Embed Size (px)
Citation preview
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
Lundstrom Purdue
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
Lundstrom Purdue
1. Introduction
MOSFET
Bachtold, et al.,Science, Nov. 2001
CNTFET
MolecularFETs?
Drain
Source
GATE
Lundstrom Purdue
1. Introduction
EF
EF - qVDS
Gate
DrainSource
VD
1) self-consistent electrostatics
2) transport
Lundstrom Purdue
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)
Lundstrom Purdue
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 ≈ −( )
Lundstrom Purdue
1. Introduction
Now……
let’s see how these ideas work out for MOSFETs
Lundstrom Purdue
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)
Lundstrom Purdue
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)
Lundstrom Purdue
1. Introduction energy band diagrams
Ene
rgy
(eV
)
ε1
ε2
z
ε1
EC(z)
ε2
x
zy
Lundstrom Purdue
1. Introduction transport
x
zy
VGS=VDS=0.6
• 2D Electrostatics• Strong off-equilibrium transport• Scattering
Lundstrom Purdue
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)
Lundstrom Purdue
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
Lundstrom Purdue
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
Lundstrom Purdue
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
Lundstrom Purdue
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)
---
>
Lundstrom Purdue
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)
---
>
Lundstrom Purdue
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 --->
Lundstrom Purdue
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
Lundstrom Purdue
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
Lundstrom Purdue
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 --->
Lundstrom Purdue
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.....
Lundstrom Purdue
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.....
Lundstrom Purdue
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.....
Lundstrom Purdue
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
Lundstrom Purdue
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
Lundstrom Purdue
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.....
Lundstrom Purdue
• 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
Lundstrom Purdue
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
Lundstrom Purdue
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
Lundstrom Purdue
4. Beyond the Si MOSFET..... the Schottky barrier MOSFET
equivalent MOSFET
φBn = −0 25. eV
φBn = 0 0. eV
φBn = 0 1. eV
Lundstrom Purdue
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
Lundstrom Purdue
4. Beyond the Si MOSFET..... the Schottky barrier MOSFET
E(k)EF
EF -qVDS
E(k)EF
EF -qVDS
MOSFET SBFETφBn <( )0
Lundstrom Purdue
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
Lundstrom Purdue
4. Beyond the Si MOSFET.....
VS VDVG
insulator gate
coaxial geometry
the CNTFET
planar geometry CNTFET
Gate1 nm κ=4
Lundstrom Purdue
4. Beyond the Si MOSFET..... the CNTFET
D = 1 nmtins = 1 nmκins = 4VDD = 0.4
Lundstrom Purdue
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
www.ece.purdue.edu/celab
