© Digital Integrated Circuits 2nd Devices Digital Integrated Circuits A Design Perspective The...

© Digital Integrated Circuits2nd Devices

Digital Integrated Digital Integrated CircuitsCircuitsA Design PerspectiveA Design Perspective

The DevicesThe Devices

Jan M. RabaeyAnantha ChandrakasanBorivoje Nikolic

July 30, 2002


Goal of this chapterGoal of this chapter

Present intuitive understanding of device operation

Introduction of basic device equations Introduction of models for manual

analysis Introduction of models for SPICE

simulation Analysis of secondary and deep-sub-

micron effects Future trends


The DiodeThe Diode

n

p

p

n

B A SiO2Al

A

B

Al

A

B

Cross-section of pn-junction in an IC process

One-dimensionalrepresentation diode symbol

Mostly occurring as parasitic element in Digital ICs


Depletion RegionDepletion Regionhole diffusion

electron diffusion

p n

hole driftelectron drift

ChargeDensity

Distancex+

-

ElectricalxField

x

PotentialV

W2-W1

(a) Current flow.

(b) Charge density.

(c) Electric field.

(d) Electrostaticpotential.


Diode CurrentDiode Current


Models for Manual AnalysisModels for Manual Analysis

VD

ID = IS(eVD/T – 1)+

–

VD

+

–

+

–VDon

ID

(a) Ideal diode model (b) First-order diode model


Diode ModelDiode Model

ID

RS

CD

+

-

VD


SPICE ParametersSPICE Parameters


What is a Transistor?What is a Transistor?

VGS VT

RonS D

A Switch!

|VGS|

An MOS Transistor


The MOS TransistorThe MOS Transistor

Polysilicon Aluminum


MOS Transistors -MOS Transistors -Types and SymbolsTypes and Symbols

D

S

G

D

S

G

G

S

D D

S

G

NMOS Enhancement NMOS

PMOS

Depletion

Enhancement

B

NMOS withBulk Contact


Threshold Voltage: ConceptThreshold Voltage: Concept

n+n+

p-substrate

DSG

B

VGS

+

-

Depletion

Region

n-channel


The Threshold VoltageThe Threshold Voltage


The Body EffectThe Body Effect

-2.5 -2 -1.5 -1 -0.5 00.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

VBS

(V)

VT (

V)


Current-Voltage RelationsCurrent-Voltage RelationsA good ol’ transistorA good ol’ transistor

QuadraticRelationship

0 0.5 1 1.5 2 2.50

1

2

3

4

5

6x 10

-4

VDS (V)

I D (

A)

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

Resistive Saturation

VDS = VGS - VT


Transistor in LinearTransistor in Linear

n+n+

p-substrate

D

SG

B

VGS

xL

V(x) +–

VDS

ID

MOS transistor and its bias conditions


Transistor in SaturationTransistor in Saturation

n+n+

S

G

VGS

D

VDS > VGS - VT

VGS - VT+-

Pinch-off


Current-Voltage RelationsCurrent-Voltage RelationsLong-Channel DeviceLong-Channel Device


A model for manual analysisA model for manual analysis


Current-Voltage RelationsCurrent-Voltage RelationsThe Deep-Submicron EraThe Deep-Submicron Era

LinearRelationship

-4

VDS (V)0 0.5 1 1.5 2 2.5

0

0.5

1

1.5

2

2.5x 10

I D (

A)

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

Early Saturation


Velocity SaturationVelocity Saturation

(V/µm)c = 1.5

n

(m/s

)

sat = 105

Constant mobility (slope = µ)

Constant velocity


PerspectivePerspective

IDLong-channel device

Short-channel device

VDSVDSAT VGS - VT

VGS = VDD


IIDD versus V versus VGSGS

0 0.5 1 1.5 2 2.50

1

2

3

4

5

6x 10

-4

VGS (V)

I D (

A)

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5x 10

-4

VGS (V)

I D (

A)

quadratic

quadratic

linear

Long Channel Short Channel


IIDD versus V versus VDSDS

-4

VDS (V)0 0.5 1 1.5 2 2.5

0

0.5

1

1.5

2

2.5x 10

I D (

A)

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

0 0.5 1 1.5 2 2.50

1

2

3

4

5

6x 10

-4

VDS (V)

I D (

A)

