Vijay K. AroraVijay K. AroraWilkes UniversityWilkes University

E-mail: varora@wilkes.eduE-mail: varora@wilkes.edu

Emerging TechnologiesEmerging Technologies

Our Motivation and Our Motivation and EconomicsEconomics

Adam Smith, “An Enquiry into Nature and Causes of the Wealth of Nations” (1776)The wealth is created by laisse-faire economy and free trade

John Maynard Keynes, “The General Theory of Employment, Interest, and Money” (1936)The wealth is created by careful government planning and government stimulation of economy

1990’s and BeyondThe wealth is created by innovations and inventions

2020thth Century Paradigm Century Paradigm Formulate a hypothesis or theoryFormulate a hypothesis or theory

Accumulate dataAccumulate data

Do extensive experimentation and CheckDo extensive experimentation and Check

Publish if newsworthyPublish if newsworthy

Respect others’ work helping them to grow in the Respect others’ work helping them to grow in the professionprofession

Demonstrate character ethics that puts community Demonstrate character ethics that puts community interests above personal aggrandizementinterests above personal aggrandizement

2121stst Century Paradigm Century Paradigm Formulate a hypothesis or theory or designFormulate a hypothesis or theory or design

Make a prototype structureMake a prototype structure

Patent itPatent it

Raise 17 million dollars and start an IPORaise 17 million dollars and start an IPO

Sue your competitor for stealing your ideaSue your competitor for stealing your idea

Demonstrate personality ethics that lubricates the Demonstrate personality ethics that lubricates the process of human interaction for personal process of human interaction for personal aggrandizementaggrandizement

Gross world product and Gross world product and sales volumessales volumes

Exponential GrowthExponential GrowthSIA roadmapSIA roadmap

Historical TrendsHistorical Trends

New Technology generation every three years

For each generation, memory density increase by 4 times and logic density increases by 2.5 times

Rule of Two: In every two generations (6 years), the feature size decreased by 2, transistor current density, circuit speed, chip area, chip current and maximum I/O pins increased by 2

Research ScenarioResearch Scenario A comprehensive transport theory for A comprehensive transport theory for

quantum processes at nanosaclequantum processes at nanosacle High-field distribution in quantum High-field distribution in quantum

wellswells Optimization of the shape and size of Optimization of the shape and size of

quantum wells for high frequenciesquantum wells for high frequencies Quantum Computing: Multi-state logic Quantum Computing: Multi-state logic

by using quantum statesby using quantum states Failure of Ohm’s Law: Re-assessment Failure of Ohm’s Law: Re-assessment

of the circuit theory principlesof the circuit theory principles

Goals for High Speed Goals for High Speed PerformancePerformance

Large transistor currentLarge transistor current• Time constantsTime constants• InterconnectsInterconnects• Cross talkCross talk

Reduced transit timeReduced transit time• Increased MobilityIncreased Mobility• High Saturation VelocityHigh Saturation Velocity• Reduced SizeReduced Size

RC and Transit Time RC and Transit Time DelaysDelays

Source: CadenceSource: Cadence

Interconnect ProblemsInterconnect ProblemsRC Time DelaysRC Time Delays

RC time delay is increasing rapidlyRC time delay is increasing rapidly Wire resistance is rising Wires have larger cross-section …

introduce coupling Electromigration imposes current limits System performance, area and reliability

are determined by interconnect quality, not devices!!!

Increased cross-section improves performance but also increases noise and capacitive and inductive coupling

1

0.5

0.25

Increasin

g P

erform

ance

Decreasin

g C

ou

plin

g E

ffect

Interconnect PerformanceInterconnect Performance

substrate

layer m

Cs CsCf CfCfCf

CcR1 R2

Cf

layer m

CoCf

CfCf

R3

layer n R4

Cint = Cf + Cs + Co + Cload

= Rint * ( Cint + Cc/(Cint+ Cc) )

= Rint * (Cint2 + Cint.Cc +Cc)/(Cint + Cc)

• Cc depends on dimensional shrink due to increased in cross-section• In VLSI, make Cc becomes insignificant as possible, then = Rint * Cint

RC Delay ConsiderationsRC Delay Considerations

Physical EffectsPhysical Effects

Quantum EffectsQuantum Effects nmfewaL D ,

TkqEorqE BD

cm

kV

m

V

L

VE 50

1

5

High-Field EffectsHigh-Field Effects

Field Broadening Field Broadening

Nano-Scale Nano-Scale Quantum EngineeringQuantum Engineering

Tkm

h

p

h

B

D

*3

Bulk SemiconductorsBulk Semiconductors

All 3 cartesian directions analog-type

DzyxL ,,

Density of States:

212

3

2

*24

1)( co

ec EE

h

m

dE

dN

VEg

Quasi-Two-Dimensional Quasi-Two-Dimensional QWQW

z-direction digital-typex,y-directions analog-type

,......3,2,1

*2

)( 2222

n

nm

kkEE oz

e

yxconk

oz

2 2

2 me* Lz

2

DyxDz LL ,

oz

coec

EEInt

m

dE

dN

AEg

2

*

2

1)(

Density of States:

AlGaAs/GaAs/AlGaAs AlGaAs/GaAs/AlGaAs Prototype Quantum WellPrototype Quantum Well

.

