EE105 Fall 2007 Lecture 17, Slide 1 Prof. Liu, UC Berkeley
Lecture 17
OUTLINE
• NMOSFET in ON state (cont’d)
– Body effect
– Channel-length modulation
– Velocity saturation
• NMOSFET in OFF state
• MOSFET models
• PMOSFET
Reading: Finish Chapter 6
ANNOUNCEMENTS
• Wed. discussion section moved (again) to 6-7PM in 293 Cory

EE105 Fall 2007 Lecture 17, Slide 2 Prof. Liu, UC Berkeley
The Body Effect
   
B
SB
B
TH
B
SB
B
ox
Si
A
TH
ox
SB
B
Si
A
ox
B
Si
A
ox
B
Si
A
B
FB
ox
SB
B
Si
A
B
FB
TH
V
V
V
C
qN
V
C
V
qN
C
qN
C
qN
V
C
V
qN
V
V
















2
2
2
2
2
)
2
(
2
)
2
(
2
)
2
(
2
2
)
2
(
2
2
0
0 

















• VTH is increased by reverse-biasing the body-source PN junction:
 is the body effect parameter.

EE105 Fall 2007 Lecture 17, Slide 3 Prof. Liu, UC Berkeley
Body Effect Example
 
ox
Si
A
B
SB
B
TH
TH
C
qN
V
V
V





2
where
2
2
0






EE105 Fall 2007 Lecture 17, Slide 4 Prof. Liu, UC Berkeley
Channel-Length Modulation
• The pinch-off point moves toward the source as VDS increases.
 The length of the inversion-layer channel becomes shorter with increasing VDS.
 ID increases (slightly) with increasing VDS in the saturation region of operation.
   
 
sat
D
DS
TH
GS
ox
n
sat
D V
V
V
V
L
W
C
I ,
2
, 1
2
1



 

 is the channel length modulation coefficient.





 





L
L
L
L
L
IDsat 1
1
1
DSsat
DS V
V
L 



EE105 Fall 2007 Lecture 17, Slide 5 Prof. Liu, UC Berkeley
 and L
• The effect of channel-length modulation is less for a long-
channel MOSFET than for a short-channel MOSFET.

EE105 Fall 2007 Lecture 17, Slide 6 Prof. Liu, UC Berkeley
Velocity Saturation
• In state-of-the-art MOSFETs, the channel is very short (<0.1m);
hence the lateral electric field is very high and carrier drift
velocities can reach their saturation levels.
– The electric field magnitude at which the carrier velocity saturates is Esat.






Si
in
holes
for
cm/s
10
6
Si
in
s
on
for electr
cm/s
10
8
6
6
sat
v
v
E

EE105 Fall 2007 Lecture 17, Slide 7 Prof. Liu, UC Berkeley
Impact of Velocity Saturation
• Recall that
• If VDS > Esat×L, the carrier velocity will saturate and hence the
drain current will saturate:
• ID,sat is proportional to VGS–VTH rather than (VGS – VTH)2
• ID,sat is not dependent on L
• ID,sat is dependent on W
)
(
)
( y
v
y
WQ
I inv
D 
  sat
TH
GS
ox
sat
inv
sat
D v
V
V
WC
v
WQ
I 


,

EE105 Fall 2007 Lecture 17, Slide 8 Prof. Liu, UC Berkeley
• ID,sat is proportional to VGS-VTH rather than (VGS-VTH)2
• VD,sat is smaller than VGS-VTH
• Channel-length modulation is apparent (?)
Short-Channel MOSFET ID-VDS
P. Bai et al. (Intel Corp.),
Int’l Electron Devices Meeting, 2004.

EE105 Fall 2007 Lecture 17, Slide 9 Prof. Liu, UC Berkeley
• In a short-channel MOSFET, the source & drain regions each “support”
a significant fraction of the total channel depletion charge Qdep×W×L
 VTH is lower than for a long-channel MOSFET
• As the drain voltage increases, the reverse bias on the body-drain PN
junction increases, and hence the drain depletion region widens.
VTH decreases with increasing drain bias.
(The barrier to carrier diffusion from the source into the channel is reduced.)
 ID increases with increasing drain bias.
Drain Induced Barrier Lowering (DIBL)

EE105 Fall 2007 Lecture 17, Slide 10 Prof. Liu, UC Berkeley
NMOSFET in OFF State
• We had previously assumed that there is no channel current
when VGS < VTH. This is incorrect!
• As VGS is reduced (toward 0 V) below VTH, the potential barrier to
carrier diffusion from the source into the channel is increased.
ID becomes limited by carrier diffusion into the channel, rather
than by carrier drift through the channel.
(This is similar to the case of a PN junction diode!)
ID varies exponentially with the potential barrier height at the
source, which varies directly with the channel potential.

