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EE 330Lecture 16
Model RelationshipsCMOS Process Flow
Quiz 13 Determine the current ID for the following circuit. Assume the MOS transistor can be modeled by the basic square-law model with parameters VT=0.8V, µCOX=100µA/V2 and COX=4fF/µ2 and the device has dimensions W=10µ and L=2µ.
Bφ
And the number is ….
6
31
2
45
7
8
9
And the number is ….
6
31
2
4
5
7
8
9
Quiz 13 Determine the current ID for the following circuit. Assume the MOS transistor can be modeled by the basic square-law model with parameters VT=0.8V, µCOX=100µA/V2 and COX=4fF/µ2 and the device has dimensions W=10µ and L=2µ.
Bφ
Solution:
1. Guess the device is operating in the Saturation Region
2. Analyze the circuit with the device in this region3. Verify region of operation
4. Repeat steps 1-3 if guess was not correct
Quiz 13 Determine the current ID for the following circuit. Assume the MOS transistor can be modeled by the basic square-law model with parameters VT=0.8V, µCOX=100µA/V2 and COX=4fF/µ2 and the device has dimensions W=10µ and L=2µ.
Solution: 2. Analyze the circuit with the device in this region
( )⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
−≥≥−
−<≥⎟⎠⎞
⎜⎝⎛ −−
≤
=
TGSDSTGS2
TGSOX
TGSDSGSDSDS
TGSOX
TGS
D
VVVVVVV2LWµC
VVVVVV2
VVVLWµC
VV0
I T
Quiz 13 Determine the current ID for the following circuit. Assume the MOS transistor can be modeled by the basic square-law model with parameters VT=0.8V, µCOX=100µA/V2 and COX=4fF/µ2 and the device has dimensions W=10µ and L=2µ.
Solution: 2. Analyze the circuit with the device in this region
( )
( )24 1010 1 5 0 82 2
123
2D OX GS T
WI µC V V2L
. .
Aµ
−
= −
= −•
=3. Verify region of operation
GS DS GS T? ?V V V V VT≥ > −
1.5V > 0.8V 3V> 1.5V- 0.8V
ID
Verifies!
n-Channel MOSFET Operation and Model
VBS
VGS
VDS
Increase VDS even moreID=?IG=0IB=0
Inversion layer disappears near drain
IDIG
IB
(VBS small)
Termed “saturation”region of operationSaturation first occurs when VDS=VGS-VT
Review from Last Time
Graphical Interpretation of MOS Model
Saturation
Triode
2OXD DS
µC WI = V2L
( )
GS T
DSD OX GS T DS GS DS GS T
2
OX GS T GS T DS GS T
0 V VVWI µC V V V V V V V V
L 2WµC V V V V V V V2L
T
⎧⎪ ≤⎪⎪ ⎛ ⎞= − − ≥ < −⎨ ⎜ ⎟
⎝ ⎠⎪⎪
− ≥ ≥ −⎪⎩
Cutoff
VGS1
VGS3
VGS2
VGS4
Review from Last Time
Model Status
Square-Law Model
( )
GS T
DSD OX GS T DS GS DS GS T
2
OX GS T GS T DS GS T
0 V VVWI µC V V V V V V V V
L 2WµC V V V V V V V2L
T
⎧⎪ ≤⎪⎪ ⎛ ⎞= − − ≥ < −⎨ ⎜ ⎟
⎝ ⎠⎪⎪
− ≥ ≥ −⎪⎩
VGS1
VGS3
VGS2
VGS4
Switch-Level Models
Switch-level model including gate capacitance and drain resistance
Switch closed for VGS=“1”
CGS and RSW dependent upon device sizes and process
For minimum-sized devices in a 0.5u process
1.5fFCGS ≅⎭⎬⎫
−−
≅channelp6KΩchanneln2KΩ
Rsw
Considerable emphasis will be placed upon device sizing to manage CGS and RSW
Drain
Gate
Source
Extended Square-Law Model
( ) ( )1
GS T
DSD OX GS T DS GS DS GS T
2
OX GS T DS GS T DS GS T
0 V VVWI µC V V V V V V V V
L 2WµC V V V V V V V V2L
T
λ
⎧⎪ ≤⎪⎪ ⎛ ⎞= − − ≥ < −⎨ ⎜ ⎟
⎝ ⎠⎪⎪
− • + ≥ ≥ −⎪⎩
( )φφγ −−+= BST0T VVV
Model Parameters : µ,COX,VT0,φ,γ,λ
Design Parameters : W,L but only one degree of freedom W/L
0I0I
B
G
==
Short-Channel Model
( ) ( )
( ) ( )
1
1
GS T
2 2 2D OX GS T DS GS DS GS
1
22 OX GS T GS T DS GS
0 V VWI µC V V V V V V VL
WµC V V V V V VL
T T
T
V
V
α α
αα
θ θθ
θ θ
⎧⎪ ≤⎪⎪= − ≥ < −⎨⎪⎪
− ≥ ≥ −⎪⎩
α is the velocity saturation index, 2 ≥ α ≥ 1
Channel length modulation (λ) and bulk effects can be added to the velocitySaturation as well
BSIM model
BSIM Binning Model - multiple BSIM models !
