1
Introduction toCMOS VLSI
Design
Lecture 3: CMOS Transistor Theory
David Harris
Harvey Mudd CollegeSpring 2004
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3: CMOS Transistor Theory Slide 2CMOS VLSI Design
OutlineIntroductionMOS CapacitornMOS I-V CharacteristicspMOS I-V CharacteristicsGate and Diffusion CapacitancePass TransistorsRC Delay Models
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3: CMOS Transistor Theory Slide 3CMOS VLSI Design
IntroductionSo far, we have treated transistors as ideal switchesAn ON transistor passes a finite amount of current– Depends on terminal voltages– Derive current-voltage (I-V) relationships
Transistor gate, source, drain all have capacitance– I = C (ΔV/Δt) -> Δt = (C/I) ΔV– Capacitance and current determine speed
Also explore what a “degraded level” really means
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MOS Transistors MOS Transistors -- Types and SymbolsTypes and Symbols
D
S
G
D
S
G
G
S
D D
S
G
NMOS Enhancement NMOS
PMOS
Depletion
Enhancement
B
NMOS withBulk Contact
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The MOS TransistorThe MOS Transistor
Polysilicon Aluminum
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Controlling current flow in an Controlling current flow in an nFETnFET..
Introduction to Circuits, Fourth Edition by Peter Uyemura, Copyright © 2004 John Wiley & Sons. All rights reserved.
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© Digital Integrated Circuits2nd DevicesIntroduction to Circuits, Fourth Edition by Peter Uyemura, Copyright © 2004 John Wiley & Sons. All rights reserved.
Controlling current flow in a Controlling current flow in a pFETpFET..
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What is a Transistor?What is a Transistor?
VGS ≥ VT
RonS D
A Switch!
|VGS|
A MOS Transistor
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I-V Curves
ResistorI = V/R
DiodeI = Is*exp(k*V-Vt)
Current (I) vs. Voltage (V)I = f(V)
0 0.5 1 1.5 2 2.50
1
2
3
4
5
6x 10-4
VDS
I D(A
)
MOSI = f(Vgs, Vds)
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3: CMOS Transistor Theory Slide 10CMOS VLSI Design
Terminal VoltagesMode of operation depends on Vg, Vd, Vs
– Vgs = Vg – Vs
– Vgd = Vg – Vd
– Vds = Vd – Vs = Vgs - Vgd
Source and drain are symmetric diffusion terminals– By convention, source is terminal at lower voltage– Hence Vds ≥ 0
nMOS body is grounded. First assume source is 0 too.Three regions of operation– Cutoff– Linear– Saturation
Vg
Vs Vd
VgdVgs
Vds+-
+
-
+
-
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3: CMOS Transistor Theory Slide 11CMOS VLSI Design
MOS CapacitorGate and body form MOS capacitorOperating modes– Accumulation– Depletion– Inversion
polysilicon gate
(a)
silicon dioxide insulator
p-type body+-
Vg < 0
(b)
+-
0 < Vg < Vt
depletion region
(c)
+-
Vg > Vt
depletion regioninversion region
In general, MOS gate capacitance is not constant
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© Digital Integrated Circuits2nd DevicesCopyright © 2005 Pearson Addison-Wesley. All rights reserved.
