vijay k. arora wilkes university e-mail: varora@wilkes
Post on 20-Jan-2016
37 Views
Preview:
DESCRIPTION
TRANSCRIPT
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
top related