1 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
CMOS Transistor Theory(and its effects on scaling)
Michael Niemier
(Some slides based on lecture notes by David Harris)
2 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Nanowire-based Gates
If each wire was just 5 nm in diameter, would you be excited about this technology?
Can make very small pn junctions and diode based lgoic
3 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
MOSFET cross section…
n
P
With applied Vgs,depletion region
forms
n
4 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
To recap…• 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 (ΔV/Δt) -> Δt = (C/I) ΔV– Capacitance and current determine speed
5 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
MOS Capacitor• Gate and body form MOS capacitor• Operating modes
polysilicon gate
(a)
silicon dioxide insulator
p-type body+-
Vg < 0
(b)
+-
0 < Vg < V
t
depletion region
(c)
+-
Vg > V
t
depletion region
inversion region
polysilicon gate
(a)
silicon dioxide insulator
p-type body+-
Vg < 0
(b)
+-
0 < Vg < V
t
depletion region
(c)
+-
Vg > V
t
depletion region
inversion region
polysilicon gate
(a)
silicon dioxide insulator
p-type body+-
Vg < 0
(b)
+-
0 < Vg < V
t
depletion region
(c)
+-
Vg > V
t
depletion region
inversion region
6 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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
Vgd
Vgs
Vds
+-
+
-
+
-
7 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
nMOS Cutoff• No channel formed, so no current flows• Ids = 0
+-
Vgs
= 0
n+ n+
+-
Vgd
p-type body
b
g
s d
8 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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
Vgs > VtVds = 0, no current
+-
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
Vgs > VtVds > 0, but < (Vgs - Vt)
(current flows)
9 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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
Vds > Vgs - VtEssentially, voltage difference over induced channel fixed at Vgs - Vt
(current flows, but saturates)(or ids no longer a function of Vds)
10 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Outline (part 2)• Today…
– nMOS & pMOS I-V characteristics• Why (part 1):
– Quantify - or at least estimate - how we represent & moveinformation
• Why (part 2):– This way we can estimate what happens when we make device
smaller -- and in theory, better.• Possibly today…
– A very brief discussion of RC delay models• Why?
– Important because delay = one of the 2 performance metrics wecare most about.
• Another, “why”– Can leverage in 1st HW :-)
• David Frank talk - starts with 1st principles, extrapolatesto practical, chip-level performance
11 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
A little bit of foreshadowing
Board digression #0S2S2/U21P/AreaPower Density11/U21/S2IsatVP
1/S1/S1/SRonCgateIntrinsic Delay
111V/IsatRon
S2S2/USIsat/AreaCurrent Density11/U1/SCoxWVIsat
SSSCoxW/Lkn, kp
1/S1/S1/SCoxWLCgate
SSS1/toxCox
1/S21/S21/S2WLArea/deviceS2S2/USV/Wdepl
2NSUB
11/U1/SVdd, Vt
1/S1/S1/SW, L, tox
Fixed-VoltageScaling
General ScalingFull ScalingRelationParameter
12 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
A little bit of foreshadowing
Board digression #0
13 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
A little bit of foreshadowing
Board digression #0
14 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
tox
350 nm
250 nm
180 nm
150 nm
120 nm90 nm65 nm
350/250=1.4
250/180~1.39
180/150~1.2
150/120~1.25120/90~1.33
90/65~1.38
8/6~1.333
6/3.8~1.58
3.8/2.6~1.46
2.6/1.5~1.71.5/1.2~1.251.25/1~1.25
15 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Ok, let’s derive some I-Vrelationships
16 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
I-V Characteristics• In Linear region, Ids depends on
– How much charge is in the channel?– How fast is the charge moving?
17 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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)
polysilicon
gate
Board digression #1
18 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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)
polysilicon
gate
19 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Channel Charge• MOS structure looks like parallel plate capacitor while
operating in inversion– Gate – oxide – channel
• Qchannel = CV• C = Cg = εoxWL/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)
polysilicon
gate
Cox = εox / tox
20 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Channel Charge• MOS structure looks like parallel plate capacitor while
operating in inversion– Gate – oxide – channel
• Qchannel = CV• C = Cg = εoxWL/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)
polysilicon
gate
Cox = εox / tox
Board digression #2
21 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Carrier velocity• Charge is carried by e-• Carrier velocity v proportional to lateral E-field
between source and drain• v =
22 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Carrier velocity• Charge is carried by e-• Carrier velocity v proportional to lateral E-field
between source and drain• v = µE µ called mobility• E =
Board digression #3
How I try notto teach…
23 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Carrier velocity• Charge is carried by e-• Carrier velocity v proportional to lateral E-field
between source and drain• v = µE µ called mobility• E = Vds/L• Time for carrier to cross channel:
– t =
24 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Carrier velocity• Charge is carried by e-• Carrier velocity v proportional to lateral E-field
between source and drain• v = µE µ called mobility• E = Vds/L• Time for carrier to cross channel:
– t = L / v
Board digression #4
25 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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 =
26 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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
ds
QI
t=
=
27 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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
t
W VC V V V
L
VV V V
µ
!
=
" #= $ $% &' (
" #= $ $% &' (
ox =
WC
L! µ
Board digression #5
28 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Let’s go back to…
Board digression #6S2S2/U21P/AreaPower Density11/U21/S2IsatVP
1/S1/S1/SRonCgateIntrinsic Delay
111V/IsatRon
S2S2/USIsat/AreaCurrent Density11/U1/SCoxWVIsat
SSSCoxW/Lkn, kp
1/S1/S1/SCoxWLCgate
SSS1/toxCox
1/S21/S21/S2WLArea/deviceS2S2/USV/Wdepl
2NSUB
11/U1/SVdd, Vt
1/S1/S1/SW, L, tox
Fixed-VoltageScaling
General ScalingFull ScalingRelationParameter
29 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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 =
30 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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 dsat
VI V V V! " #= $ $% &
' (
31 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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
!
!
" #= $ $% &' (
= $
Board digression #7
32 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
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
33 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Again, let’s go back to…
Board digression #8S2S2/U21P/AreaPower Density11/U21/S2IsatVP
1/S1/S1/SRonCgateIntrinsic Delay
111V/IsatRon
S2S2/USIsat/AreaCurrent Density11/U1/SCoxWVIsat
SSSCoxW/Lkn, kp
1/S1/S1/SCoxWLCgate
SSS1/toxCox
1/S21/S21/S2WLArea/deviceS2S2/USV/Wdepl
2NSUB
11/U1/SVdd, Vt
1/S1/S1/SW, L, tox
Fixed-VoltageScaling
General ScalingFull ScalingRelationParameter
34 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Look at IDS in context of scaling
Board digression #8
35 Lecture 02 - CMOS Transistor Theory & the Effects of Scaling - CSE 40547/60547
Board digression #8