Vijay K. AroraVijay K. AroraWilkes UniversityWilkes University

EE--mail: varora@mail: varora@wilkeswilkes..eduedu

Emerging TechnologiesEmerging Technologies

Our Motivation and EconomicsOur Motivation and EconomicsAdam 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 ParadigmCentury Paradigm

ØØ Formulate a hypothesis or theoryFormulate a hypothesis or theory

ØØ Accumulate dataAccumulate data

ØØ Do extensive experimentation and CheckDo extensive experimentation and Check

ØØ Publish if newsworthyPublish if newsworthy

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

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

2121stst Century ParadigmCentury ParadigmØØ Formulate a hypothesis or theory or designFormulate a hypothesis or theory or design

ØØ Make a prototype structureMake a prototype structure

ØØ Patent itPatent it

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

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

ØØ 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 sales Gross world product and sales volumesvolumes

Exponential GrowthExponential GrowthSIA roadmapSIA roadmap

Historical TrendsHistorical Trends

Ø New Technology generation every three years

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

Ø 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

ØØ A comprehensive transport theory for A comprehensive transport theory for quantum processes at quantum processes at nanosaclenanosacle

ØØ HighHigh--field distribution in quantum wellsfield distribution in quantum wells

ØØ Optimization of the shape and size of Optimization of the shape and size of quantum wells for high frequenciesquantum wells for high frequencies

ØØ Quantum Computing: MultiQuantum Computing: Multi--state logic by state logic by using quantum statesusing quantum states

ØØ Failure of Ohm’s Law: ReFailure of Ohm’s Law: Re--assessment of the assessment of the circuit theory principlescircuit theory principles

Goals for High Speed PerformanceGoals for High Speed Performance

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

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

RC and Transit Time DelaysRC and Transit Time Delays

Source: CadenceSource: Cadence

Interconnect ProblemsInterconnect ProblemsRC Time DelaysRC Time Delays

ØØ RC time delay is increasing rapidlyRC time delay is increasing rapidlyØWire resistance is risingØWires have larger cross-section …

introduce couplingØ Electromigration imposes current limitsØ System performance, area and reliability

are determined by interconnectquality, not devices!!!

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

1 µ

0.5 µ

0.25 µ

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

CoCfCf

Cf

R3

layer n R4

Cint = Cf + Cs + Co + Cload

τ = Rint * ( Cint + Cc/(Cint+ Cc) )

τ = 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

τ = Rint * Cint

RC Delay ConsiderationsRC Delay Considerations

Physical EffectsPhysical Effects

ØØ Quantum EffectsQuantum Effects nmfewaL D ,λ≤

TkqEorqE BD ≥≥ lhτ

λ

cmkV

mV

LV

E 5015

===µ

ØØHighHigh--Field EffectsField Effects

ØØField Broadening Field Broadening

NanoNano--Scale Scale Quantum EngineeringQuantum Engineering

Tkmh

ph

B

D

*3=

=λ

*)(

2222

)()(

2

)(

he

zyxovc

vck m

kkkEE

++±=h

Bulk SemiconductorsBulk Semiconductors

All 3 cartesian directions analog-type

DzyxL λ>>,,

Density of States:

( )212

3

2

*24

1)( co

ec EE

hm

dEdN

VEg −

== π

QuasiQuasi--TwoTwo--Dimensional QWDimensional QW

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

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

*2

)( 2222

=

++

+=

n

nm

kkEE oz

e

yxconk ε

h

εoz =

π2 h2

2 me* Lz

2

DyxDz LL λλ >>≤ ,

−==

oz

coec

EEInt

mdEdN

AEg

επ 2

*

21

)(h

Density of States:

AlGaAsAlGaAs//GaAsGaAs//AlGaAs AlGaAs Prototype Quantum WellPrototype Quantum Well

.

Pot

entia

l

GaAs

AlGaAsGround State

x

yx

y

z

QuasiQuasi--OneOne--Dimensional QWDimensional QW

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

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

222

*

22

=

+++=

nm

nmmk

EE ozoyx

conk

e

εεh

2,

*

22

),( 2 zyezyo Lm

hπε =

DxDzy LL λλ >>≤,

Density of States:( ) ( ) 2

122

2/1*

1 )(21

)(−

++−== ozoycoe

xc nmEE

mdEdN

LEg εε

πh

QuasiQuasi--ZeroZero--DimensionalDimensionalQuantum WellQuantum Well

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

222

=

+++=

l

l

nm

nmEE ozoyoxcnk εεε

2,,

*

22

),,( 2 zyxezyxo Lm

hπε =

DzyxL λ≤,,

All 3 cartesian directions digital-typeQuantum box (dot)

