tunnel transistor mechanism based on density of states
TRANSCRIPT
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.