Physics of Nanoscale Transistors Lundstrom... · Lundstrom Purdue Mark Lundstrom Electrical and...
Transcript of Physics of Nanoscale Transistors Lundstrom... · Lundstrom Purdue Mark Lundstrom Electrical and...
Lundstrom Purdue
Mark LundstromElectrical and Computer Engineering
Purdue University, West Lafayette, IN
Physics of Nanoscale
Transistors
1. Introduction2. The Ballistic MOSFET3. Scattering Theory of the MOSFET4. Beyond the Si MOSFET5. Summary
additional information at: www.ece.purdue.edu/celab
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Acknowledgements
collaborators: Professor Supriyo Datta, Jing Guo, Sayed Hasan, Zhibin Ren, Jung-Hoon Rhew, Anisur Rahman, Ramesh Venugopal, Jing Wang sponsors: NSF, SRC
MARCO Focus Center on Materials, Devices Structures ARO DURINT Indiana 21st Century Research and Technology Fund
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1. Introduction
MOSFET
Bachtold, et al.,Science, Nov. 2001
CNTFET
MolecularFETs?
Drain
Source
GATE
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1. Introduction
EF
EF - qVDS
Gate
DrainSource
VD
1) self-consistent electrostatics
2) transport
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1. Introduction
EF
EF - qVDS
Gate
Drain
Source VD
Q C V C VGS GS DS DS= +
Q Q E Q E qVF F DS= + −+ −( ) ( )
I I E I E qVD F F DS= − −+ −( ) ( )
+k-k
E(k)
EF
EF - qVDS
Q E qVF DS− −( )
I E qVF DS− −( )
Q E qVF DS+ −( )
I E qVF DS+ −( )
(electrostatics)
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1. Introduction
EF
EF - qVDS
Gate
Drain
Source VD
Q x( )
x
at x = 0…..
Q C V C VGS GS GD GD( )0 ≈ +
C CGS ox≈ (constant)
C CDS GS<<
1) Compute Q(VGS,VDS) 2) Determine EF 3) Compute ID
Q C V Vox GS T( )0 ≈ −( )
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1. Introduction
Now……
let’s see how these ideas work out for MOSFETs
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1. Introduction nanoMOS simulations
effective massHamiltonian
VG
VDVS
L=10nm
tox= 0.6 nmtSi= 3 nm
Z. Ren, R. Venugopal, S. Datta, and M. Lundstrom, IEDM, 2001
position (nm)
ener
gy (
eV)
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1. Introduction energy band diagrams
.
VGS VGS
VDS VDS
VDS =0.05
VGS =0.05 VGS =0.6
VDS =0.6
(a) (b)
(d)(c)
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1. Introduction energy band diagrams
Ene
rgy
(eV
)
ε1
ε2
z
ε1
EC(z)
ε2
x
zy
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1. Introduction transport
x
zy
VGS=VDS=0.6
• 2D Electrostatics• Strong off-equilibrium transport• Scattering
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2. The Ballistic MOSFET Natori’s theory
VDS
IDS
VGS
E(k)
E(k)
Gate
Source Drain ε1(x)
“on-current”
linear current
EF EF -qVDS
EF
EF -qVDS
ε1(x)
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2. The Ballistic MOSFET..... thermionic emission
f
fυx
υx
Small VDS
Large VDS
+
+
-
VG
x
y EC(x)
f e eoE k T m k TB x B= − −/ /~
*υ 2 2
n (E
)
Qi(0)
n (E
)ε1(x)
small VDS
large VDS
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2. The Ballistic MOSFET.... charge control in a “well-tempered MOSFET”
f
fυx
υx
Qi(0) ≈ Cox (VGS - VT )
+
+
-
VG
x
y
Small VDS
Large VDS
ε1(x)
small VDS
large VDS
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2. The Ballistic MOSFET..... numerical solution of the ballistic BTE
Increasing VDS
ε 1 (
eV)
---
>
-10 -5 0 5 10
f (kx, ky)ε1 vs. x for VGS = 0.5V
J.-H. Rhew, Purdue University
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Increasing VDS
charge control2. The Ballistic MOSFET.....
X (nm) ---> VDS (V) --->
Qin
v(0
) --
->
i) Qi(0) ≈ constant
-10 -5 0 5 10
Qinv(0)
ε1 vs. x for VGS = 0.5V
ε 1 (
eV)
---
>
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Increasing VDS
X (nm) --->
Increasing VDS
2. The Ballistic MOSFET.....
-10 -5 0 5 10
i) Qi(0) ≈ constantii) <υ(0)> --> υT
ε1 vs. x for VGS = 0.5V
υ ave
(10
7 cm
/s)
---
>
X (nm) --->
ε 1 (
eV)
---
>
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Increasing VDS
velocity saturation in a ballistic FET2. The Ballistic MOSFET.....
X (nm) --->
-10 -5 0 5 10
i) Qi(0) ≈ constantii) <υ(0)> --> υT
υ(0)
ε1 vs. x for VGS = 0.5V
υ υ( ) ˜0 → T
ε 1 (
eV)
---
>
υ inj (
107
cm/s
) -
-->
VDS --->
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2. The Ballistic MOSFET.....
IDS
VDS
I on W C V VDS ox T GS T( ) ˜= −( )υI WQ V
F U
FF U
F
DS i GS T
F DS
F
F DS
F
= ×−
−
+ −
( ) ˜
( )
( )( )
( )
/
/υ
ηη
ηη
1
1
1 2
1 2
0
0
quantum conductanceG = M 2e2/h
V VG T−( )α
IDS
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2. The Ballistic MOSFET..... comparison with measurements.....