AlGaAs

GaAs inside

Quantumwire

Quantum box

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

AlGaAs GaAs AlGaAs

5 nm

1.43 eV 1.85 eV

doped AlGaAsgate

Quantum Wire

AlGaAsGaAs

AlGaAs

L

L

y

z

Quantum Well ArraysQuantum Well Arrays

Density of StatesDensity of States

N ( E ) =1

Lx Ly Lz

δ E − Eα( )α s∑

0.0

0.2

0.4

0.6

0.8

1.0

1.2

DE

NSI

TY

OF

ST

AT

ES

( 10

26 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 = 1 +1P

a

P =

2m * ∆Eh 2

12 a

2

Zn z( )=2Lz

sinnπzLz

Triangular Quantum WellTriangular Quantum Well

( )

−

−= n

oonn z

zAi

zAizZ ξ

ξ 2/1'1

)(

Ln =2an

2 zo

an =0.53556Ai' −ξ n( )

Z n z( ) =2Ln

sinnπ zLn

Approximate:

Exact:

Quantum-Confined Mobility Degradation

ØØ Changes in the Density of StatesChanges in the Density of States

DzD

z

isotropicbulk

QW LL

λλπ

µ

µ≤=

ØØ Changes in the relative strength of Changes in the relative strength of each scattering interactioneach scattering interaction

Mobility Degradation Versus Mobility Degradation Versus Quantum ConfinementQuantum Confinement

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.1 1

T = 4 KT = 77 KT = 300 Kµ 2D

/ µb

1 / Lz (nm -1)

GateGate--Field ConfinementField ConfinementMobility Degradation in a TQWMobility Degradation in a TQW

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 / µm)

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

e

e

e

eh

h

h

hElectronsHoles

Ions

h

0=thvr

smm

Tkv B

th /10*

3 5≈=

Quantum EmissionQuantum EmissionQl Ql

eh

h

Electrons

Holes

Atoms

eh

ol

Ql

oωh

e

oQq ωhl =EEq

oQ

ωhl =

Es

Randomness to StreamliningRandomness to Streamlining

Velocity Vectors in Equilibrium Randomness:

Velocity Vectors in a Very High Field Streamlined:

0== thd vvrr

d th th ˆv v v ε= = −r r

Ultimate VelocityUltimate Velocity--BulkBulk

( ) ∫∞

−++Γ=

0 1)1(1

ηη x

j

j ex

jF

( )( )ηη

π 2/13

2FF1

thDvv =

TkE

B

c−=

ςη

Fermi Integral

Normalized Fermi Energy

*2m

Tkv B

th =

Saturation Velocity LimitsSaturation Velocity Limits

Bsat th *

8k T2v v

mππ= =

13

sat *

3 h 3nv

4 m 8π =

Non-degeneratelimit

Degeneratelimit

Velocity versus TemperatureVelocity versus Temperature--NondegenerateNondegenerate

Velocity versus TemperatureVelocity versus Temperature--DegenerateDegenerate

Saturation VelocitySaturation Velocity--Q2DQ2D

( )( )ηηπ

0

2/12 2 F

FthD

vv =

TkE

B

c−=

ςη

( ) ( )ηη e+= 1ln0F

ozcoc EE ε+=

Saturation VelocitySaturation Velocity--Q1DQ1D

( )( )ηη

π 2/1

01

1

−

=FF

thDvv

TkE

B

c−=

ςη ozoycoc EE εε ++=

Modeling TransportModeling Transport

c

thvv-

mq

dtdv

τ−

−=*E

Transient Response:

−−=

−c

t

c emq

v ττ1

*E

=0

EE oc

d mq

v µτ

−=−=*

:ctStateSteady τ>>

Quantum EmissionQuantum Emission

Effective Collision time:

−=

−c

Q

eceffτ

τ

ττ 1

Effective collision length:

−=

−o

o

Q

e l

l

ll 1

th

oQ vqE

ωτ

h=oQq ωhl =E

Eqo

Qωh

l =

11--D Random Walk in a D Random Walk in a BandgapBandgapsemiconductorsemiconductor

