lecture9 transistors
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8/10/2019 Lecture9 Transistors
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EE141
EE141 EECS141 1 Lecture #9
Guest Lecturer:
Andrei Vladimirescu
EE141 EECS141 2 Lecture #9
!
Midterm on Friday Febr 19 6:30-8pm in 2060Valley LSB" Open book
" Do not forget your important class material norcalculator
" Covers from start of semester to optimization ofcomplex logic – wires not included!
! Review session tomorrow Th 2/18 at 6:30pm" Room to be announced on web-site
!
No lab this week
!
Hw 4 due next week Friday
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EE141
EE141 EECS141 3 Lecture #9
!
Last lecture
" Wiring + first glimpse at transitors
(threshold)
!
Today’s lecture
" Transistor models
! Reading (Ch 3)
EE141 EECS141 4 Lecture #9
What do digital IC designers
need to know?
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EE141
EE141 EECS141 5 Lecture #9
" With positive gate bias, electrons pulled toward the gate
" With large enough bias, enough electrons will be pulled to "invert"the surface (p!n type)
" Voltage at which surface inverts: “magic” threshold voltage VT
EE141 EECS141 6 Lecture #9
! Threshold
!
Fermi potential
2!F is approximately 0.6V for p-type substrates
! is the body factor
V T 0 is approximately 0.45V for our process
Depletion charge
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EE141
EE141 EECS141 7 Lecture #9
EE141 EECS141 8 Lecture #9
Pinch-off
0< V GS
- V T < V
DS
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EE141
EE141 EECS141 9 Lecture #9
!
For (V GS – VT) < V DS , the effective drain voltageand current saturate:
’
!
Of course, real drain current isn’t totally
independent of VDS
" For example, approx. for channel-length modulation:
’
EE141 EECS141 10 Lecture #9
Cutoff:
V GS -VT< 0
Linear (Resistive):
V GS -V T > V DS
Saturation:
0 < V GS
-V T < V
DS
’
’
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EE141
EE141 EECS141 11 Lecture #9
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 )
EE141 EECS141 12 Lecture #9
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 )
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EE141
EE141 EECS141 13 Lecture #9
" (V/µm)
#
n ( m
/ s )
# sat = 10 5
Constant mobility
(slope = µ)
Constant velocity
" c
!
Velocity saturates due to carrier scatteringeffects
EE141 EECS141 14 Lecture #9
I D
Long-channel device
Short-channel device
V DS V DSAT V GS - V T
V GS = V DD
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EE141
EE141 EECS141 15 Lecture #9
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)
EE141 EECS141 16 Lecture #9
Approximate velocity:
Continuity requires that:
Integrating to find the current again:
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EE141
EE141 EECS141 17 Lecture #9
-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
V DSAT V GS-VT
EE141 EECS141 18 Lecture #9
! 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
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EE141
EE141 EECS141 19 Lecture #9 19
" (V/µm)
#
n ( m
/ s )
# sat = 10 5
Constant velocity
!
Assume velocity perfectly linear until hit #sat
" c = #sat/µ
EE141 EECS141 20 Lecture #9
V GS -V T (V)
! Assume V DSAT = "c L when (V GS – V T ) > "c L
"cL
V D S A T
( V )
"cL
Actual V DSAT
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EE141
EE141 EECS141 21 Lecture #9
B
D
G
I D
S
for V GT
! 0: I D = 0
with V DS,eff = min (V GT , V DS, V D,VSAT )
for V GT
" 0:
define V GT = V GS – V T
EE141 EECS141 22 Lecture #9
-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 )
V DS = V GT
V GT = V D,VSAT
Saturation
Linear
V DS = V D,VSAT
!
Define V GT = V GS – V T , V D,VSAT = ! c·L
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EE141
EE141 EECS141 23 Lecture #9
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 )
V DS=V D,VSAT
V DS=V GT
EE141 EECS141 24 Lecture #9
!
If device always operates in velocity sat.:
!
“VT*” model:
!
Good for first cut, simple analysis
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EE141
EE141 EECS141 25 Lecture #9 25
Textbook: page 103
V
EE141 EECS141 26 Lecture #9
-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 withabsolute values – makes
life easier.
VGS = -1.0V
VGS = -1.5V
VGS = -2.0V
VGS = -2.5V
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EE141
EE141 EECS141 27 Lecture #9
EE141 EECS141 28 Lecture #9
= C GCS + C GSO = C GCD + C GDO
= C GCB = C diff
G
S D
B
= C diff
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EE141
EE141 EECS141 29 Lecture #9
! Capacitance (per area) from gate across
the oxide is W·L·Cox, where Cox=%ox/tox
EE141 EECS141 30 Lecture #9
!
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
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EE141
EE141 EECS141 31 Lecture #9
" When the transistor is off, no carriers in channelto form the other side of the capacitor. – Substrate acts as the other capacitor terminal
–
Capacitance becomes series combination of gateoxide and depletion capacitance
EE141 EECS141 32 Lecture #9
" 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)
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EE141
EE141 EECS141 33 Lecture #9
" 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
EE141 EECS141 34 Lecture #9 34
"
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
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EE141
EE141 EECS141 35 Lecture #9
" Drain voltage no longer affects channel charge
– Set by source and VDS_sat
"
If change in charge is 0, CGCD = 0
EE141 EECS141 36 Lecture #9
Cgate vs. VGS
(with VDS = 0)
Cgate vs. operating region
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EE141
EE141 EECS141 37 Lecture #9 37
Off/Lin/Sat # CGSO = CGDO = CO"W
EE141 EECS141 38 Lecture #9
" 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