Introduction to CMOS VLSI Design Lecture 19: Nonideal Transistors David Harris Harvey Mudd College Spring 2007

Introduction toCMOS VLSI

Design

Lecture 19: Nonideal Transistors

David Harris

Harvey Mudd College

Spring 2007

19: Nonideal Transistors Slide 2CMOS VLSI Design

Outline Transistor I-V Review Nonideal Transistor Behavior

– Velocity Saturation– Channel Length Modulation– Body Effect– Leakage– Temperature Sensitivity

Process and Environmental Variations– Process Corners


Ideal Transistor I-V Shockley 1st order transistor models

2

cutoff

linear

saturatio

0

2

2n

gs t

dsds gs t ds ds dsat

gs t ds dsat

V V

VI V V V V V

V V V V


Ideal vs. Simulated nMOS I-V Plot

180 nm TSMC process

Ideal Models– = 155(W/L) A/V2

– Vt = 0.4 V

– VDD = 1.8 VIds (A)

Vds0 0.3 0.6 0.9 1.2 1.5 1.8

100

200

300

400

Vgs = 0.6

Vgs = 0.9

Vgs = 1.2

Vgs = 1.5

Vgs = 1.8

0

Vds

0 0.3 0.6 0.9 1.2 1.5

Vgs = 1.8

Ids (A)

0

50

100

150

200

250

Vgs = 1.5

Vgs = 1.2

Vgs = 0.9

Vgs = 0.6

BSIM 3v3 SPICE models


Simulated nMOS I-V Plot 180 nm TSMC process BSIM 3v3 SPICE models What differs?

– Less ON current– No square law– Current increases

in saturation

Vds

0 0.3 0.6 0.9 1.2 1.5

Vgs = 1.8

Ids (A)

0

50

100

150

200

250

Vgs = 1.5

Vgs = 1.2

Vgs = 0.9

Vgs = 0.6


Velocity Saturation We assumed carrier velocity is proportional to E-field

– v = Elat = Vds/L

At high fields, this ceases to be true– Carriers scatter off atoms

– Velocity reaches vsat

• Electrons: 6-10 x 106 cm/s• Holes: 4-8 x 106 cm/s

– Better modelEsat0

0

slope =

Elat

2Esat3Esat

sat

sat / 2

latsat sat

lat

sat

μμ

1

Ev v E

EE


Vel Sat I-V Effects Ideal transistor ON current increases with VDD

2

Velocity-saturated ON current increases with VDD

Real transistors are partially velocity saturated– Approximate with -power law model

– Ids VDD

– 1 < < 2 determined empirically

2

2

ox 2 2gs t

ds gs t

V VWI C V V

L

ox maxds gs tI C W V V v


-Power Model

Ids (A)

Vds0 0.3 0.6 0.9 1.2 1.5 1.8

100

200

300

400

Vgs = 0.6

Vgs = 0.9

Vgs = 1.2

Vgs = 1.5

Vgs = 1.8

0

-lawSimulated

Shockley

0 cutoff

linear

saturation

gs t

dsds dsat ds dsat

dsat

dsat ds dsat

V V

VI I V V

V

I V V

/ 2

2dsat c gs t

dsat v gs t

I P V V

V P V V


Channel Length Modulation Reverse-biased p-n junctions form a depletion region

– Region between n and p with no carriers

– Width of depletion Ld region grows with reverse bias

– Leff = L – Ld

Shorter Leff gives more current

– Ids increases with Vds

– Even in saturation

n+

p

GateSource Drain

bulk Si

n+

VDDGND VDD

GND

LLeff

Depletion RegionWidth: Ld


Chan Length Mod I-V

= channel length modulation coefficient– not feature size– Empirically fit to I-V characteristics

21

2ds gs t dsI V V V

Ids (A)

Vds0 0.3 0.6 0.9 1.2 1.5 1.8

100

200

300

400

Vgs = 0.6Vgs = 0.9

Vgs = 1.2

Vgs = 1.5

Vgs = 1.8

0


Body Effect Vt: gate voltage necessary to invert channel

Increases if source voltage increases because source is connected to the channel

Increase in Vt with Vs is called the body effect


Body Effect Model

s = surface potential at threshold

– Depends on doping level NA

– And intrinsic carrier concentration ni

= body effect coefficient

0t t s sb sV V V

2 ln As T

i

Nv

n

sioxsi

ox ox

2q2q A

A

NtN

C


OFF Transistor Behavior What about current in cutoff? Simulated results What differs?

