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Agenda
MOS Transistor ModelingLarge-Signal DC Model
Small-Signal AC Model
MOS Capacitors
3
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Drawn & Effective Channel Lengths
The transistor gate overlaps both the source and drainregion by a length of LD due to side diffusion in the
fabrication process This results in the effective transistor gate length, Leff,
being shorter than the drawn length, Ldrawn Throughout the remainder of the course, L will generally
refer to Leff 4
Ddrawneff LLL 2=
[Razavi]
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Finite Output Resistance in Saturation
In saturation, as VDS is increased the channel
pinch-off point moves slightly towards the source
This phenomenon is called channel-lengthmodulation and is characterized by a parameter
5
[Sedra/Smith]
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Finite Output Resistance in Saturation
The current will increase slightlywith VDS in saturation, resulting
in a finite incremental outputresistance
Note, the channel-lengthmodulation parameter is
inversely proportional to L 6
( )
( )
( )
( )
( ) ( )DSTnGS
oxn
D
DS
TnGS
oxn
D
DS
TnGS
oxn
TnGS
oxn
TnGSoxn
D
VVVL
WCI
L
L
VVV
L
WCI
VL
L
LVVL
WC
VV
L
LL
WC
VVLL
WCI
+=
=
+=
=
+
=
=
12
1
2
12
1
1
2
2
2
2
2
2
2
[Sedra/Smith]
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TAMU-474-08 J. Silva-Martinez
- 7 -
OUTPUT RESISTANCE (SATURATION REGION)
Drain current
substrate
P+ P+
S G D
N+
B
Depletion region
Channel length modulation is a second
(unreliable) order effect!
(Badly) Represented in SPICE by using
or a more complex model.
Simulated and experimental results
might be off by more than 100%
Channel Length Modulation
[ ] [ ]DSTGSeffOX
D VVVL
WC
i +
122
Leff
Lch
0
VD
S
IDS
VGS2
=0
Measure this parameter!
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MOS Large-Signal Output Characteristicwith Finite Output Resistance
8
[Sedra/Smith]
( )
( ) ( )DSTnGSoxn
D
DSDSTnGSoxnD
VVVL
WCI
VVVVL
WCI
+=
=
12:Saturation
5.0:Triode
2
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MOS Large-Signal Transfer Characteristic
9
[Sedra/Smith]
( ) ( )DSTnGS
oxn
DVVV
L
WCI
+= 1
2
2
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Impact of Bulk Voltage
10
[Razavi]( ) ( )
DSTnGS
oxn
DVVV
L
WCI
+= 1
2
2
00022
=++=
SBVTFSBFTT
VVVV
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Large-Signal DC Response
11
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Large-Signal DC +Small-Signal AC Response
12
For small-signal analysis, we linearize the response
about the DC operating point
If the signal is small enough, linearity holds and thecomplete response is the summation of the large-signalDC response and the small-signal AC response
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Low-Frequency Small-Signal Model
13
[Razavi]
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Transistor transfer characteristic is used to extracttransconductance, gm
Transconductance, gm
14
( )
( )Q
TGS
eff
OX
Qgs
D
m
TGS
eff
OX
D
VVL
WC
v
ig
VVL
WC
I
=
=
2
2
Effects)g(NeglectinSaturationIn
[Sedra/Smith]
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Transistor output characteristic is used to extract outputconductance, go
Output Conductance, go
15
( ) ( )
( )D
Q
TGS
eff
OX
Qds
D
o
DSTGS
eff
OX
D
IVVL
WC
v
ig
VVV
L
WCI
=
+=
2
21
2
Effects)(IncludingSaturationIn
[Sedra/Smith]
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The small-signal drain current changes with VBS modulationdue to changes in VT
Body Transconductance, gmb
16
[Razavi]
[ ] SBFm
Qbs
T
Q
TGSeff
OX
Qbs
D
mb V
g
v
V
VVL
W
Cv
i
g +
=
22*
Effects)g(NeglectinSaturationIn
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Low-Frequency Small-Signal Model
17
( )
( )
[ ]SBF
m
Qbs