Pote

ntia

l

GaAs

AlGaAs

Ground State

x

y

x

y

z

Quasi-One-Dimensional Quasi-One-Dimensional QWQW

y, z-direction digital-typex-directions analog-type (QWW)

,......3,2,1,

222

*

22

nm

nmm

kEE ozoy

xconk

e

2,

*

22

),( 2 zyezyo Lm

DxDzy LL ,

Density of States:

2

122

2/1*

1 )(21

)(

ozoycoe

xc nmEE

m

dE

dN

LEg

Quasi-Zero-DimensionalQuasi-Zero-DimensionalQuantum WellQuantum Well

,......3,2,1,,

222

nm

nmEE ozoyoxcnk

2,,

*

22

),,( 2 zyxezyxo Lm

DzyxL ,,

All 3 cartesian directions digital-typeQuantum box (dot)

AlGaAs

GaAs inside

Quantumwire

Quantum box

Quantum Well WireQuantum Well WireQuantum Box (Dot)Quantum Box (Dot)

Quantum Well ArraysQuantum Well Arrays

Density of StatesDensity of States

N ( E) 1

Lx Ly Lz

E E s

0.0

0.2

0.4

0.6

0.8

1.0

1.2

DE

NS

ITY

OF

ST

AT

ES

( 1

026 e

V-1

m-3

)

0.0 0.2 0.4 0.6 0.8 1.0E - E c (eV)

3D2D1D

Quantum Well with Finite Quantum Well with Finite BoundariesBoundaries

Lz 11

P

a

P

2m * E

2

1

2 a

2

Z n z 2

Lz

sinnz

Lz

Triangular Quantum WellTriangular Quantum Well

n

oonn z

zAi

zAizZ

2/1'

1)(

Ln 2

an2

zo

an 0.53556

Ai' n

Zn z 2

Ln

sinnz

Ln

Approximate:

Exact:

Quantum-Confined Mobility Degradation

Changes in the Density of StatesChanges in the Density of States

DzD

z

isotropicbulk

QW LL

Changes in the relative strength Changes in the relative strength of each scattering interactionof each scattering interaction

Mobility Degradation Mobility Degradation Versus Quantum Versus Quantum

ConfinementConfinement

Gate-Field ConfinementGate-Field ConfinementMobility Degradation in a Mobility Degradation in a

TQWTQW

0.045

0.05

0.055

0.06

0.065

0.07

0.075

0.08

10 15 20 25 30 35 40 45 50

TheoryExperiment

MO

BIL

ITY

(m

2 /

V.s

)

ELECTRIC FIELD (V / m)

Electron and Hole Mobility in Electron and Hole Mobility in Submicron CMOSSubmicron CMOS

Courtesy: Y. Taur and E. Novak, IBM Microelectronics, IEDM97 Invited Talk.

Random Thermal MotionRandom Thermal Motion

0thv

smm

Tkv B

th /10*

3 5

Quantum EmissionQuantum Emission

oQq EEq

oQ

EF

Randomness to Randomness to StreamliningStreamlining

Velocity Vectors in Equilibrium Randomness:

Velocity Vectors in a Very High Field Streamlined:

0 thd vv

2 ththd vvv

Saturation Velocity-BulkSaturation Velocity-Bulk

0 1)1(

1

x

j

j e

x

jF

2/13

2

FF1

thDvv

Tk

E

B

c

Fermi Integral

Normalized Fermi Energy

*

2

m

Tkv B

th

Saturation Velocity LimitsSaturation Velocity Limits

Bsat th *

8k T2v v

m

1

3

sat *

3 h 3nv

4 m 8

Non-degeneratelimit

Degeneratelimit

Saturation Velocity-Q2DSaturation Velocity-Q2D

0

2/12 2 F

FthD

vv

Tk

E

B

c

e 1ln0F

ozcoc EE

Saturation Velocity-Q1DSaturation Velocity-Q1D

2/1

01

1

FF

thDvv

Tk

E

B

c ozoycoc EE

Modeling TransportModeling Transport

c

thvv-

m

q

dt

dv

*

E

Transient Response:

c

t

c em

qv

1*

E

=0

EE oc

d m

qv

*

:ctStateSteady

Quantum EmissionQuantum Emission

Effective Collision time:

c

Q

eceff

1

Effective collision length:

o

o

Q

e

1

th

oQ vqE

oQq E

Eqo

Q

1-D Random Walk in a 1-D Random Walk in a Bandgap semiconductorBandgap semiconductor

