Post on 23-Dec-2015
transcript
IEEE Central NC EDS/MTT/SSC Society Friday, Nov. 5th, 2010
The Nanoscale MOSFET:Physics and Limits
Mark Lundstrom
1
Electrical and Computer Engineeringand
Network for Computational NanotechnologyBirck Nanotechnology Center
Purdue University, West Lafayette, Indiana USA
2
21st Century: microelectronics nanoelectronics
transistors per cpu chip
Lundstrom
3
nanoscale MOSFETs 2010
source drain
SiO
2
silicon
channel~ 32 nm
gate oxideEOT ~ 1.1 nm
gateelectrode
S G D
VGS
4
MOSFET IV characteristic
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
S
D
G
circuitsymbol
VDS
VGS
IDS
gate-voltage controlled
current source
gate-voltage controlledresistor
5
MOSFET IV: low VDS
VG>VT VD0
ID W Qi x x (x)
ID W Cox VGS VT effEx
Ex VDS
L
Q
ix C
oxV
GS V
T
ID W
Leff Cox VGS VT VDS
VGS
gate-voltage controlledresistor
6
MOSFET IV: “pinch-off” at high
VDS
VG VD0
Qi x Cox VGS VT V (x)
V x VGS VT
Qi x 0
7
MOSFET IV: high VDS
VG VD0
ID W Cox VGS VT effE x (0)
ID W
Leff Cox VGS VT 2
2 E x (0)
VGS VT
L
Qi x Cox VGS VT V (x)
V x VGS VT
VGS
gate-voltage controlled
current source
ID W Qi x x (x)W Qi 0 x (0)
8
velocity saturation
electric field V/cm --->
velo
city
cm
/s -
-->
107
104
E
sat
VDS
L
1.0V
30nm3105 V/cm
105
9
MOSFET IV: velocity saturation
VG VD0
ID W Qi x x (x)
ID W Cox VGS VT sat
ID W Coxsat VGS VT
E x 104
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
10
carrier transport nanoscale MOSFETs
SAT
Lundstrom
Vel
ocity
(cm
/s)
D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992.
m
m
11
~1995 - 2000
Lundstrom
1950 1970 1990 2010 2030 20501 nm
10 nm
100 nm
1 m
10 m
100 m
Year
Min
imum
Fea
ture
Siz
e 1
1K
1M
1P
?1G
1T
Moore’s Law? Molecular electronics
http://www.eng.yale.edu/reedlab/
12
objectives
1) Present a simple, physical picture of the nanoscale MOSFET (to complement, not supplement simulations).
2) Discuss ballistic limits, velocity saturation, and quantum limits in nanotransistors.
3) Compare to experimental results for Si and III-V FETs
4) Discuss scattering in nano-MOSFETs
Lundstrom
13
outline
Lundstrom
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
14
how transistors work
2007 N-MOSFET
electron energy vs. position
VDS 0.05 V
VGS
EC
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
VDS 1.0 V
VGS
electron energy vs. position
EC
E.O. Johnson, “The IGFET: A Bipolar Transistor in Disguise,” RCA Review, 1973
MOSFETs are barrier controlled devices
EC x
x
E
3) Additional increases in VDS drop near the drain and have a small effect on ID
A. Khakifirooz, O. M. Nayfeh, D. A. Antoniadis, IEEE TED, 56, pp. 1674-1680, 2009.
2) region under strong\
control of gateQI 0 CG VG VT 1) “Well-tempered MOSFET”
M. Lundstrom, IEEE EDL, 18, 361, 1997.
15
16
current flows when the Fermi-levels are different
D(E)
2
EF1 EF 2
1f1 E 1
1 e E EF1 kBTf2 E 1
1 e E EF 2 kBT
gate
I 2q
hT E M E f1 f2 dE
N D E
2f1 E f2 E dE
Lundstrom
17
“top of the barrier model”en
ergy
position
contact 1 contact 2
“device”
LDOS
U EC q S
EF1
EF 2
1 x EC x
Lundstrom
18
outline
Lundstrom
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
19
ballistic MOSFET: linear region
VDS
IDSVGS VDD
Lundstrom
near-equilibrium f1 f2
IDS GCHVDS
20
linear region with MB statistics
Lundstrom
GCH 2q2
hT E M 2 D E f0
E
dEEC
M
2DE g
VW
2m* E EC
h
T E 1
nS N2 De EF EC kBT
gV
m*
h2 e EF EC kBT
GCH WnS
T
2kBT q
GCH WCox
T
2kBT qVGS VT
nS Cox VGS VT (MOS electrostatics)
✔
f
0E 1 1 e
E EF kBTL
T 2kBTL m* x
Boltzmann statistics:
f0 E f0 kBTL
f0 e EF E kBTL
21
ballistic MOSFET: linear region
VDS
IDVGS VDD
Lundstrom
near-equilibrium f1 f2
IDS GCHVDS
IDS GCHVDS
ID WCox
T
2kBT qVGS VT VDS
22
relation to conventional expression
Lundstrom
IDS WCox
T
2kBT qVGS VT VDS
ballistic MOSFET conventional MOSFET
IDS W
LCoxn VGS VT VDS
IDS W
LCox
T L
2kBT qVGS VT VDS
Dn T0
2n
Dn
kBT q
IDS W
LCoxB VGS VT VDS
B T L
2 kBTL q
n B
23
ballistic MOSFET: on-current
VDS
ID
VGS VDD
Lundstrom
f1 f2
ID 2q
hT E M E f1 f2 dE ID
2q
hT E M E f1 dE
24
saturated region with MB statistics
Lundstrom
IDS 2q2
hT E M 2 D E f1 E dE
EC
M
2DE g
VW
2m* E EC
h
T E 1
Boltzmann statistics: f0 e EC EF kBT
nS N2 D
2e EF EC kBT
gV
m*
2h2 e EF EC kBT
IDS WqnST
T 2kBTL m* x
IDS WCoxT VGS VT ✔
25
under low VDS
x
E
EF1 EF 2
I I nS
T
Lundstrom
I I nS
T
I ; I nS ; nS
nS nS nS
nS ; nS
nS
2
nS Cox VGS VT
26
under high VDS
x
E
EF1
EF 2
I
Lundstrom
I nST I nS
T
I 0 nS 0
nS nS nS
nS
nS Cox VGS VT
27
velocity vs. VDS
x
E
EF1
EF 2
I I
I
qnS
I I
nS
I nST I nS
T
Lundstrom
nS nS nS
nS
nS e qVDS kBTL
T
1 e qVDS kBT 1 e qVDS kBT
28
velocity vs. VDS
x
E
EF1
EF 2
I I
VDS
T
Velocity saturates in a ballistic MOSFET but at the top of the barrier, where E-field = 0.
