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Introduction toCMOS VLSI
Design
Lecture 4: CMOS Transistor Theory
David Harris
Harvey Mudd College
Spring 2007
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4: CMOS Transistor Theory Slide 2CMOS VLSI Design
Outline Introduction MOS Capacitor nMOS I-V Characteristics pMOS I-V Characteristics Gate and Diffusion Capacitance
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4: CMOS Transistor Theory Slide 3CMOS VLSI Design
Introduction So far, we have treated transistors as ideal switches An 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 (V/t) -> t = (C/I) V– Capacitance and current determine speed
Also explore what a “degraded level” really means
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4: CMOS Transistor Theory Slide 4CMOS VLSI Design
MOS Capacitor Gate and body form MOS capacitor Operating 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
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4: CMOS Transistor Theory Slide 5CMOS VLSI Design
Terminal Voltages Mode 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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4: CMOS Transistor Theory Slide 6CMOS VLSI Design
nMOS Cutoff No channel Ids = 0
+-
Vgs = 0
n+ n+
+-
Vgd
p-type body
b
g
s d
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4: CMOS Transistor Theory Slide 7CMOS VLSI Design
nMOS Linear Channel forms Current 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 dIds
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4: CMOS Transistor Theory Slide 8CMOS VLSI Design
nMOS Saturation Channel pinches off Ids independent of Vds
We say current saturates Similar to current source
+-
Vgs > Vt
n+ n+
+-
Vgd < Vt
Vds > Vgs-Vt
p-type body
b
g
s d Ids
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4: CMOS Transistor Theory Slide 9CMOS VLSI Design
I-V Characteristics In Linear region, Ids depends on
– How much charge is in the channel?– How fast is the charge moving?
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4: CMOS Transistor Theory Slide 10CMOS VLSI Design
Channel Charge MOS 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, ox = 3.9)
polysilicongate
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4: CMOS Transistor Theory Slide 11CMOS VLSI Design
Channel Charge MOS structure looks like parallel plate capacitor
while operating in inversion– Gate – oxide – channel
Qchannel = CV
C =
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, ox = 3.9)
polysilicongate
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4: CMOS Transistor Theory Slide 12CMOS VLSI Design
Channel Charge MOS structure looks like parallel plate capacitor
while operating in inversion– Gate – oxide – channel
Qchannel = CV
C = Cg = oxWL/tox = CoxWL
V =
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, ox = 3.9)
polysilicongate
Cox = ox / tox
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4: CMOS Transistor Theory Slide 13CMOS VLSI Design
Channel Charge MOS structure looks like parallel plate capacitor
while operating in inversion– Gate – oxide – channel
Qchannel = CV
C = Cg = oxWL/tox = CoxWL
V = 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, ox = 3.9)
polysilicongate
Cox = ox / tox
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4: CMOS Transistor Theory Slide 14CMOS VLSI Design
Carrier velocity Charge is carried by e- Carrier velocity v proportional to lateral E-field
between source and drain v =
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4: CMOS Transistor Theory Slide 15CMOS VLSI Design
Carrier velocity Charge is carried by e- Carrier velocity v proportional to lateral E-field
between source and drain v = E called mobility E =
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4: CMOS Transistor Theory Slide 16CMOS VLSI Design
Carrier velocity Charge is carried by e- Carrier velocity v proportional to lateral E-field
between source and drain v = E called mobility E = Vds/L
Time for carrier to cross channel:– t =
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4: CMOS Transistor Theory Slide 17CMOS VLSI Design
Carrier velocity Charge is carried by e- Carrier velocity v proportional to lateral E-field
between source and drain v = E called mobility E = Vds/L
Time for carrier to cross channel:– t = L / v
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4: CMOS Transistor Theory Slide 18CMOS VLSI Design
nMOS Linear I-V Now we know
– How much charge Qchannel is in the channel
– How much time t each carrier takes to cross
dsI
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4: CMOS Transistor Theory Slide 19CMOS VLSI Design
nMOS Linear I-V Now we know
– How much charge Qchannel is in the channel
– How much time t each carrier takes to cross
channelds
QI
t
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4: CMOS Transistor Theory Slide 20CMOS VLSI Design
nMOS Linear I-V Now 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
QI
tW VC V V VL
VV V V
ox = W
CL
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4: CMOS Transistor Theory Slide 21CMOS VLSI Design
nMOS Saturation I-V If Vgd < Vt, channel pinches off near drain
– When Vds > Vdsat = Vgs – Vt
Now drain voltage no longer increases current
dsI
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4: CMOS Transistor Theory Slide 22CMOS VLSI Design
nMOS Saturation I-V If 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 V
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4: CMOS Transistor Theory Slide 23CMOS VLSI Design
nMOS Saturation I-V If 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
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4: CMOS Transistor Theory Slide 24CMOS 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 V
VI V V V V V
V V V V
Shockley 1st order transistor models
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4: CMOS Transistor Theory Slide 25CMOS VLSI Design
Example We will be using a 0.6 m process for your project
– From AMI Semiconductor
– tox = 100 Å
– = 350 cm2/V*s
– Vt = 0.7 V
Plot Ids vs. Vds
– Vgs = 0, 1, 2, 3, 4, 5
– Use W/L = 4/2
14
28
3.9 8.85 10350 120 /
100 10ox
W W WC A V
L L L
0 1 2 3 4 50
0.5
1
1.5
2
2.5
Vds
I ds (m
A)
Vgs = 5
Vgs = 4
Vgs = 3
Vgs = 2
Vgs = 1
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4: CMOS Transistor Theory Slide 26CMOS VLSI Design
pMOS I-V All dopings and voltages are inverted for pMOS
– Source is the more positive terminal Mobility p is determined by holes
– Typically 2-3x lower than that of electrons n
– 120 cm2/V•s in AMI 0.6 m process Thus pMOS must be wider to
provide same current– In this class, assume
n / p = 2-5 -4 -3 -2 -1 0
-0.8
-0.6
-0.4
-0.2
0
I ds(m
A)
Vgs = -5
Vgs = -4
Vgs = -3
Vgs = -2
Vgs = -1
Vds
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4: CMOS Transistor Theory Slide 27CMOS VLSI Design
Capacitance Any two conductors separated by an insulator have
capacitance Gate 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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4: CMOS Transistor Theory Slide 28CMOS VLSI Design
Gate Capacitance Approximate channel as connected to source Cgs = oxWL/tox = CoxWL = CpermicronW
Cpermicron is typically about 2 fF/m
n+ n+
p-type body
W
L
tox
SiO2 gate oxide(good insulator, ox = 3.90)
polysilicongate
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4: CMOS Transistor Theory Slide 29CMOS VLSI Design
Diffusion Capacitance Csb, Cdb
Undesirable, called parasitic capacitance Capacitance depends on area and perimeter
– Use small diffusion nodes
– Comparable to Cg
for contacted diff
– ½ Cg for uncontacted
– Varies with process