Leff = 115/125 nm technology
NMOS: ~ 50% of limit
PMOS: ~ 33% of limit
ballistic(with measured Rs)
• F. Assad, et al. (1999 IEDM)• G. Timp, J. Bude, et al., (1999 IEDM)• D. Rumsey (TECHON 2000)• A. Lochtefeld, D. Antoniadis (EDL, Feb 2001)
measured
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Increasing VDS ballistic
ballistic
-10 -5 0 5 10
X (nm) --->
3. Scattering Theory of the MOSFET.....
scattering
scattering
ε 1 (
eV)
---
>
υ inj (
107
cm/s
) -
-->
VDS --->
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EF - qVDSEF
Qi ≈ constant ≈ Cox (VGS - VT)
J nT
+ + += υ̃
J T J TJball− + −= − +( )1
I Wq J JD = −( )+ −
Q Vq J J
i GST
( )˜
=+( )+ −
+υ
I WQ VT
T
F U
FT
T
F U
F
DS i GS T
F DS
F
F DS
F
=−
×
−−
+−
−
( ) ˜
( )
( )( )
( )
/
/υ
ηηη
η2
1
12
1 2
1 2
0
0
J +J −
3. Scattering Theory of the MOSFET.....
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I WC V VT
TDS ox GS T T= −( )−
×υ̃
2
F
e
F U
F
T
T
e
e
F
F DS
FUF F DS
F
1 2
1 2
1 2
1
1
12
11
/
/
/
ln( )
( )
( )ln( )
ln( )
ηη
ηη η
η
( )+
×−
−
+−
++
−
T V VGS DS( , )
Landauer/McKelvey model
VDS (V)
I DS (
µA/µ
m)
NEGFsimulation
ballistic
inelasticscattering
•
T ≈≈≈≈ 0.6
T ≈≈≈≈ 0.1
3. Scattering Theory of the MOSFET.....
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computing T: low VDS
a
(1-T)aTa T
L=
+λ
λ0
0
xL
I W Ck T q
T V V VDS oxT
BGS T DS=
−( )υ/
I CW
LV V VDS eff ox GS T DS=
+
−( )µλ0
3. Scattering Theory of the MOSFET.....
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3. Scattering Theory of the MOSFET.....
position, x
ener
gy
Eb
Ei X
qV(x)
px
pyp’
ppi
?
1 2 21m qV xxυ > ( )
x1
ε1(x)
longitudinal energy
first scattering event
computing T: high VDS
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ε1(x)
1
1-T
l
mobility is important for nanoscale FETs
computing T: high VDS 3. Scattering Theory of the MOSFET.....
qV E Ei b( )l ≈ −( )
P(x1): probability of returningto the source after
scattering first at x1
x1 < P(x1) large
x1 > P(x1) small
≈ −( )E Ei b
T o
o
≈+λ
λl
l
l
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I W CT
TV VD ox T GS T=
−
−( )υ
2
I W Ck T q
T V V VD oxT
BGS T DS=
−( )υ //2
VDS
ID
T ≈≈≈≈ 0.1
T ≈≈≈≈ 0.6 I WC V VT
TDS ox GS T T= −( )−
×υ̃
2
1
12
11
1 2
1 2
−−
+−
++
−
F U
F
T
T
e
e
F DS
FUF DS
F
/
/
( )
( )ln( )
ln( )
ηη
η
η
Landauer/McKelvey model
T o
o
=+λ
λl
3. Scattering Theory of the MOSFET.....
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• transmission theory provides a clear picture of MOSFETs at the scaling limit:
-source velocity is limited by thermal injection
-velocity saturation occurs at the source
-the scattering that matters occurs near the source
-”mobility” is relevant to nanoscale MOSFETs
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4. Beyond the Si MOSFET.....
VG
VDVS
VG
VDVS
Bachtold, et al.,Science, Nov.2001
3) CNTFET1) MOSFET
2) SBFET
4) MolecularFETs?
Drain
Source
GATE
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4. Beyond the Si MOSFET.....
Jing Guo (Purdue)
VG
VDVS
tox= 0.6 nmtsi= 3 nm
off-state
on-state
φBn
φBn
EF
EF
the Schottky barrier MOSFET
12 nm
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4. Beyond the Si MOSFET..... the Schottky barrier MOSFET
equivalent MOSFET
φBn = −0 25. eV
φBn = 0 0. eV
φBn = 0 1. eV
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4. Beyond the Si MOSFET..... the Schottky barrier MOSFET
EF
EF
EF
EF
φBn = −0 25. eV
φBn = 0 0. eV
φBn = 0 1. eV
MOSFET
SBFETφBn = −( )0 25. eV
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4. Beyond the Si MOSFET..... the Schottky barrier MOSFET
E(k)EF
EF -qVDS
E(k)EF
EF -qVDS
MOSFET SBFETφBn <( )0
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4. Beyond the Si MOSFET.....
C a a1 2= +n m
graphene
E
(n, m) carbon nanotube
k C• = 2πq
E E
ky
kx
ky
kx
ky
kx
(n-m) = multiple of 3 (n-m) ≠ multiple of 3
the CNTFET
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4. Beyond the Si MOSFET.....
VS VDVG
insulator gate
coaxial geometry
the CNTFET
planar geometry CNTFET
Gate1 nm κ=4
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4. Beyond the Si MOSFET..... the CNTFET
D = 1 nmtins = 1 nmκins = 4VDD = 0.4
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5. Summary
• Essential physics of nanoscale transistors is controlled by: -electrostatics -state filling
-transmission
• Transmission theory provides insights into nanoscale MOSFET physics
-velocity saturation at the source-importance of scattering near the source-relevance of mobility
• The performance of transistors based on charge control is largely material-independent
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