Model RelationshipsDetermine RSW and CGS for an n-channel MOSFET from square-law model In the 0.5u CMOS process if L=1u, W=1u
(Assume µCOX=100µAV-2, COX=2.5fFu-2,VT0=1V, VDD=3.5V, VSS=0)
( )
GS T
DSD OX GS T DS GS DS GS T
2
OX GS T GS T DS GS T
0 V VVWI µC V V V V V V V V
L 2WµC V V V V V V V2L
T
⎧⎪ ≤⎪⎪ ⎛ ⎞= − − ≥ < −⎨ ⎜ ⎟
⎝ ⎠⎪⎪
− ≥ ≥ −⎪⎩
When SW is on, operation is “deep” triode
Model Relationships
(Assume µCOX=100µAV-2, COX=2.5fFu-2,VT0=1V, VDD=3.5V, VSS=0)
( )DSD OX GS T DS OX GS T DS
VW WI µC V V V µC V V VL 2 L⎛ ⎞= − − ≅ −⎜ ⎟⎝ ⎠
( ) ( )
1 414 3 5 11
KE
= = = Ω⎛ ⎞− − −⎜ ⎟⎝ ⎠
GS DD
GS
DSSQ
D V =VOX GS T
V =3.5V
V 1R = WI µC V V ( ) .L
CGS= COXWL = (2.5fFµ-2)(1µ2) = 2.5fF
Determine RSW and CGS for an n-channel MOSFET from square-law model In the 0.5u CMOS process if L=1u, W=1u
Model Relationships
( COX=2.5fFu-2,VT0=1V, VDD=3.5V, VSS=0)
( )
GS T
DSD OX GS T DS GS DS GS T
2
OX GS T GS T DS GS T
0 V VVWI µC V V V V V V V V
L 2WµC V V V V V V V2L
T
⎧⎪ ≤⎪⎪ ⎛ ⎞= − − ≥ < −⎨ ⎜ ⎟
⎝ ⎠⎪⎪
− ≥ ≥ −⎪⎩
When SW is on, operation is “deep” triode
Determine RSW and CGS for an p-channel MOSFET from square-law model In the 0.5u CMOS process if L=1u, W=1u
Observe µn\ µp≈3
Model Relationships
( COX=2.5fFu-2,VT0=1V, VDD=3.5V, VSS=0)
( )
GS T
DSD OX GS T DS GS DS GS T
2
OX GS T GS T DS GS T
0 V VVWI µC V V V V V V V V
L 2WµC V V V V V V V2L
T
⎧⎪ ≤⎪⎪ ⎛ ⎞= − − ≥ < −⎨ ⎜ ⎟
⎝ ⎠⎪⎪
− ≥ ≥ −⎪⎩
When SW is on, operation is “deep” triode
Determine RSW and CGS for an p-channel MOSFET from square-law model In the 0.5u CMOS process if L=1u, W=1u
Observe µn\ µp≈3
Model Relationships
( )⎛ ⎞= − − ≅ −⎜ ⎟⎝ ⎠
DSD p OX GS T DS p OX GS T DS
VW WI µ C V V V µ C V V VL 2 L
( ) ( )
1 121 14 3 5 13 1
KE
= = = Ω⎛ ⎞ ⎛ ⎞− − −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
GS DD
GS
DSSQ
D V =Vp OX GS T
V =3.5V
V 1R = WI µ C V V ( ) .L
CGS= COXWL = (2.5fFµ-2)(1µ2) = 2.5fF
Determine RSW and CGS for an p-channel MOSFET from square-law model In the 0.5u CMOS process if L=1u, W=1u
( COX=2.5fFu-2,VT0=1V, VDD=3.5V, VSS=0)
Observe µn\ µp≈3
Observe the resistance of the p-channel device is approximately 3 times larger than that of the n-channel device for same bias and dimensions !
