EE141. 3. EECS141. Class Material. ❑ Last lecture. ▫ CMOS manufacturing
process. ▫ Design rules. ❑ Today's lecture. ▫ MOS transistor operation and
modeling.
EE141
EE141-Spring 2007 Digital Integrated Circuits
Announcements Lab
starts next week!
Stop by 253 Cory to activate lab card keys Show up at first lab of your choice and sign up w/ TA Observe lab rules, see http://iesg.eecs.berkeley.edu/labs/labinfo/labrules.asp
Lecture 4 MOS Transistor
Homework
#1 is (was) due today Homework #2 posted, due next Th 5pm 1
EE141 EECS141
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Class Material Last
lecture
CMOS manufacturing process Design rules Today’s
MOS Transistor
lecture
MOS transistor operation and modeling Reading
(3.3.1-3.3.2)
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What is a Transistor?
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Switch Model of MOS Transistor G
A MOS Transistor
|VGS|
A Switch!
S
G |VGS| S
|VGS| ≥ |VT| D
S
Ron
Ron
D S
D |VGS| < |VT|
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D
5
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S
D |VGS| > |VT| 6
1
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MOS Transistors: Types and Symbols
NMOS and PMOS
D
NMOS Transistor
PMOS Transistor
G
G
VGS > 0 D
G
G
S NMOS Depletion
S NMOS Enhancement
VGS < 0
S
D
D
S
D
D
G S PMOS Enhancement 7
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Threshold Voltage: Concept S –
VG S
VT = VT 0 + γ ⋅ Fermi
n+
8
The Threshold Voltage
D
G
S NMOS with Bulk Contact
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Threshold +
B
G
(
2φF + VSB − 2φF
)
potential
n+
n-channel
N φF = φT ⋅ ln A ni
Depleti on region
2ΦF is approximately −0.6V for p-type substrates γ is the body factor VT0 is approximately 0.45V for our process
p-substrate B 9
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The Body Effect
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Transistor in Linear Mode
0.9
VGS > VDS + VT
0.85 0.8
S
VGS
VDS G
0.75
ID
D
n+
0.65
T
V (V)
0.7
–
V(x)
n+
+
0.6
L
x
0.55 0.5
reverse body bias
p-substrate
VT0
0.45 0.4 -2.5
-2
-1.5
-1
V EE141 EECS141
BS
-0.5
B
0
(V) 11
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12
2
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The Drain Current
The Drain Current
Charge in the channel is controlled by the gate voltage: Q i ( x ) = −Cox ⋅ [VGS − V ( x ) − VT ]
Cox =
Combining velocity and charge: ID ⋅ dx = μ n ⋅ Cox ⋅ W ⋅ (VGS − V − VT ) ⋅ dV
ε ox
tox
Integrating over the channel:
Drain current is proportional to charge and velocity:
ID = k n’ ⋅
I D = − υn ( x ) ⋅ Q i ( x ) ⋅ W
υn ( x ) = −μ n ⋅ ξ( x ) = μ n ⋅
Transconductance:
dV dx 13
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VGS
For VGD < VT, the drain current saturates: k’ W ID = n ⋅ ⋅ (VGS − VT )2 2 L
VDS > VGS - VT
G
μ ⋅ε k n’ = μ n ⋅ Cox = n ox t ox
Saturation
Transistor in Saturation VT < VGS < VDS + VT
V2 ⎤ W ⎡ ⋅ ⎢(VGS − VT ) ⋅VDS − DS ⎥ L ⎢ 2 ⎥ ⎦ ⎣
D
S
n+
-
VGS - VT
