Download - Early Voltage in MOSFETs
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
1
Early Voltage in MOSFETs• Due to channel length modulation:
E
DSTHGSPNDS
THGSPN
DSTHGSoxnDS
V
VVVSKI
L
LVVSK
VVVL
WCI
12
1
12
1
12
1
2
2
2
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
2
Saturation Voltage• Vpinchoff = VDS,sat = VGS – VTH
– Separates resistive from saturation region
• The drain current is given by
• Solving for VDS,sat:
• Good to solve for quiescent voltage-current.
PNoxnL
WNTHTN
TNGSNDS
SKCVV
VVI
and
NFETfor ,2
21
N
DSTNGSsatDS
IVVV
2
,
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
3
Ex: Find VDS,sat for an NFET
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
4
Variations in VTH Across Channel
• We assume VTH is constant across channel
THIS IS NOT TRUE!
• Depletion region is thick at S and thin at D.
Fox
depmsTH
C
QV 2
Cox
Cdep
inversionlayer
Gate oxidecapacitance
Depletion cap,function of x
5.11factor slope ldsubthresho2
2
ox
dep
TNGSN
DS
C
Cn
VVn
I
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Notes on PFETs• PFETs typically have a shape factor 3 or 4
times larger than NFETs
• Body effect can be eliminated in PFETs by tying the n-well to VDD
– Need 6m spacing between n-wells to isolate.– Dr. Engel always does this on input devices,
not always elsewhere.
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Weak Inversion• What really happens if VGS < VTN?
• In digital design, IDS = 0.
• We call it “weak inversion” or W.I.
• IDS is primarily due to Idrift in strong inversion and Idiffusion in weak inversion.
V1
V950
TH
GS
V
.V
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Modes of Inversion• IDS = Idrift + Idiffusion
• If VGS > VTN the channel has been inverted.
• To be more precise, we can say the channel has been “strongly inverted” (S.I.) due to an abundance of carriers in the channel.
• Inversion is independent of whether the FET is in the linear or saturation region.
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
8
Weak Inversion Idiffusion
• Drain is more reverse biased than source:
• To find Idiff, compute gradient
• Because no carriers are lost as they travel from S to D, current is the same for all x and gradient is not a function of x.
• Note: This is not really true due to recombination, but its close!
kT
VVqNN SGO
S
exp0
kT
VVqNN SGO
D
exp0
dxdN
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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W.I. Surface Potential
oxd
d
oxd
oxs
CjCj
Cj
CC
C
11
1
oxC
dC
GV
potentialsurface
S
factor slopeldsubthresho ,5.11
ox
d
C
Cn
device law lExponentia
Uexp1
Uexp
nUexp
0
T
DS
T
S
T
GDDS SII
v-v-v
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Deriving Weak Inversion IDS
T
S
T
D
T
GSSD
L
NN
L
NN
dx
dN
Uexp
Uexp
Uexp0 v-v-v
iprelationshEinstein thea.k.a. ,
coeff.diffusion is where,
:unit widthper current The
q
kTD
Ddx
dNqD
W
I
nn
nnDS
T
D
T
S
T
GDDS I
L
WI
Uexp
Uexp
nUexp
0
v-v-v
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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W.I. FET As Exp. Law Dev.• S must be big for device to be useful.
• If VDS = 100mV, can be neglected.
• For W.I. vDS,Sat 100mV
• Looks like a BJT
T
DS
Uexp
v-
mV100for ,U
expnU
exp0
DS
T
S
T
GDDS VSII
v-v
T
BESC II
Uexp
v
BEv
Ci
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Inversion Coefficient• Let
• Shape factor as a function of :
Lets you chose shape to match inversion mode.
2U2 t coefficieninversion
T
DS
n
i o
< 0.1 Weakly Inverted (W.I.)
> 10 Strongly Inverted (S.I.)
0.1 < < 10 Moderately Inverted (M.I.)
2U2 TPN
DS
Kn
iS
o
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Ex. Using Inversion Coeff.
W.I. 049.0
(100))(26mV)2(1.5)(100
1uA ,100 uA,1
2
SiO
DS
M.I. 9.4
(100))(26mV)2(1.5)(100
100uA ,100 uA,100
2
SiO
DS
S.I. 49
(100))(26mV)2(1.5)(100
1mA ,100 mA,1
2
SiO
DS
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Small Signal Analysis
GSV
gsGS vv
Bias DCChange SmallVoltage Total
O
GSv O
BSv
O
DSv
O
DSi
GSO V GSvVoltageQuiescent
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Ex: Quiescent PointV75.00 TV
V81EV
59.02V
A50 PNK
m
mS
10μ
μ100
O
GSv O
BSv
O
DSv
O
DSi
EFFPN
VSK
O
OOO DS
SBGSDS
vvvvi T0 122
2
1 2
mA34375.181
5175.0350
10
100
2
1 2
2
V
A
m
mO
DSi
Question: How many digits are significant?
V3O
GSv
V5O
DSv
V0O
BSv
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Small Signal Model Limits• Suppose the previous circuit is the input
device of an amplifier.
• Small-signal model holds as long as the deviations are small qkT
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Taylor Series Expansion• Taking a Taylor expansion of one variable:
SBSB
SBDS
DS
DSGS
GS
DS
DSDSiii
ii vv
vv
vv
0000
mg dsg mbg
gsvv-vvGSGSGS O
dsvvDS sbvv
SB
DSDSiii O
DS
202
100 ))(())(()()( xxxfxxxfxfxf
Approx.Linear
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Small Signal Model Params
dsE
DS
DS
DSds
rV
iig
O 10
v
1typically ,22
where0
O
SBF
mSB
SBmb g
ig
vv
OO
O
DSmEDSEGS
DSm igVi
V
ig 2 , largefor ,12
0
DSv
v
dsmrgGain
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Example: Small Signal Analysis
μA57.30)26)(0166.0()26)(1592.1(
2
:analysis signal small Using
μA65.31 mA 3754.1
:) work!of (lotsequation full Using
V026.5 V,0 ,)by (up V026.3Let
250 V,81 mA,34375.1
mVmSmVmS
2V
μA
dsE
DSgsdsdsgsm
DSBSGS
E
V
iiggi
ii
qkT
Vi
O
O
O
vvvv
vvv
DS
DS
DS
DSDS
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Small Signal Low-Freq Model
gsmg v dsmbg v dsr
dsi
gsv
small
signals
S.I.
Sat
1.5factor slope ldsubthresho where,2
nn
ig
ODS
m
OO
ds
E
ds
Eds
i
LV
i
Vr
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Ex: Find gm and rO
μm10
μm4
μA10
L
W
iO
DS
M10μA10
μm10μmV10
μS235.1
uA10μA/V1001042
so, If saturated? and S.I.it Is
2
ODS
ENds
m
i
LVr
g
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ECE 584, Summer 2002 Brad NobleChapter 3 Slides
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Transconductance: W.I. & M.I.• What is gm for a weakly inverted FET?
• What is gm for a moderately inverted FET?
T
DS
GS
DSm
n
iig
O
U
0
v
exp1
where,U
0
T
DS
GS
DSm
n
iig
O
v
modes allfor E
DSds
V
ig
O
Not
in te
xtbo
oks!