Modeling of the MOSFETGoal: Obtain a mathematical relationship between the port variables of a device. ( )
( )( ) ⎪
⎭
⎪⎬
⎫
===
BSDSGS3B
BSDSGS2G
BSDSGS1D
V,,VVfIV,,VVfIV,,VVfI
Small-Signal Model
Goal with small signal model is to predict performance of circuit or device in the vicinity of an operating point
Operating point is often termed Q-point
Small-Signal Modely
x
Q-point
XQ
YQ
Technology Files• Design Rules
• Process Flow (Fabrication Technology) (will discussion next )
• Model Parameters (will discuss in substantially more detail after device operation and more advanced models are introduced)
This table discusses a p-well process flow, an n-well process flow is actually used in the following set of slides with straightforward modifications of this process flow.
Bulk CMOS Process Description
• n-well process• Single Metal Only Depicted• Double Poly
Components Shown
• n-channel MOSFET• p-channel MOSFET• Poly Resistor• Doubly Poly Capacitor
A A’
B’B
C
C’
D
D’
Consider Basic Components Only
Well Contacts and Guard Rings Will be Discussed Later
A A’
B’B
A A’
B’B
A A’
B’B
n-channel MOSFET
S
D
G
S
D
BG
A A’
B’B
S
D
BG
W L
A A’
B’B
n-channel MOSFET
Capacitor
p-channel MOSFET
Resistor
A A’
B’B
N-well Mask
A A’
B’B
N-well Mask
Detailed Description of First Photolithographic Steps Only
• Top View• Cross-Section View
~
Blank Wafer
p-doped Substrate
ExposeDevelop
Photoresistn-well MaskImplant
~
A A’
B’B
A-A’ Section
B-B’ Section
PhotoresistN-well MaskExposureDevelop
A-A’ Section
B-B’ Section
Implant
N-well Mask
A-A’ Section
B-B’ Sectionn-well
A A’
B’B
Active Mask
A A’
B’B
Active Mask
Active Mask
A-A’ Section
B-B’ Section
Field Oxide Field Oxide Field Oxide
Field Oxide
A A’
B’B
Poly1 Mask
A A’
B’B
Poly1 Mask
A A’
B’B
n-channel MOSFET
Capacitor
P-channel MOSFET
Resistor
Poly 1 Mask
A-A’ Section
B-B’ Section
Gate Oxide Gate Oxide
A A’
B’B
Poly 2 Mask
A A’
B’B
Poly 2 Mask
Poly 2 Mask
A-A’ Section
B-B’ Section
A A’
B’B
P-Select
A A’
B’B
P-Select
P-Select Mask – n-diffusion
A-A’ Section
B-B’ Section
n-diffusion
P-Select Mask – p-diffusion
A-A’ Section
B-B’ Section
p-diffusion
A A’
B’B
Contact Mask
A A’
B’B
Contact Mask
Contact Mask
A-A’ Section
B-B’ Section
A A’
B’B
Metal 1 Mask
A A’
B’B
Metal 1 Mask
Metal Mask
A-A’ Section
B-B’ Section
A A’
B’B
A A’
B’B
n-channel MOSFET
Capacitor
P-channel MOSFET
Resistor
A A’
B’B
C
C’
D
D’
That’s all folks!
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