+
Including channel-length modulation:
n+
k’ W ID = n ⋅ ⋅ (VGS − VT )2 ⋅ (1 + λ ⋅ VDS ) 2 L CLM
Pinch-off 15
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Current-Voltage Relations: A Good Ol’ Transistor
Modes of Operation Cutoff: VGS < VT
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ID = 0
6
x 10
-4
VGS= 2.5 V
5
VGS > VDS + VT
Saturation: VT < VGS < VDS + VT
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ID = k n’ ⋅
W L
⎡ V2 ⎤ ⋅ ⎢(VGS − VT ) ⋅ VDS − DS ⎥ 2 ⎥ ⎢ ⎦ ⎣
Resistive
k’ W ID = n ⋅ ⋅ (VGS − VT )2 2 L
VGS= 2.0 V 3
VGS= 1.5 V
1
VGS= 1.0 V 0
0.5
1
1.5
VDS (V) EE141 EECS141
Quadratic Relationship
VDS = VGS - VT
2
0
17
Saturation
4
ID (A)
Resistive (Linear):
2
2.5
18
3
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Current-Voltage Relations: The Deep Sub-Micron Transistor
A Model for Manual Analysis VDS > VGS – VT
D
2.5
-4
Early Saturation
VGS= 2.5 V
Resistive:
VDS < VGS – VT
ID
VGS= 2.0 V 1.5
V2 ⎤ W ⎡ ID = k n’ ⋅ ⋅ ⎢(VGS − VT ) ⋅ VDS − DS ⎥ L ⎢ 2 ⎥ ⎣ ⎦
S
with
VT = VT 0 + γ ⋅
(
2φF + VSB − 2φF 19
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)
0
Linear Relationship
VGS= 1.5 V
1
VGS= 1.0 V
0.5
0
0.5
1
1.5
2
2.5
VDS (V)
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Velocity Saturation
Velocity Saturation Velocity saturates due to carrier scattering effects
ID Long-channel device
υ n (m/s)
x 10
2
ID (A)
G
Saturation:
k’ W ID = n ⋅ ⋅ (VGS − VT )2 ⋅ (1 + λ ⋅ VDS ) 2 L
υsat = 105
VGS = VDD Short-channel device
Constant velocity
Constant mobility (slope = µ)
V DSAT
ξc = 1.5
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Regions of Operation
-4
x 10
6
-4
x 10 2.5
x 10
-4
2.5
VGS= 2.5 V
5 5
Resistive
2 4
1
Saturation VGS= 2.0 V
3
VGS= 1.5 V
1
VGS= 1.0 V
2 0.5
1 0 0
0.5
1
1.5
2
VGS(V)
Long Channel (L=2.5μm) EE141 EECS141
2.5
0 0
0 0
quadratic 0.5
1
1.5
2
0.5
1
1.5
2
-4
Velocity Saturation
VGS= 1.0 V
0.5
2.5
0
VGS= 2.0 V VGS= 1.5 V
1
0
VDS (V)
2.5
VGS= 2.5 V
Resistive
1.5
VDS = VGS - VT
2
x 10
2
ID (A)
ID (A)
ID (A)
linear
1.5
quadratic
ID (A)
4 3
VDS
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ID versus VGS 6
VGS - V T
ξ (V/µm)
0.5
1
1.5
2
2.5
VDS (V)
VGS(V)
Short Channel (L=0.25μm) 23
Long Channel (L=2.5μm) EE141 EECS141
W/L=1.5
Short Channel (L=0.25μm) 24
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Regions of Operation
Including Velocity Saturation 6
Approximate velocity:
x 10
-4
2.5
VGS= 2.5 V
Resistive
Saturation
1.5
VDS = VGS - VT
2
VGS= 1.5 V
1
VGS= 1.0 V
0 0
VGS= 2.0 V
VGS= 2.0 V
3
0.5
1
1.5
VGS= 1.5 V
1
VGS= 1.0 V
0.5
2
2.5
0
0
VDS (V)
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Regions of Operation – Simplified
2.5
x 10
1
1.5
2
2.5
W/L=1.5
Short Channel (L=0.25μm) 26
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A Unified Model for Manual Analysis
VDSAT ≈ L·ξc
Define VGT = VGS – VT
0.5
VDS (V)
Long Channel (L=2.5μm)
In deep submicron, there are four regions of operation: (1) cutoff, (2) resistive, (3) saturation and (4) velocity saturation