Modeling the DistributionModeling the Distribution

1

1

1

1 = ),(

x

Tk

q ee

f

B

E

E

o 1 eQ

o

cocoB

oo V

V

Tk

q

EEE

TkB

oQ

Tkx

B

Left-Right AsymmetryLeft-Right AsymmetryItinerant Electron Itinerant Electron

PopulationPopulation

)(cosh 2)(

e

ee

e

xn

xn

Streamlining the Streamlining the RandomnessRandomness

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5

n+/n

n- /n

Drift-DiffusionDrift-Diffusion

dx

dnvq

vqxnxJ

th

th

tanh )( )(

tanhthd vv

otnothn VvD

**

n

cn

thn

ono m

q

m

q V

Drift Velocity

Diffusion

Drift

Diffusion Coefficient

q

TkV B

t

Single-Valley Single-Valley v-Ev-E CharacteristicsCharacteristics

Velocity-Field Velocity-Field CharacterisitcsCharacterisitcs

Effect of Degeneracy (2-D) Effect of Degeneracy (2-D)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 4 8 12 16 20

N=.01

N=.1

Nor

mal

ized

Dri

ft V

eloc

ity (

v d /(1/

2 vth

/2 )

)

N=1

Non-Degen

Tkm

h

B

D *2

2

DsnN

Mobility DegradationMobility Degradation

Diffusion Coefficient Diffusion Coefficient DegradationDegradation

I-V Characteristics Microresistors

0.00

0.25

0.50

0.75

1.00

0.0

0

2.5

0

5.0

0

7.5

0

10

.00

V/Vc

Normalized I-V Characteristics

L=100 µm

L=10 µm

L=1 µm

I/Isat

Resistance Blow-UpResistance Blow-Up

0

2

4

6

8

10

0 0.2 0.4 0.6 0.8 1

R/Ro (Experiment)R/Ro(Theory)r/Ro(Experiment)r/Ro(Theory)

R/R

o

I/Isat

Multi-Valley Transport in Multi-Valley Transport in GaAsGaAsIntervalley Electron Intervalley Electron TransferTransfer

Multi-Valley Transport in Multi-Valley Transport in GaAsGaAsVelocity-Field Velocity-Field CharacteristicsCharacteristics

High-Frequency TransportHigh-Frequency Transport

j tdc oE E e

E dc

o o

E

dc Conductivity Degradation

Ehf 2 2

eff

( E, )1

ac Conductivity Degradation

ConclusionsConclusionsQuantum ConfinementQuantum Confinement

Transport properties function of Transport properties function of confinement length in QW’s because confinement length in QW’s because of the change in the Density of Statesof the change in the Density of States

Relative strength of each scattering Relative strength of each scattering changes.changes.

Electrons tend to stay away from the Electrons tend to stay away from the interface as wave function vanishes interface as wave function vanishes near the interfacenear the interface

ConclusionsConclusionsHigh-Field Driven High-Field Driven

TransportTransport Electric field puts an order into otherwise Electric field puts an order into otherwise

completely random motioncompletely random motion

Higher mobility may not necessary lead to Higher mobility may not necessary lead to higher saturation velocity higher saturation velocity

Saturation velocity is limited by Fermi Saturation velocity is limited by Fermi /thermal velocity depending on degeneracy/thermal velocity depending on degeneracy

Saturation velocity is lowered by the Saturation velocity is lowered by the quantum remission processquantum remission process

RC time constants will dominate over RC time constants will dominate over transit time delay because of enhanced transit time delay because of enhanced resistanceresistance

ConclusionsConclusionsFailure of Ohm’s LawFailure of Ohm’s Law

Effective resistance may rise Effective resistance may rise dramatically as current dramatically as current approaches saturation levelapproaches saturation level

Familiar voltage divider and Familiar voltage divider and current divider rule may not be current divider rule may not be valid on submicron scalesvalid on submicron scales

Golden RuleGolden Rule

No matter what the size, make it smallerNo matter what the size, make it smaller

No matter what the speed, make it fasterNo matter what the speed, make it faster

No matter what the function, make it largerNo matter what the function, make it larger

No matter what the cost, make it cheaperNo matter what the cost, make it cheaper

No matter how little it heats up, make it No matter how little it heats up, make it coolercooler