2q

22

2

b

3/222

π

2mL

T4k

1γπ2

h

2q

Tk

γπ

h

2q

b

22

Tk

γ

4

2π

h

2q

b

3/22

Tk

γ

L

W

4

π

h

2q

bX

22

XE)(2/πγ

deviceOL

2

V2q

Th T4k

qV

2q

b

deviceOL

2

T

h

deviceOL

2

OL

2

*

V2q

2

qV

4π

AmT

h T4k

qV

2q

2

qV

4π

Am

b

deviceOL

2

OL

2

*

T

h

The Milli-Volt Switch

Key Scientific Questions:

• Fundamental band edge abruptness is very poorly understood.

•New examples of Type III Energy band offsets need to be discovered.

• Do we need to concentrate on 2d/2d pn junctions?

• Will that guarantee reproducible thresholds?

The Backward Diode as a Switch:

EFc

EFv

Bias Voltage

Cu

rren

t

Sharp Step

The Backward Diode:

These have been routinely

made in Ge homo-junctions,

since the 1960's.