IEEE Central NC EDS/MTT/SSC Society Friday, Nov. 5th, 2010
The Nanoscale MOSFET:
Physics and Limits
Mark Lundstrom
Electrical and Computer Engineering
and
Network for Computational Nanotechnology
Birck Nanotechnology Center
Purdue University, West Lafayette, Indiana USA
1
21st Century: microelectronics  nanoelectronics
transistors per cpu chip
2
Lundstrom
nanoscale MOSFETs 2010
S
G
D
source
drain
silicon
3
SiO2
gate
electrode
gate oxide
EOT ~ 1.1 nm
channel
~ 32 nm
MOSFET IV characteristic
gate-voltage
controlled
current source
circuit
symbol
D
I DS
VDS
G
VGS
S
4
VGS
gate-voltage
controlled
resistor
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
MOSFET IV: low VDS
0
VG>VT
VD
VGS


Qi x  Cox VGS  VT

I D  W Qi x  x (x)
ID  W Cox VGS VT effE x
VDS
Ex 
L
5
gate-voltage
controlled
resistor
W
ID  eff Cox VGS VT VDS
L
MOSFET IV: “pinch-off” at high VDS
0
VG
VD
V x   VGS  VT 
Qi x   Cox VGS  VT  V (x)
Qi x   0
6

MOSFET IV: high VDS
0
VG
VD
gate-voltage
controlled
current source
V x   VGS  VT 
VGS
Qi x   Cox VGS  VT  V (x)

ID  W Qi x  x (x)  W Qi 0 x (0)
I D  W Cox VGS  VT effE x (0)
E x (0) 
7
VGS  VT
L
W
2
ID  eff Cox VGS VT 
2L
velocity saturation
velocity cm/s --->
VDS 1.0 V

 3  10 5 V/cm
L
30 nm
107
   sat
  E
105
electric field V/cm --->
104
8


MOSFET IV: velocity saturation
0
VG
VD
E x  10 4
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
I D  W Qi x  x (x)
ID  W Cox VGS  VT  sat
9
I D  W Cox  sat VGS  VT 
Velocity (cm/s) 
carrier transport nanoscale MOSFETs
m 
 SAT
m 
D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992.
10
Lundstrom
~1995 - 2000
Minimum Feature Size
Moore’s Law?
100 m
Molecular electronics
1
10 m
1K
1M
1 m
1G
100 nm
1T
10 nm
?
1P
1 nm
1950
1970
1990
2010
2030
2050
Year
11
Lundstrom
http://www.eng.yale.edu/reedlab/
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
12
Lundstrom
outline
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
Lundstrom
13
how transistors work
VDS  1.0 V
2007 N-MOSFET
VGS
EC
electron energy
vs. position
electron energy
vs. position
VDS  0.05 V
VGS
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
EC
E.O. Johnson, “The IGFET: A Bipolar Transistor in Disguise,”
14
RCA Review, 1973
MOSFETs are barrier controlled devices
1) “Well-tempered MOSFET”
QI 0   CG VG  VT 
2) region under strong\
control of gate
E
EC x 
3) Additional increases in VDS
drop near the drain and
have a small effect on ID
x
M. Lundstrom, IEEE EDL, 18, 361, 1997.
A. Khakifirooz, O. M. Nayfeh, D. A. Antoniadis, IEEE TED, 56, pp. 1674-1680, 2009.
15
current flows when the Fermi-levels are different
gate
EF1
f1 E  
EF 2
D(E)
1
1  eE  EF1  kBT
2
1
f2 E  
D E 
N
 f1 E   f2 E  dE
2
I
16
2q
T E M E  f1  f2 dE

h
Lundstrom
1
1  eE  EF 2  kBT
“top of the barrier model”
energy
U  EC  q S
EF1
LDOS
EC x 
“device”
contact 1
EF 2
1 x 
contact 2
position
17
Lundstrom
outline
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
Lundstrom
18
ballistic MOSFET: linear region
I DS
VGS  VDD
VDS
near-equilibrium
f1  f2
I DS  GCH VDS
19
Lundstrom
linear region with MB statistics
GCH
2q 2

h

 f0 
E T E M 2 D E   E  dE
C

Boltzmann statistics: f0  e
EF E  kBTL
 f0 E  f0 kBTL
GCH  WnS
T
2k BT q
nS  Cox VGS  VT  (MOS electrostatics)
GCH  WCox
20
T
2kBT
VGS  VT 

q
✔
Lundstrom

M 2D E  gV W

2m* E  EC
h

T E 1


E E
f0 E  1 1 e F
k BTL
nS  N 2 D eEF EC  kBT
m* EF EC  kBT
 gV 2 e
h
T  2kBTL  m*   x



ballistic MOSFET: linear region
ID
VGS  VDD
I DS  GCH VDS
VDS
near-equilibrium
f1  f2
I D  WCox
I DS  GCH VDS
21
Lundstrom
T
2kBT
VGS  VT VDS

q
relation to conventional expression
ballistic MOSFET
I DS  WCox
I DS 
Dn 
I DS 
22
T
2kBT
conventional MOSFET
VGS  VT VDS

q
I DS
W
T L
Cox
VGS  VT VDS

L
2kBT q
 T 0
2
n 
W
 Cox n VGS  VT VDS
L
n   B
Dn
T L
B 
2 k B TL q
kBT q 
W
Cox  B VGS  VT VDS
L
Lundstrom
ballistic MOSFET: on-current
ID
VGS  VDD
f1  f2
VDS
ID 
23
2q
2q
T
E
M
E
f

f
dE

I

T E M E  f1 dE





1
2
D


h
h
Lundstrom
saturated region with MB statistics
I DS
2q 2

h

 T E M E  f E dE
2D
1
EC
Boltzmann statistics:
f0  eEC EF  kBT
24
h

T E 1
N 2 D EF EC  kBT
e
2
m* EF EC  kBT
 gV
e
2
2 h
nS 
I DS  WqnST
I DS  WCoxT VGS  VT 

