vijay k. arora - new jersey institute of technologyieeenj/archived_slides/2005-09-21... · 2005. 9....
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Vijay K. AroraVijay K. AroraWilkes UniversityWilkes University
EE--mail: varora@mail: [email protected]
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