Lundstrom
VDS
29
velocity saturation in a ballistic MOSFET
VDS 1.0 V
VGS
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
2007 N-MOSFETvelocity
saturation
sat 1.0107 cm/s
Lundstrom
T 1.2107 cm/s
30
aside: relation to conventional expression
Lundstrom
ION WCoxT VGS VT
ballistic MOSFET conventional MOSFET
IDS WCoxsat VGS VT
sat T
31
the ballistic IV (Boltzmann statistics)
V
G V
T 1
K. Natori, JAP, 76, 4879, 1994.
IDS (on)W T Cox VGS VT
IDS GCHVDS W Cox
T
2kBT q VGS VT VDS
VDS
ID
ballisticchannel resistance
ballisticon-current
Lundstrom
32
comparison with experiment: Silicon
A. Majumdar, Z. B. Ren, S. J. Koester, and W. Haensch, "Undoped-Body Extremely Thin SOI MOSFETs With Back Gates," IEEE Transactions on Electron Devices, 56, pp. 2270-2276, 2009.
Device characterization and simulation: Himadri Pal and Yang Liu, Purdue, 2010.
LG 40 nm
ION Iballistic 0.6
IDlin Iballistic 0.2
• Si MOSFETs deliver > one-half of the ballistic on-current. (Similar for the past 15 years.)
• MOSFETs operate closer to the ballistic limit under high VDS.
33
comparison with experiment: InGaAs HEMTscomparison with experiment: InGaAs HEMTs
Jesus del Alamo group (MIT)
Lundstrom
34
outline
Lundstrom
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
35
transmission and carrier scattering
T 0
0 L
0 T 1
R 1 T
1
L
X
X X
λ0 is the mean-free-path for backscattering
IDS TIDS ?
Lundstrom
?
ID T WCox VGS VT T
2kBT q
VDS
36
the quasi-ballistic MOSFET
VDS
IDS
Tlin 0.2
Lundstrom
37
on current and transmission
Lundstrom
ION T
2 T
IBALL
EF1EF 2
ID TI I 1 T I Qi 0 I 1 T I WT
Qi 0 IBALL
WT
I IBALL
2 T
ID WT
T
2 T
Cox VGS VT
ID T WCox VGS VT T
2kBT q
VDS
38
the quasi-ballistic MOSFET
VDS
IDS
Tsat 0.7
Tlin 0.2
Tsat Tlin why?
Lundstrom
39
scattering under high VDS
x
E
EF1
EF 2
Tsat
0
0 l
L
Tlin 0
0 L
L l
Tsat Tlin
Lundstrom
40
connection to traditional model (low VDS)
ID W
LnCox VGS VT VDS
ID W
L 0
nCox VGS VT VDS
ID T WCox VGS VT T
2kBT q
VDS
Lundstrom
T 0
0 L
ID W
LappCox VGS VT VDS
1 app 1 n 1 B
41
connection to traditional model (high VDS)
how do we interpret this result?
ID WCox VGS VT T
T
2 T
ID W
1
T
1
Dn l
1
Cox VGS VT
ID WCoxsat VGS VT
Lundstrom
42
the MOSFET as a BJT
ID W (0) Cox VGS VT
1 x x
E
1
(0)
1
T
1
Dn l
‘bottleneck’“collector”
“base”
Lundstrom
43
outline
Lundstrom
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
44
physics of nanoscale MOSFETs
VDS
ID
1) Transistor-like I-V characteristics are a result of electrostatics.
2) The channel resistance has a lower limit - no matter how high the mobility is.
3) The on-current is controlled by the ballistic injection velocity - not the high-field, bulk saturation velocity.
4) Channel velocity saturates near the source, not at the drain end.
Lundstrom
45
limits to barrier control: quantum tunneling
from M. Luisier, ETH Zurich / Purdue
4) 3)
2) 1)
46
21st Century electronics?
Lundstrom
1950 1970 1990 2010 2030 20501 nm
10 nm
100 nm
1 m
10 m
100 m
Year
Min
imum
Fea
ture
Siz
e 1
1K
1M
1P
?1G
1T
Moore’s Law?
47
21st Century electronics
Lundstrom
1) Information processing dominated by “Si CMOS”
2) SOC’s complemented by “CMOS+” technologies
3) and…..
macroelectronics, power electronics, PV, solid-state lighting, thermoelectrics, …
48
for more information
Lundstrom
1) “Physics of Nanoscale MOSFETs,” a series of eight lectures on the subject presented at the 2008 NCN@Purdue Summer School by Mark Lundstrom, 2008.http://nanohub.org/resources/5306
2) “Electronic Transport in Semiconductors,” Lectures 1-7, by Mark Lundstrom, 2009.http://nanohub.org/resources/7281
49
questions
Lundstrom
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary