ee141ee141--spring 2008spring 2008 digital integrated...

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EE141EE141--Spring 2008Spring 2008Digital Integrated Digital Integrated CircuitsCircuitsCircuitsCircuits

Lecture 5Lecture 5

EE141EECS141 1Lecture #5

MOS Transistor ModelMOS Transistor Model

AnnouncementsAnnouncementsDue to family emergency, Prof. Rabaey will be out of town this week and next.

We 2/6 : NO lecture – moved to 2/19Fr. 2/8:: Prof. AlonWe 2/13: NO lecture – moved to 2/26Fr 2/15: Simone GambiniTu 2/19: Make up lecture (203 McLaughlin)Tu 2/26: Make up lecture (203 McLaughlin)


p ( g )Lab 2 this week!

Lab 3 next weekHomework #2 is due Fr.

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Class MaterialClass MaterialLast lecture

Design RulesStarted MOS modeling

Today’s lectureMOS transistor modeling

– Will see how to use these models to


understand tradeoffs between CMOS gate delay, power, etc.

Reading (3.3.1-3.3.2)

MOS TransistorMOS Transistor

Last lecture: what causes a transistor to turn on - concept


transistor to turn on concept of the threshold voltage

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DSGVGS

+

–

Threshold Voltage: ConceptThreshold Voltage: Concept

n+

p-substrate

B

Depletionregion

n-channel

n+


BWith positive gate bias, electrons pulled toward the gateWith large enough bias, enough electrons will be pulled to "invert" the surface (p→n type)Voltage at which surface inverts: “magic” threshold voltage VT

The Threshold VoltageThe Threshold VoltageThreshold

Depletion charge2 BT FB F

QVC

ϕ ϕ= + +

iA

TF nNln⋅φ=φ

Fermi potential( )0 2 2T T F SB FV V Vγ ϕ ϕ= + ⋅ + −

oxC


2ΦF is approximately 0.6V for p-type substratesγ is the body factorVT0 is approximately 0.45V for our process

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SVGS VDS

Transistor with Gate and Drain BiasTransistor with Gate and Drain Bias

n+n+

D

SG

xL

V(x) +–

ID


p-substrate

B

The Drain CurrentThe Drain Current

( )iQ x =

Charge density:

i

Velocity:

( )n xυ =

Current:


DI =

Current:

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Solving the Drain CurrentSolving the Drain CurrentIntegrate along the channel:


Plot of IPlot of I--V CurveV Curve


Is this really what happens?

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VGS

Transistor in SaturationTransistor in Saturation0< VGS - VT < VDS

n+n+

S

G

D

VDS > VGS - VT

VGS - VT+-


Pinch-off

SaturationSaturationFor (VGS – VT) < VDS, the effective drain voltage and current saturate:

( )22 TGSn

D VVL

WkI −⋅⋅=’

Of course, real drain current isn’t totally independent of VDS

F l f h l l th d l ti

( ),DS eff GS TV V V= −


For example, approx. for channel-length modulation:

( ) ( )DSTGSn

D VVVL

WkI ⋅λ+⋅−⋅⋅= 12

2’

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Modes of OperationModes of OperationCutoff:

VGS -VT< 0 0=DI

Linear (Resistive):VGS-VT > VDS ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⋅−⋅⋅=

2

2DS

DSTGSnDV

VVVL

WkI ’


Saturation:0 < VGS-VT < VDS ( ) ( )2 1

2n

D GS T DSk WI V V V

Lλ= ⋅ ⋅ − ⋅ + ⋅

’

6x 10

-4

VGS= 2.5 V

CurrentCurrent--Voltage Relations:Voltage Relations:A Good Ol’ TransistorA Good Ol’ Transistor

QuadraticRelationship

2

3

4

5

VGS= 2.0 V

V = 1 5 V

Resistive Saturation

VDS = VGS - VTI D(A

)


0 0.5 1 1.5 2 2.50

1

VGS= 1.5 V

VGS= 1.0 V

VDS (V)

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-4

2.5x 10

V = 2 5 VEarly

CurrentCurrent--Voltage Relations:Voltage Relations:The Deep SubThe Deep Sub--Micron TransistorMicron Transistor