MOS Transistors MOS Transistors –– Operating regions Operating regions
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3: CMOS Transistor Theory Slide 13CMOS VLSI Design
nMOS CutoffNo channelIds = 0
+-
Vgs = 0
n+ n+
+-
Vgd
p-type body
b
g
s d
d
s
g
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3: CMOS Transistor Theory Slide 14CMOS VLSI Design
nMOS LinearChannel formsCurrent flows from d to s – e- from s to d
Ids increases with Vds
Similar to linear resistor
+-
Vgs > Vt
n+ n+
+-
Vgd = Vgs
+-
Vgs > Vt
n+ n+
+-
Vgs > Vgd > Vt
Vds = 0
0 < Vds < Vgs-Vt
p-type body
p-type body
b
g
s d
b
g
s d Ids
d
s
g
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n+n+
p-substrate
D
SG
B
VGS
xL
V(x) +–
VDS
ID
Linear Region Linear Region VVgsgs>>VVtt & & VVgdgd>>VVtt
Positive Charge on Gate:Channel exists, Current Flows
since Vds > 0Ids = k’(W/L)((Vgs-Vt)Vds-Vds
2/2)
R
Vgd
Vgs
Ids
Vds
I=V/R
R= 1/(k’(W/L)(Vgs-Vt))
Ids
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3: CMOS Transistor Theory Slide 16CMOS VLSI Design
nMOS SaturationChannel pinches offIds independent of Vds
We say current saturatesSimilar to current source
+-
Vgs > Vt
n+ n+
+-
Vgd < Vt
Vds > Vgs-Vt
p-type bodyb
g
s d Ids
d
s
g
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n+n+
S
G
VGS
D
VDS > VGS - VT
VGS - VT+-
Saturation: Saturation: VVgsgs>>VVtt & & VVgdgd<<VVtt
Positive Charge on Gate:Channel exists, Current Flows
since Vds > 0But: channel is “pinched off”
Ids = (k’/2)(W/L)(Vgs-Vt)2
Vgd
Vgs
Ids
Ids
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3: CMOS Transistor Theory Slide 18CMOS VLSI Design
I-V CharacteristicsIn Linear region, Ids depends on– How much charge is in the channel?– How fast is the charge moving?
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© Digital Integrated Circuits2nd DevicesCopyright © 2005 Pearson Addison-Wesley. All rights reserved.
MOS Transistors MOS Transistors –– Regions Transitions Regions Transitions
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3: CMOS Transistor Theory Slide 20CMOS VLSI Design
Channel ChargeMOS structure looks like parallel plate capacitor while operating in inversion– Gate – oxide – channel
Qchannel =
n+ n+
p-type body
+
Vgd
gate
+ +source
-
Vgs
-drain
Vds
channel-
Vg
Vs Vd
Cg
n+ n+
p-type body
W
L
tox
SiO2 gate oxide(good insulator, εox = 3.9)
polysilicongate
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3: CMOS Transistor Theory Slide 21CMOS VLSI Design
Channel ChargeMOS structure looks like parallel plate capacitor while operating in inversion– Gate – oxide – channel
Qchannel = CVC =
n+ n+
p-type body
+
Vgd
gate
+ +source
-
Vgs
-drain
Vds
channel-
Vg
Vs Vd
Cg
n+ n+
p-type body
W
L
tox
SiO2 gate oxide(good insulator, εox = 3.9)
polysilicongate
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3: CMOS Transistor Theory Slide 22CMOS VLSI Design
Channel ChargeMOS structure looks like parallel plate capacitor while operating in inversion– Gate – oxide – channel
Qchannel = CVC = Cg = εoxWL/tox = CoxWLV =
n+ n+
p-type body
+
Vgd
gate
+ +source
-
Vgs
-drain
Vds
channel-
Vg
Vs Vd
Cg
n+ n+
p-type body
W
L
tox
SiO2 gate oxide(good insulator, εox = 3.9)
polysilicongate
Cox = εox / toxCox = 8.6*fF/um2
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3: CMOS Transistor Theory Slide 23CMOS VLSI Design
Channel ChargeMOS structure looks like parallel plate capacitor while operating in inversion– Gate – oxide – channel
Qchannel = CVC = Cg = εoxWL/tox = CoxWLV = Vgc – Vt = (Vgs – Vds/2) – Vt
n+ n+
p-type body
+
Vgd
gate
+ +source
-
Vgs
-drain
Vds
channel-
Vg
Vs Vd
Cg
n+ n+
p-type body
W
L
tox
SiO2 gate oxide(good insulator, εox = 3.9)
polysilicongate
Cox = εox / tox
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3: CMOS Transistor Theory Slide 24CMOS VLSI Design
Carrier velocityCharge is carried by e-Carrier velocity v proportional to lateral E-field between source and drainv =
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3: CMOS Transistor Theory Slide 25CMOS VLSI Design
Carrier velocityCharge is carried by e-Carrier velocity v proportional to lateral E-field between source and drainv = μE μ called mobilityE =
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3: CMOS Transistor Theory Slide 26CMOS VLSI Design
Carrier velocityCharge is carried by e-Carrier velocity v proportional to lateral E-field between source and drainv = μE μ called mobilityE = Vds/LTime for carrier to cross channel:– t =
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3: CMOS Transistor Theory Slide 27CMOS VLSI Design
