VLSI Design

Lecture 3a: Nonideal Transistors

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 nMOS I-V Plot

180 nm TSMC process

Ideal Models = 155(W/L) A/V2

Vt = 0.4 V

VDD = 1.8 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

Simulated nMOS I-V Plot

180 nm TSMC process BSIM 3v3 SPICE models What differs?

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

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 model

Esat00

slope =

Elat

2Esat3E

sat

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)

Vds

0 0.3 0.6 0.9 1.2 1.5 1.8

100

200

300

400

Vgs

= 0.6V

gs = 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

LL

eff

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 pA100 pA

1 nA

10 nA

100 nA1 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

SSFS

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

SSFS

SF

Environmental Variation

VDD and T also vary in time and space Fast:

VDD: ____ T: ____

70 C1.8T

S

F

TemperatureVoltageCorner

Environmental Variation

VDD and T also vary in time and space Fast:

VDD: high T: low

70 C1.8T

125 C1.62S

0 C1.98F

TemperatureVoltageCorner

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

Pseudo-nMOS

Subthrehold

leakage

Power

Cycle time

TempVDDpMOSnMOSPurpose

Important Corners

Some critical simulation corners include

??FSPseudo-nMOS

SFFFSubthrehold

leakage

FFFFPower

SSSSCycle time

TempVDDpMOSnMOSPurpose