EE105 Fall 2007 Lecture 17, Slide 11 Prof. Liu, UC Berkeley
Sub-Threshold Leakage Current
• Recall that, in the depletion (sub-threshold) region of operation,
the channel potential is capacitively coupled to the gate potential.
A change in gate voltage (VGS) results in a change in channel
voltage (VCS):
• Therefore, the sub-threshold current (ID,subth) decreases
exponentially with linearly decreasing VGS/m
m
V
C
C
C
V
V GS
dep
ox
ox
GS
CS /















log (ID)
VGS
ID
VGS
mV/dec
60
)
10
(
ln
)
(log
1
10












T
GS
DS
mV
S
dV
I
d
S
“Sub-threshold swing”:

EE105 Fall 2007 Lecture 17, Slide 12 Prof. Liu, UC Berkeley
Short-Channel MOSFET ID-VGS
P. Bai et al. (Intel Corp.),
Int’l Electron Devices Meeting, 2004.

EE105 Fall 2007 Lecture 17, Slide 13 Prof. Liu, UC Berkeley
VTH Design Trade-Off
• Low VTH is desirable for high ON-state current:
ID,sat  (VDD - VTH) 1 <  < 2
• But high VTH is needed for low OFF-state current:
VTH cannot be
reduced aggressively.
Low VTH
High VTH
IOFF,high VTH
IOFF,low VTH
VGS
log ID
0

EE105 Fall 2007 Lecture 17, Slide 14 Prof. Liu, UC Berkeley
MOSFET Large-Signal Models (VGS > VTH)
• Depending on the value of VDS, the MOSFET can be represented
with different large-signal models.
   
 
 
 
sat
D
DS
TH
GS
ox
sat
sat
D
sat
D
DS
TH
GS
ox
n
sat
D
V
V
V
V
WC
v
I
or
V
V
V
V
L
W
C
I
,
,
,
2
,
1
)
(
1
2
1











VDS << 2(VGS-VTH)
)
(
1
TH
GS
ox
n
ON
V
V
L
W
C
R



VDS < VD,sat
DS
DS
TH
GS
ox
n
tri
D V
V
V
V
L
W
C
I 








2
)
(
, 
VDS > VD,sat

EE105 Fall 2007 Lecture 17, Slide 15 Prof. Liu, UC Berkeley
MOSFET Transconductance, gm
• Transconductance (gm) is a measure of how much the drain
current changes when the gate voltage changes.
• For amplifier applications, the MOSFET is usually operating in
the saturation region.
– For a long-channel MOSFET:
– For a short-channel MOSFET:
   
 
 
  D
sat
D
DS
ox
n
m
sat
D
DS
TH
GS
ox
n
m
I
V
V
L
W
C
g
V
V
V
V
L
W
C
g
,
,
1
2
1











GS
D
m
V
I
g



 
 
sat
D
DS
ox
sat
m V
V
WC
v
g ,
1 

 

EE105 Fall 2007 Lecture 17, Slide 16 Prof. Liu, UC Berkeley
MOSFET Small-Signal Model
(Saturation Region of Operation)
D
D
DS
o
I
I
V
r

1




• The effect of channel-length modulation or DIBL (which cause
ID to increase linearly with VDS) is modeled by the transistor
output resistance, ro.

EE105 Fall 2007 Lecture 17, Slide 17 Prof. Liu, UC Berkeley
Derivation of Small-Signal Model
(Long-Channel MOSFET, Saturation Region)
ds
o
bs
mb
gs
m
ds
DS
D
bs
BS
D
gs
GS
D
d v
r
v
g
v
g
v
V
I
v
V
I
v
V
I
i
1












   
 
sat
D
DS
TH
GS
ox
n
D V
V
V
V
L
W
C
I ,
2
1
2
1



 


EE105 Fall 2007 Lecture 17, Slide 18 Prof. Liu, UC Berkeley
PMOS Transistor
• A p-channel MOSFET behaves similarly to an n-channel
MOSFET, except the polarities for ID and VGS are reversed.
• The small-signal model for a PMOSFET is the same as that for
an NMOSFET.
– The values of gm and ro will be different for a PMOSFET vs. an NMOSFET,
since mobility & saturation velocity are different for holes vs. electrons.
Circuit symbol
Schematic cross-section

EE105 Fall 2007 Lecture 17, Slide 19 Prof. Liu, UC Berkeley
PMOS I-V Equations
• For |VDS| < |VD,sat|:
• For |VDS| > |VD,sat|:
 
 
sat
D
DS
DS
DS
TH
GS
ox
p
tri
D V
V
V
V
V
V
L
W
C
I ,
, 1
2
)
( 









 

   
 
 
 
sat
D
DS
TH
GS
ox
sat
sat
D
sat
D
DS
TH
GS
ox
p
sat
D
V
V
V
V
WC
v
I
or
V
V
V
V
L
W
C
I
,
,
,
2
,
1
)
(
1
2
1











 for long channel
for short channel

EE105 Fall 2007 Lecture 17, Slide 20 Prof. Liu, UC Berkeley
CMOS Technology
• It possible to form deep n-type regions (“well”) within a p-type
substrate to allow PMOSFETs and NMOSFETs to be co-fabricated
on a single substrate.
• This is referred to as CMOS (“Complementary MOS”) technology.
Schematic cross-section of CMOS devices

EE105 Fall 2007 Lecture 17, Slide 21 Prof. Liu, UC Berkeley
Comparison of BJT and MOSFET
• The BJT can achieve much higher gm than a MOSFET, for a
given bias current, due to its exponential I-V characteristic.