Carrier velocityCharge is carried by e-Carrier velocity v proportional to lateral E-field between source and drainv = μE μ called mobilityE = Vds/LTime for carrier to cross channel:– t = L / v
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3: CMOS Transistor Theory Slide 28CMOS VLSI Design
nMOS Linear I-VNow we know– How much charge Qchannel is in the channel– How much time t each carrier takes to cross
dsI =
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3: CMOS Transistor Theory Slide 29CMOS VLSI Design
nMOS Linear I-VNow we know– How much charge Qchannel is in the channel– How much time t each carrier takes to cross
channelds
QIt
=
=
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3: CMOS Transistor Theory Slide 30CMOS VLSI Design
nMOS Linear I-VNow we know– How much charge Qchannel is in the channel– How much time t each carrier takes to cross
channel
ox 2
2
ds
dsgs t ds
dsgs t ds
QIt
W VC V V VL
VV V V
μ
β
=
⎛ ⎞= − −⎜ ⎟⎝ ⎠
⎛ ⎞= − −⎜ ⎟⎝ ⎠
ox = WCL
β μ
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Computed CurvesComputed Curves
Vgs = 5v
Vgs = 4.5v
Vgs = 4.0v
Linear Resistor
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3: CMOS Transistor Theory Slide 32CMOS VLSI Design
nMOS Saturation I-VIf Vgd < Vt, channel pinches off near drain– When Vds > Vdsat = Vgs – Vt
Now drain voltage no longer increases current
dsI =
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3: CMOS Transistor Theory Slide 33CMOS VLSI Design
nMOS Saturation I-VIf Vgd < Vt, channel pinches off near drain– When Vds > Vdsat = Vgs – Vt
Now drain voltage no longer increases current
2dsat
ds gs t dsatVI V V Vβ ⎛ ⎞= − −⎜ ⎟
⎝ ⎠
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3: CMOS Transistor Theory Slide 34CMOS VLSI Design
nMOS Saturation I-VIf Vgd < Vt, channel pinches off near drain– When Vds > Vdsat = Vgs – Vt
Now drain voltage no longer increases current
( )2
2
2
dsatds gs t dsat
gs t
VI V V V
V V
β
β
⎛ ⎞= − −⎜ ⎟⎝ ⎠
= −
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3: CMOS Transistor Theory Slide 35CMOS VLSI Design
Computed Curves
Vgs = 5v
Vgs = 4.5v
Vgs = 4.0v
Linear Resistor
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3: CMOS Transistor Theory Slide 36CMOS VLSI Design
nMOS I-V Summary
( )2
cutoff
linear
saturatio
0
2
2n
gs t
dsds gs t ds ds dsat
gs t ds dsat
V VVI V V V V V
V V V V
β
β
⎧⎪ <⎪⎪ ⎛ ⎞= − − <⎜ ⎟⎨ ⎝ ⎠⎪⎪
− >⎪⎩
Shockley 1st order transistor models
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3: CMOS Transistor Theory Slide 37CMOS VLSI Design
ExampleWe will be using a 0.180 μm process for your project– From TSMC Semiconductor– tox = 40 Å– μ = 180 cm2/V*s– Vt = 0.4 V
Plot Ids vs. Vds
– Vgs = 0, 0.3,…, 1.8 – Use W/L = 4/2 λ
( )14
28
3.9 8.85 10350 120 /100 10ox
W W WC A VL L L
β μ μ−
−
⎛ ⎞• ⋅ ⎛ ⎞= = =⎜ ⎟⎜ ⎟⋅ ⎝ ⎠⎝ ⎠180
40155
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3: CMOS Transistor Theory Slide 38CMOS VLSI Design
pMOS I-VAll dopings and voltages are inverted for pMOSMobility μp is determined by holes– Typically 2-3x lower than
that of electrons μn
Thus pMOS must be wider to provide same current– Often, assume μn / μp = 2
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CurrentCurrent--Voltage RelationsVoltage RelationsLongLong--Channel DeviceChannel Device
Cut-off (VGS – VT < 0) “no current” (not really)
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IIDD versus Vversus VDS DS short channel deviceshort channel device
-4
VDS(V)0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5x 10
I D(A
)
VGS= 2.5 V
VGS= 2.0 V
VGS= 1.5 V
VGS= 1.0 V
0 0.5 1 1.5 2 2.50
1
2
3
4
5
6x 10-4
VDS(V)
I D(A
)
VGS= 2.5 V
VGS= 2.0 V
VGS= 1.5 V
VGS= 1.0 V
Resistive Saturation
VDS = VGS - VT
Long Channel Short Channel
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RabaeyRabaey’’ss unified modelunified modelfor manual analysisfor manual analysis
S D
G
B
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Transistor Model Transistor Model for Manual Analysisfor Manual Analysis
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Simple Model versus SPICE Simple Model versus SPICE
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5x 10
-4
VDS (V)
I D(A
)
VelocitySaturated
Linear
Saturated
VDSAT=VGT
VDS=VDSAT
VDS=VGT
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Even Simpler:Even Simpler:The Transistor as a SwitchThe Transistor as a Switch
VGS ≥ VT
RonS D
ID
VDS
VGS = VD D
VDD/2 VDD
R0
Rmid
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The Transistor as a SwitchThe Transistor as a Switch
This week’s Lab – find Req for our TSMC 180nm process
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Saturation EffectsSaturation Effects
Which is the resistor?