– Current doesn’t go

to 0 in cutoff

Vt

Sub-threshold

Slope

Sub-thresholdRegion

SaturationRegion

Vds = 1.8

Ids

Vgs

0 0.3 0.6 0.9 1.2 1.5 1.8

10 pA

100 pA

1 nA

10 nA

100 nA

1 A

10 A

100 A

1 mA


Leakage Sources Subthreshold conduction

– Transistors can’t abruptly turn ON or OFF Junction leakage

– Reverse-biased PN junction diode current Gate leakage

– Tunneling through ultrathin gate dielectric

Subthreshold leakage is the biggest source in modern transistors


Subthreshold Leakage Subthreshold leakage exponential with Vgs

n is process dependent, typically 1.4-1.5

0e 1 egs t ds

T T

V V V

nv vds dsI I

2 1.80 eds TI v


DIBL Drain-Induced Barrier Lowering

– Drain voltage also affect Vt

– High drain voltage causes subthreshold leakage to ________.

ttdsVVVt t dsV V V


DIBL Drain-Induced Barrier Lowering

– Drain voltage also affect Vt

– High drain voltage causes subthreshold leakage to increase.

ttdsVVVt t dsV V V


Junction Leakage Reverse-biased p-n junctions have some leakage

Is depends on doping levels

– And area and perimeter of diffusion regions– Typically < 1 fA/m2

e 1D

T

V

vD SI I

n well

n+n+ n+p+p+p+

p substrate


Gate Leakage Carriers may tunnel thorough very thin gate oxides Predicted tunneling current (from [Song01])

Negligible for older processes May soon be critically important

VDD

0 0.3 0.6 0.9 1.2 1.5 1.8J G

(A

/cm2

)

10-9

10-6

10-3

100

103

106

109

tox

0.6 nm0.8 nm

1.0 nm1.2 nm

1.5 nm

1.9 nm

VDD trend


Temperature Sensitivity Increasing temperature

– Reduces mobility

– Reduces Vt

ION ___________ with temperature

IOFF ___________ with temperature


Temperature Sensitivity Increasing temperature

– Reduces mobility

– Reduces Vt

ION decreases with temperature

IOFF increases with temperature

Vgs

dsI

increasingtemperature


So What? So what if transistors are not ideal?

– They still behave like switches. But these effects matter for…

– Supply voltage choice– Logical effort– Quiescent power consumption– Pass transistors– Temperature of operation


Parameter Variation Transistors have uncertainty in parameters

– Process: Leff, Vt, tox of nMOS and pMOS

– Vary around typical (T) values Fast (F)

– Leff: ______

– Vt: ______

– tox: ______

Slow (S): opposite Not all parameters are independent

for nMOS and pMOS

nMOS

pM

OS

fastslow

slow

fast

TT

FF

SS

FS

SF


Parameter Variation Transistors have uncertainty in parameters

– Process: Leff, Vt, tox of nMOS and pMOS

– Vary around typical (T) values Fast (F)

– Leff: short

– Vt: low

– tox: thin

Slow (S): opposite Not all parameters are independent

for nMOS and pMOS

nMOS

pM

OS

fastslow

slow

fast

TT

FF

SS

FS

SF


Environmental Variation VDD and T also vary in time and space

Fast:

– VDD: ____

– T: ____

Corner Voltage Temperature

F

T 1.8 70 C

S


Environmental Variation VDD and T also vary in time and space

Fast:

– VDD: high

– T: low

Corner Voltage Temperature

F 1.98 0 C

T 1.8 70 C

S 1.62 125 C


Process Corners Process corners describe worst case variations

– If a design works in all corners, it will probably work for any variation.

Describe corner with four letters (T, F, S)– nMOS speed– pMOS speed– Voltage– Temperature


Important Corners Some critical simulation corners include

Purpose nMOS pMOS VDD Temp

Cycle time

Power

Subthrehold

leakage

Pseudo-nMOS


Important Corners Some critical simulation corners include

Purpose nMOS pMOS VDD Temp

Cycle time S S S S

Power F F F F

Subthrehold

leakage

F F F S

Pseudo-nMOS S F ? ?

Documents

Introduction to CMOS VLSI Design Lecture 19: Nonideal Transistors David Harris Harvey Mudd College Spring 2007