M 2D E  gV W

2m* E  EC
✔
T  2kBTL  m*   x
Lundstrom

under low VDS
E
I
EF1
I   nST
I

I ; I
EF 2
I   nST
nS ; nS

nS  nS  nS
nS ; nS 
x
25
Lundstrom
nS
2
nS  Cox VGS  VT 
under high VDS
E
I
EF1
I   nST
I  0
nS  0
nS  nS  nS  nS
EF 2
x
26
I   nST
Lundstrom
nS  Cox VGS  VT 
velocity vs. VDS
E
I
I   nST
I

EF1
I  I
I
 

qnS
nS
EF 2

nS  nS  nS
x
nS
qVDS

e
nS
  T
27
I   nST
Lundstrom
k B TL
1 e
1 e
qVDS kBT
qVDS kBT


velocity vs. VDS
E
I
I
  T

EF1
EF 2
 VDS
x
VDS
Velocity saturates in a ballistic
MOSFET but at the top of the
barrier, where E-field = 0.
28
Lundstrom
velocity saturation in a ballistic MOSFET
velocity
2007 N-MOSFET saturation
  T  1.2  10 7 cm/s
VDS  1.0 V
VGS
   sat  1.0  10 7 cm/s
29
(Courtesy, Shuji Ikeda, ATDF, Dec. 2007)
Lundstrom
aside: relation to conventional expression
ballistic MOSFET
conventional MOSFET
I DS  WCox sat VGS  VT 
I ON  WCoxT VGS  VT 
 sat  T
30
Lundstrom
the ballistic IV (Boltzmann statistics)
I DS (on)  W T Cox VGS  VT 
ID
ballistic
on-current

VG  VT

1
ballistic
channel resistance
VDS
I DS  GCH VDS W Cox
31
T
2kBT
VGS  VT VDS
q
Lundstrom
K. Natori, JAP, 76, 4879, 1994.
comparison with experiment: Silicon
LG  40 nm
I Dlin I ballistic  0.2
I ON I ballistic  0.6
• 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.
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.
32
Device characterization and simulation: Himadri Pal and Yang Liu, Purdue, 2010.
comparison with experiment: InGaAs HEMTs
Jesus del Alamo group (MIT)
33
Lundstrom
outline
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
Lundstrom
34
transmission and carrier scattering
T
1
X
X
0
0  L
X
0  T 1
R  1 T
L
λ0 is the mean-free-path for backscattering
I DS  TI DS ?
35
Lundstrom
the quasi-ballistic MOSFET
?
I DS
VDS


T
I D  T  WCox VGS  VT 
VDS

2kBT q 

36
Lundstrom
 Tlin  0.2
on current and transmission

I BALL
Qi 0  
W T
I   1 T I 
Qi 0  
W T

I BALL
I 
2  T 

I ON
37
1  T I

EF1
I

I D  TI 
EF 2
 T 

I
 2  T  BALL
Lundstrom
the quasi-ballistic MOSFET
I DS
 T 
I D  W T 
C V  VT 
 2  T  ox GS
 Tsat  0.7
Tsat  Tlin
why?
VDS


T
I D  T  WCox VGS  VT 
VDS

2kBT q 

38
Lundstrom
 Tlin  0.2
scattering under high VDS
Tlin 
E
EF1
0
0  L
Ll
Tsat 
EF 2
x
0
0  l
 L
Tsat  Tlin
39
Lundstrom
connection to traditional model (low VDS)
ID 
W
nCox VGS  VT VDS
L


T
I D  T  WCox VGS  VT 
VDS

2kBT q 

W
ID 
nCox VGS  VT VDS
L  0
ID 
T
0
0  L
W
appCox VGS  VT VDS
L
1 app  1 n  1  B
40
Lundstrom
connection to traditional model (high VDS)
I D  WCox sat VGS  VT 
 T 
I D  WCox VGS  VT T 
 2  T 
1
1
1 
ID  W  
 Cox VGS  VT 
 T Dn l 
how do we interpret this result?
41
Lundstrom
the MOSFET as a BJT
I D  W  (0) Cox VGS  VT 
1
1
1


 (0) T Dn l
“base”
E
‘bottleneck’
“collector”
1 x 
x
42
Lundstrom
outline
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
Lundstrom
43
physics of nanoscale MOSFETs
ID
3) The on-current is controlled by the ballistic
injection velocity - not the high-field, bulk
saturation velocity.
2) The channel
resistance has a
lower limit - no
matter how high
the mobility is.
4) Channel velocity saturates near the
source, not at the drain end.
VDS
1) Transistor-like I-V characteristics are a result
of electrostatics.
44
Lundstrom
limits to barrier control: quantum tunneling
45
4)
3)
2)
1)
from M. Luisier, ETH Zurich / Purdue
21st Century electronics?
Minimum Feature Size
Moore’s Law?
100 m
1
10 m
1K
1M
1 m
1G
100 nm
1T
10 nm
1P
1 nm
1950
1970
1990
Year
46
?
Lundstrom
2010
2030
2050
21st Century electronics
1) Information processing dominated by “Si CMOS”
2) SOC’s complemented by “CMOS+” technologies
3) and…..
macroelectronics, power electronics, PV, solid-state
lighting, thermoelectrics, …
47
Lundstrom
for more information
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
48
Lundstrom
questions
1) Introduction
2) The nano-MOSFET
3) The ballistic MOSFET
4) Scattering in nano-MOSFETs
5) Summary
Lundstrom
49