Modeling the DistributionModeling the Distribution

11

1

1 = ),(

+=

+±⋅+− δζεα

αε x

Tkq e

e

fB

lrr

rE

E

δ = δ o 1 − e−

δ Q

δ o

cocoB

oo V

VTk

q===

EEEl

δTkB

oQ

ω=δ

h

Tkx

B

ςεα −=

LeftLeft--Right AsymmetryRight AsymmetryItinerant Electron PopulationItinerant Electron Population

( ))(cosh 2)( δ

δ

δδ

δ ±

−+

±± =

+=

eee

exnxn

Streamlining the RandomnessStreamlining the Randomness

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5

n +/n

δ

n- /n

DriftDrift--DiffusionDiffusion

( )

dxdn

vq

vqxnxJ

th

th

tanh )( )(

l+

= δ

( )δtanhthd vv =

otnothn VvD

δδ

µ == l

**

n

cn

thn

ono m

qmq τ

µ ==Vl

Drift Velocity

Diffusion

Drift

Diffusion Coefficient

qTk

V Bt =

SingleSingle--Valley Valley vv--EE CharacteristicsCharacteristics

VelocityVelocity--Field Field CharacterisitcsCharacterisitcs

0

4.0 10 4

8.0 10 4

1.2 10 5

1.6 10 5

2.0 10 5

0 2 4 6 8 10

Normalized Electric Field, δ

Dri

ft V

eloc

ity, v

d (in

m/s

ec)

3D

2D

1D

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

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 4 8 δ 12 16 20

N=.01

N=.1

Nor

mal

ized

Dri

ft V

eloc

ity (v

d /(π1/

2 v

th/2

))

N=1

Non-Degen

Tkm

h

B

D *2=λ

2DsnN λ=

Mobility DegradationMobility Degradation

Diffusion Coefficient Diffusion Coefficient DegradationDegradation

I-V Characteristics Microresistors

Resistance BlowResistance Blow--UpUp

tc c

0

2.6 kV for L 1 cmVV E L L

0.26 V for L 1 mµ=

= = ≈ =l

Power LawPower Law

csat

o c c

VV V VP VI tanh VI tanh

R V V

= = =

2

o

c

VP

R

V V (Ohmic )

=

<

c

o

c

VVP

R

V V

=

>>

Voltage DividerVoltage Divider

d

R1

R2

1

1

L = 5 ì m

W = 1 0 0 ì m

2

2

L = 1 0 ì m

W = 2 0 0 ì m

V

0 2 4 6 8 100

1

2

3

4

5

6

7

8

9

10

V1 O

R V

2

V

OhmicV

1(Nonohmic)

V2(Nonohmic)

Current DividerCurrent Divider

R1 R2

1

1

L = 5 ì m

W = 1 0 0 ì m

2

2

L = 1 0 ì m

W = 2 0 0 ì m

V

I

I1 I2

0 2 4 6 8 100

100

200

300

400

500

600

CU

RR

EN

T (

mA

)

POTENTIAL (V)

I=I1+I

2 Nonohmic

I=I1+I

2 Ohmic

I1 Nonohmic

I2 Nonohmic

MultiMulti--Valley Transport in Valley Transport in GaAsGaAsIntervalley Intervalley Electron TransferElectron Transfer

MultiMulti--Valley Transport in Valley Transport in GaAsGaAsVelocityVelocity--Field CharacteristicsField Characteristics

HighHigh--Frequency TransportFrequency Transport

j tdc oE E e ωε= +

( )E dc

o o

Eσ µσ µ

= dc Conductivity Degradation

Ehf 2 2

eff

( E , )1

σσ ω

ω τ=

+ ac Conductivity Degradation

ConclusionsConclusionsQuantum ConfinementQuantum Confinement

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

ØØ Relative strength of each scattering Relative strength of each scattering different from bulkdifferent from bulk

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

ConclusionsConclusionsHighHigh--Field Driven TransportField Driven TransportØØ Electric field puts an order into otherwise Electric field puts an order into otherwise

completely random motioncompletely random motion

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

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

ØØ Saturation velocity is lowered by the quantum Saturation velocity is lowered by the quantum remission processremission process

ØØ RC time constants will dominate over transit time RC time constants will dominate over transit time delay because of enhanced resistancedelay because of enhanced resistance

ConclusionsConclusionsFailure of Ohm’s LawFailure of Ohm’s Law

ØØ Effective resistance may rise Effective resistance may rise dramatically as current approaches dramatically as current approaches saturation levelsaturation level

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

Golden RuleGolden Rule

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

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

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

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

ØØ No matter how little it heats up, make it coolerNo matter how little it heats up, make it cooler