VGS= 2.5 V

VGS= 2.0 V

VGS= 1.5 V

VGS= 1.0 V

ResistiveSaturation

VDS = VGS - VT

Long Channel Short Channel


A unified modelA unified modelfor manual analysisfor manual analysis

S D

G

B

NB For PMOS, use Vmax=max(…) instead of Vmin


Simple Model versus SPICE Simple Model versus SPICE

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5x 10

-4

VDS

(V)

I D (

A)

VelocitySaturated

Linear

Saturated

VDSAT=VGT

VDS=VDSAT

VDS=VGT


A PMOS TransistorA PMOS Transistor

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

-0.8

-0.6

-0.4

-0.2

0x 10

-4

VDS (V)

I D (

A)

Assume all variablesnegative!

VGS = -1.0V

VGS = -1.5V

VGS = -2.0V

VGS = -2.5V


Transistor Model Transistor Model for Manual Analysisfor Manual Analysis


The Transistor as a SwitchThe Transistor as a Switch

VGS VT

RonS D

ID

VDS

VGS = VD D

VDD/2 VDD

R0

Rmid

ID

VDS

VGS = VD D

VDD/2 VDD

R0

Rmid



0.5 1 1.5 2 2.50

1

2

3

4

5

6

7x 10

5

VDD

(V)

Req

(O

hm)


Unified Model ExamplesUnified Model Examples


MOS CapacitancesMOS CapacitancesDynamic BehaviorDynamic Behavior


Dynamic Behavior of MOS TransistorDynamic Behavior of MOS Transistor

DS

G

B

CGDCGS

CSB CDBCGB


The Gate CapacitanceThe Gate Capacitance

tox

n+ n+

Cross section

L

Gate oxide

xd xd

L d

Polysilicon gate

Top view

Gate-bulkoverlap

Source

n+

Drain

n+W


Gate CapacitanceGate Capacitance

S D

G

CGC

S D

G

CGC

S D

G

CGC

Cut-off Resistive Saturation

Most important regions in digital design: saturation and cut-off


Gate CapacitanceGate Capacitance

WLCox

WLCox

2

2WLCox

3

CGC

CGCS

VDS /(VGS-VT)

CGCD

0 1

CGC

CGCS = CGCDCGC B

WLCox

WLCox

2

VGS

Capacitance as a function of VGS(with VDS = 0)

Capacitance as a function of the degree of saturation


Measuring the Gate CapMeasuring the Gate Cap

2 1.52 12 0.5 0

3

4

5

6

7

8

9

103 102 16

2

VGS (V)

VGS

Gate

Ca

paci

tan

ce (

F)

0.5 1 1.5 22 2

I


Diffusion CapacitanceDiffusion Capacitance

Bottom

Side wall

Side wallChannel

SourceND

Channel-stop implant NA1

SubstrateNA

W

xj

LS


Junction CapacitanceJunction Capacitance


Linearizing the Junction CapacitanceLinearizing the Junction Capacitance

Replace non-linear capacitance bylarge-signal equivalent linear capacitance

which displaces equal charge over voltage swing of interest


Capacitances in 0.25 Capacitances in 0.25 m CMOS m CMOS processprocess


Sub-Threshold ConductionSub-Threshold Conduction

0 0.5 1 1.5 2 2.510

-12

10-10

10-8

10-6

10-4

10-2

VGS (V)

I D (

A)

VT

Linear

Exponential

Quadratic

Typical values for S:60 .. 100 mV/decade

The Slope Factor

ox

DnkT

qV

D C

CneII

GS

1 ,~ 0

S is VGS for ID2/ID1 =10


Sub-Threshold Sub-Threshold IIDD vs vs VVGSGS

VDS from 0 to 0.5V

kT

qV

nkT

qV

D

DSGS

eeII 10


Sub-Threshold Sub-Threshold IIDD vs vs VVDSDS

DSkT

qV

nkT

qV

D VeeIIDSGS

110

VGS from 0 to 0.3V


Summary of MOSFET Operating Summary of MOSFET Operating RegionsRegions

Strong Inversion VGS > VT

Linear (Resistive) VDS < VDSAT

Saturated (Constant Current) VDS VDSAT

Weak Inversion (Sub-Threshold) VGS VT

Exponential in VGS with linear VDS dependence


Parasitic ResistancesParasitic Resistances

W

LD

Drain

Draincontact

Polysilicon gate

DS

G

RS RD

VGS,eff

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