LinearRelationship1

1.5

2

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

ySaturation

I D(A

)


0 0.5 1 1.5 2 2.50

0.5 VGS= 1.0 V

VDS (V)

Velocity SaturationVelocity Saturation

s)

Velocity saturates due to carrier scattering effects

υn

(m/s

υsat = 105

Constant velocity


ξ (V/µm)

Constant mobility (slope = µ)

ξc

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Velocity SaturationVelocity Saturation

IDLong-channel deviceLong channel device

Short-channel device

VGS = VDD


VDSVDSAT VGS - VT

IIDD versus Vversus VGSGS

5

6x 10-4

2.5x 10-4

1

2

3

4

5

I D(A

)

0.5

1

1.5

2

I D(A

)quadraticlinear


0 0.5 1 1.5 2 2.50

VGS(V)0 0.5 1 1.5 2 2.5

0

VGS(V)

quadratic

Long Channel(L=2.5μm)

Short Channel(L=0.25μm)

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Including Velocity SaturationIncluding Velocity Saturation

Approximate velocity:pp y

Continuity requires that:

Integrating to find the current again:

2c sat nξ υ μ=


g g g

Regions of OperationRegions of Operation-4

2

2.5 x 10VGS= 2.5 V

5

6 x 10-4

VGS= 2.5 VResistive

VDSAT VGS-VT

0

0.5

1

1.5

2

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

0

1

2

3

4VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

Resistive Saturation

VDS = VGS - VTI D(A

)

I D(A

)

VelocitySaturation


0 0.5 1 1.5 2 2.500 0.5 1 1.5 2 2.50

VDS (V) VDS (V)

Long Channel(L=2.5μm)

Short Channel(L=0.25μm)W/L=1.5

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Simplified Velocity SaturationSimplified Velocity Saturation

s)

Assume velocity linear until hit υsat

υn

(m/s

υsat = 105

Constant velocity


ξ (V/µm)ξc= υsat/μ

Simplified Velocity Saturation Simplified Velocity Saturation (cont’d)(cont’d)

Assume VDSAT = ξcL when (VGS – VT) > ξcL

V)V

DS

AT(V

ξcL

Actual VDSAT


VGS-VT (V)ξcL

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Simplified ModelSimplified Model

-4

2.5x 10

V V

Define VGT = VGS – VT, VVSAT = ξc·L

1

1.5

2 VelocitySaturation

I D(A

)

Linear

VDS = VVSAT


0 0.5 1 1.5 2 2.50

0.5

VDS (V)

VDS = VGT

VGT = VVSAT

Saturation

A Unified Model for Manual AnalysisA Unified Model for Manual Analysis

define VGT = VGS – VT

D

G

ID

S

( )2

,' 1DS effVWI k V V Vλ⎛ ⎞

+⎜ ⎟

for VGT ≤ 0: ID = 0

for VGT ≥ 0:

GT GS T


B( ),

,' 12

ffD GT DS eff DSI k V V V

Lλ= ⋅ ⋅ ⋅ − ⋅ + ⋅⎜ ⎟⎜ ⎟

⎝ ⎠

with VDS,eff = min (VGT, VDS, VVSAT)

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Simple Model versus SPICE Simple Model versus SPICE 2.5

x 10-4 VDS=VVSAT

1

1.5

2

I D(A

)


0 0.5 1 1.5 2 2.50

0.5

VDS (V)

VDS=VGT

Transistor Model for Manual AnalysisTransistor Model for Manual Analysis

V


Textbook: page 103

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A PMOS TransistorA PMOS Transistor0

x 10-4

• All variables negativeVGS = -1.0V

-0.6

-0.4

-0.2

I D(A

)

All variables negative

• I prefer to work with absolute values

VGS = -1.5V

VGS = -2.0V


-2.5 -2 -1.5 -1 -0.5 0-1

-0.8

VDS (V)

VGS = -2.5V

Next LectureNext LectureUsing the MOS model:

Inverter VTC and delay


ee141ee141--spring 2008spring 2008 digital integrated...

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