T
Q
TGS
eff
OX
Qbs
Dmb
Q
TGS
eff
OX
Qds
D
Q
TGSeff
OX
Qgs
D
m
V
g
v
V*VV
L
WC
v
ig
VVL
WC
v
ig
VVL
W
Cv
i
g
+
=
=
=
22
2
20
[Razavi]
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MOS Transistor Capacitances
181
1
CapJunctionBulk-Drain
CapJunctionBulk-Source
Cap(Fringing)OverlapDrain-Gate
Note,Cap(Fringing)OverlapSource-Gate
4CapBulk-Channel
CapChannel-Gate
00
msw
B
BX
jsw
jswm
B
BX
j
j
jswDjDDBJ
jswSjSSBJ
ovGDov
DoxovovGSov
F
subSieffCB
oxeffGC
V
CC
V
CC
CPCAC
CPCAC
WCC
LCCWCC
NqWLC
CWLC
+
=
+
=
+==
+==
==
==
==
==
[Razavi]
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MOS Transistor Capacitances (Off)
19
SBJSB
DBJDB
CBGC
CBGCGB
ovGDovGS
ovGDovGD
CC
CC
CC
CCC
WCCC
WCCC
CapBulk-Source
CapBulk-Drain
CapBulk-Gate
CapSource-Gate
CapDrain-Gate
==
==+
==
===
===
[Razavi]
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MOS Transistor Capacitances (Triode)
20
[Razavi]
CBSBJSB
CBDBJDB
GB
GCGSovGS
GCGDovGD
CCC
CCC
C
CCC
CCC
2
1CapBulk-Source
2
1CapBulk-Drain
0CapBulk-Gate
2
1CapSource-Gate
2
1CapDrain-Gate
+==
+==
=
+==
+==
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MOS Transistor Capacitances (Saturation)
21
[Razavi]
CBSBJSB
DBJDB
GB
GCGSovGS
GDovGD
CCC
CC
C
CCC
CC
3
2CapBulk-Source
CapBulk-Drain
0CapBulk-Gate
3
2CapSource-Gate
CapDrain-Gate
+==
==
=
+==
==
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MOS Gate Capacitors Response
22
[Razavi]DoxovLCC Note,
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MOS Source & Drain Junction Capacitors
23
[Razavi] ( )
( )jswjjswjDBSB
DS
DS
CEWWECPCACCC
EWPP
WEAA
++=+==
+==
==
2Junction
2
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Source/Drain Junction Perimeter CapsDisclaimer
Note, there is some ambiguity on how to model the source/drainjunction perimeter (sidewall) capacitance on the side of the gate
This is due to the channel occupying a portion of the sidewall area
Different textbooks present different approaches
The Razavi text conservatively assumes that the sidewall perimeter
capacitance is the same on all sides
The Johns/Martin text (used in 2010) optimistically sets the sidewallperimeter cap to zero under the gate
The correct answer is somewhere in the middle
This semester I will follow the Razavi method and assume that thesidewall perimeter capacitance is the same on all sides (even underthe gate)
I will try to make it clear on any problem description
24
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MOS Source & Drain Junction Capacitors
25
[Razavi] ( )
( )jswjjswjDBSB
DS
DS
CEWWECPCACCC
EWPP
WEAA
++=+==
+==
==
2Junction
2
( )
( )jswjjswDjDDB
jswjjswSjSSB
D
S
D
S
CEWECW
CPCAC
CEWWECCPCAC
EW
P
EW
P
EW
A
WEEW
A
22
Junction
22Junction
22
222
2
22
++=+=
++=+=
+=
+=
=
=
=
Folding the transistorallows for approximatelyhalf the drain junctioncapacitance with a small
increase in source junctioncapacitance
Folding into2 fingers
Folding into 2 fingers & sharing drain
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TAMU-474-08 J. Silva-Martinez
- 26 -
Other resistors: Source/Drain
Drain/Source Resistance
Drain/Source Resistance
In addition to the contact resistance ,
the diffusion resistance has to be
considered.
In SPICE, R[] is defined as RSH
( )
=
=
tW
LR
RW
LR
Rseries
[]R
series
P+
D/S
iD
Top view
iD
LR
W
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TAMU-474-08 J. Silva-Martinez
- 27 -
Small Signal Model (Saturation region)
Small signal model (saturation region)
B
gogmbvbsgmvgs
B
D
CdbCgd
Cgs
Cbs
S
S
GD
[ ] [ ]
[ ]
[ ] [ ]bs
Qbs
Dds
Qds
Dgs
Qgs
D
Q
DSTGS
eff
OXD
FSBFTT
DSTGS
eff
OXD
vv
iv
v
iv
v
iVVV
L
WCi
VVV
VVVL
WCI
+
+
++
++=
+=
12
22
12
2
0
2
( )
( )
[ ]SBF
m
Qbs
T
Q
TGS
eff
OX
Qbs
Dmb
Q
TGS
eff
OX
Qds
D
Q
TGS
eff
OX
Qgs
Dm
V
g
v
V*VV
L
WC
v
ig
VVL
WC
v
ig
VVL
WC
v
ig
+
=
=
=
22
2
20 bsmbds0gsmDD vgvgvgIi +++