Discharge of 1pf capacitor, with Vgs of 3,4,5 volts. Also, 12k resistor.
d
s
g
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3: CMOS Transistor Theory Slide 47CMOS VLSI Design
More on CapacitanceAny two conductors separated by an insulator have capacitanceGate to channel capacitor is very important– Creates channel charge necessary for operation
Source and drain have capacitance to body– Across reverse-biased diodes– Called diffusion capacitance because it is
associated with source/drain diffusion
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3: CMOS Transistor Theory Slide 48CMOS VLSI Design
Gate CapacitanceApproximate channel as connected to sourceCgs = εoxWL/tox = CoxWL = CpermicronWCpermicron is typically about 2 fF/μm
n+ n+
p-type body
W
L
tox
SiO2 gate oxide(good insulator, εox = 3.9ε0)
polysilicongate
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The Gate Capacitance The Gate Capacitance
tox
n+ n+
Cross section
L
Gate oxide
xd xd
L d
Polysilicon gate
Top view
Gate-bulkoverlap
Source
n+
Drain
n+W
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DynamicDynamic Behavior of MOS TransistorBehavior of MOS Transistor
DS
G
B
CGDCGS
CSB CDBCGB
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Physical visualization of FET Physical visualization of FET capacitancescapacitances
Introduction to Circuits, Fourth Edition by Peter Uyemura, Copyright © 2004 John Wiley & Sons. All rights reserved.
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© Digital Integrated Circuits2nd DevicesCopyright © 2005 Pearson Addison-Wesley. All rights reserved.
MOS Capacitances Behavior !MOS Capacitances Behavior !
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Gate Capacitance Gate Capacitance –– BehaviorBehavior
S D
G
CGC
S D
G
CGCS D
G
CGC
Cut-off Resistive Saturation
Most important regions in digital design: saturation and cut-off
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Measuring the Gate CapMeasuring the Gate Cap
2 1.52 1 2 0.5 0
3
4
5
6
7
8
9
103 102 16
2
VGS (V)
VGS
Gat
e C
apac
itanc
e (F
)
0.5 1 1.5 22 2
I
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3: CMOS Transistor Theory Slide 55CMOS VLSI Design
Diffusion CapacitanceCsb, Cdb
Undesirable, called parasitic capacitanceCapacitance depends on area and perimeter– Use small diffusion nodes– Comparable to Cg
for contacted diff– ½ Cg for uncontacted– Varies with process
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Diffusion CapacitanceDiffusion Capacitance
Bottom
Side wall
Side wallChannel
SourceND
Channel-stop implantNA1
Substrate NA
W
xj
L S
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Final construction of the Final construction of the nFETnFET RC RC modelmodel
Introduction to Circuits, Fourth Edition by Peter Uyemura, Copyright © 2004 John Wiley & Sons. All rights reserved.
CG
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Summary of MOSFET Operating Summary of MOSFET Operating RegionsRegions
Strong Inversion VGS > VTLinear (Resistive) VDS < VDSAT
Saturated (Constant Current) VDS ≥VDSAT
Weak Inversion (Sub-Threshold) VGS ≤VTExponential in VGS with linear VDS dependence
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