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EE141
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EE141 EECS141 1 Lecture #11
EE141 EECS141 2 Lecture #11
HW 5 posted – due in two weeks
Lab this week
Midterm graded
Project to be launched in week 7
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EE141 EECS141 5 Lecture #11
What do digital IC designers
need to know?
EE141 EECS141 6 Lecture #11
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EE141 EECS141 7 Lecture #11
Pinch-off
0< VGS
- VT < V
DS
EE141 EECS141 8 Lecture #11
For (VGS – VT) < VDS, the effective drain voltage
and current saturate:
’
Of course, real drain current isn’t totally
independent of VDS
For example, approx. for channel-length modulation:
’
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EE141 EECS141 9 Lecture #11
Cutoff:
VGS
-VT< 0
Linear (Resistive):
VGS
-VT > V
DS
Saturation:
0 < VGS
-VT < V
DS
’
’
EE141 EECS141 10 Lecture #11
Quadratic
Relationship
0 0.5 1 1.5 2 2.5 0
1
2
3
4
5
6 x 10
-4
VGS
= 2.5 V
VGS
= 2.0 V
VGS
= 1.5 V
VGS
= 1.0 V
Resistive Saturation
VDS = VGS - VT
VDS (V)
I D (
A)
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EE141 EECS141 11 Lecture #11
Linear
Relationship
-4
0 0.5 1 1.5 2 2.5 0
0.5
1
1.5
2
2.5 x 10
VGS= 2.5 V
VGS= 2.0 V
VGS= 1.5 V
VGS= 1.0 V
Early
Saturation
VDS (V)
I D (
A)
EE141 EECS141 12 Lecture #11
(V/μm)
n (
m / s
)
sat = 10 5
Constant mobility (slope = μ)
Constant velocity
c
Velocity saturates due to carrier scattering
effects
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EE141 EECS141 13 Lecture #11
I D
Long-channel device
Short-channel device
V DS V DSAT V GS - V T
V GS = V DD
EE141 EECS141 14 Lecture #11
0 0.5 1 1.5 2 2.5 0
1
2
3
4
5
6 x 10
-4
V GS (V)
I D (A
)
0 0.5 1 1.5 2 2.5 0
0.5
1
1.5
2
2.5 x 10
-4
V GS (V)
I D (A
) quadratic
quadratic
linear
Long Channel(L=2.5μm)
Short Channel(L=0.25μm)
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EE141 EECS141 15 Lecture #11
Approximate velocity:
Continuity requires that:
Integrating to find the current again:
EE141 EECS141 16 Lecture #11
-4
0 0.5 1 1.5 2 2.5 0
0.5
1
1.5
2
2.5 x 10
VGS= 2.5 V
VGS= 2.0 V
VGS= 1.5 V
VGS= 1.0 V
0 0.5 1 1.5 2 2.5 0
1
2
3
4
5
6 x 10
-4
VGS= 2.5 V
VGS= 2.0 V
VGS= 1.5 V VGS= 1.0 V
Resistive Saturation
VDS = VGS - VT
VDS (V) VDS (V)
I D (
A)
I D (
A)
Resistive
Velocity
Saturation
Long Channel(L=2.5μm)
Short Channel(L=0.25μm)
W/L=1.5
VDSAT
VGS
-VT
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EE141 EECS141 17 Lecture #11
Exact behavior of transistor in velocity sat. somewhat
challenging if want simple/easy to use models
So, many different models developed over the years
v-sat, alpha, unified, VT*, etc.
Simple model for manual analysis desirable Assume velocity perfectly linear until sat
Assume VDSAT constant
EE141 EECS141 18 Lecture #11 18
(V/μm)
n (
m / s
)
sat = 10 5
Constant velocity
Assume velocity perfectly linear until hit sat
c = sat/μ
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EE141 EECS141 19 Lecture #11
VGS-VT (V)
Assume VDSAT = cL when (VGS – VT) > cL
cL
VDSAT (
V)
cL
Actual VDSAT
EE141 EECS141 20 Lecture #11
B
D
G
ID
S
for VGT
0: ID = 0
with VDS,eff = min (VGT, VDS, VD,VSAT)
for VGT
0:
define VGT = VGS – VT
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EE141 EECS141 21 Lecture #11
-4
0 0.5 1 1.5 2 2.5 0
0.5
1
1.5
2
2.5 x 10
Velocity
Saturation
VDS (V)
I D (
A)
VDS = VGT
VGT = VD,VSAT
Saturation
Linear
VDS = VD,VSAT
Define VGT = VGS – VT, VD,VSAT = c·L
EE141 EECS141 22 Lecture #11
0 0.5 1 1.5 2 2.5 0
0.5
1
1.5
2
2.5 x 10
-4
V DS (V)
I D (
A)
VDS=VD,VSAT
VDS=VGT
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EE141 EECS141 23 Lecture #11
If device always operates in velocity sat.:
“VT*” model:
Good for first cut, simple analysis
EE141 EECS141 24 Lecture #11 24
Textbook: page 103
V
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EE141 EECS141 25 Lecture #11
-2.5 -2 -1.5 -1 -0.5 0 -1
-0.8
-0.6
-0.4
-0.2
0 x 10
-4
V DS (V)
I D (
A)
• All variables negative
• I prefer to work with absolute values
VGS = -1.0V
VGS = -1.5V
VGS = -2.0V
VGS = -2.5V
EE141 EECS141 26 Lecture #11
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EE141 EECS141 27 Lecture #11
= CGCS + CGSO = CGCD + CGDO
= CGCB = Cdiff
G
S D
B
= Cdiff
EE141 EECS141 28 Lecture #11
Capacitance (per area) from gate across
the oxide is W·L·Cox, where Cox= ox/tox
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EE141 EECS141 29 Lecture #11
Distribution between terminals is complex
Capacitance is really distributed
– Useful models lump it to the terminals
Several operating regions:
– Way off, off, transistor linear, transistor saturated
EE141 EECS141 30 Lecture #11
When the transistor is off, no carriers in channel to form the other side of the capacitor. – Substrate acts as the other capacitor terminal
– Capacitance becomes series combination of gate oxide and depletion capacitance
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EE141 EECS141 31 Lecture #11
When |VGS| < |VT|, total CGCB much smaller than
W·L·Cox
– Usually just approximate with CGCB = 0 in this region.
(If VGS is “very” negative (for NMOS), depletion
region shrinks and CGCB goes back to ~W·L·Cox)
EE141 EECS141 32 Lecture #11
Channel is formed and acts as the other terminal
– CGCB drops to zero (shielded by channel)
Model by splitting oxide cap equally between
source and drain
– Changing either voltage changes the channel charge
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EE141 EECS141 33 Lecture #11 33
Changing source voltage doesn’t change VGC
uniformly
– E.g. VGC at pinch off point still VTH
Bottom line: CGCS 2/3·W·L·Cox
EE141 EECS141 34 Lecture #11
Drain voltage no longer affects channel charge
– Set by source and VDS_sat
If change in charge is 0, CGCD = 0
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EE141 EECS141 35 Lecture #11
Cgate vs. VGS
(with VDS = 0)
Cgate vs. operating region
EE141 EECS141 36 Lecture #11 36
Off/Lin/Sat CGSO = CGDO = CO W
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EE141 EECS141 37 Lecture #11
COV not just from metallurgic overlap – get fringing
fields too
Typical value: ~0.2fF·W(in μm)/edge
n + n +
Cross section
n + n +
Cross section
Fringing fields