WIN

Collective EffectsCollective Effects

Kang L. WangKang L. WangRaytheon Distinguished Professor of Physical Raytheon Distinguished Professor of Physical

ElectronicsElectronicsDevice research LaboratoryDevice research Laboratory

Center on Functional Engineered NanoArchitectonics -- FENA (www.fena.org)

Western Institute of Nanoelectronics – WIN (www.win-nano.org)

California NanoSystems Institute – CNSI(www.cnsi.ucla.edu)

University of California - Los AngelesE-mail: wang@ee.ucla.edu)

Kang L. WangKang L. WangRaytheon Distinguished Professor of Physical Raytheon Distinguished Professor of Physical

ElectronicsElectronicsDevice research LaboratoryDevice research Laboratory

Center on Functional Engineered NanoArchitectonics -- FENA (www.fena.org)

Western Institute of Nanoelectronics – WIN (www.win-nano.org)

California NanoSystems Institute – CNSI(www.cnsi.ucla.edu)

University of California - Los AngelesE-mail: wang@ee.ucla.edu)

2WIN

Outline Introduction

Interaction in the space and the Order Parameter

Collective effects and state variables

Variability issues of spintronics versus nanoelectronics

Examples:Spin wave busMQCASPIN FETMolecules and atoms

Summary

3WIN

Conventional Electronics employs indept electron entity and Coulomb interaction

The solution:

To switch to interactions other than Coulomb

Charge State Variable (RT)

As the size of the devices goes down, the Coulomb (electrostatic) Capacitance energy arises.

Leading to the increase of the energy per one electron and thus to high variability as quantum fluctuations become important

r

ddV

C 1/r 2 /E e C

u-nm

Order Parameter

4WIN

Whatever the new interaction will be it is going to the some part of the ELECTRODYNAMIC interaction:

dynamic

(relativistic v/c) n

static

(multipole, short-ranged 1/r ,n>2)

Single electron level

Too weak to work with

Corrections for Coulomb Energy

ElectroDynamic Interaction = Coulomb + Corrections

Dynamic: of relativistic origin including spins, magnetic, multi-ferroics

Many-body or Quantum

Effective interactions in many-electron collective variables

Static: Multi-pole, short ranged ~ 1/rn, n>2

FerroelectricBig Molecules (collective variables)

E> KT

5WIN

ee

Dipole moment order parameter

(bose-condensation of plasmons)

Ferroelectric

Dr

Ferromagnetic

Mr

Magnetization

order parameter

Many-electron collective variables for information processing

Both previous order parameters

Miltiferroic

Dr

Mr

These we can call a first level collective variables, they are actually fields in space

M(x),D(x)r rr r

Excitations of these can be called a second level collective variables

Collective variable representing the state of many-electron system (e.g., position)

Molecules

Examples of the order parameters and collective variables

6WIN

Excitations of the order parameters as the second level collective variables

Domain walls in ferromagnets

MTJ memory unit can be view as a domain-wall trap

ox

ide

la

ye

r

off(no wall)

Fix

ed

la

ye

r

Fre

e l

ay

er

on(1 wall)

ox

ide

la

ye

r

Fix

ed

la

ye

r

Fre

e l

ay

er

Is it possible to use Ferroelectric or even MultiFerroic , Domain walls, Topological excitations, Goldstones?

Are they advantageous in any way ?

Topological excitations of the order parameters: for example ferromagnetic vortices

off

on

Goldstone excitations of the order parameter: for example spin waves:

7WIN

Electronics Spintronics

The Same Principle for elemental Electrics and Spintronics circuit units (FET and spin-FET)

Variability: Electronics vs Spintronics

8WIN8

Variability Issues

Electronics

Spintronics

1( )/ 1/(2 1)

2where is the Bohr magneton

per atom, and for Ni is 0.33

bulk a

bulk

NS

11/3

6/ stair

a

V V N eVN

1/3

1/320

/ 6

2.4 10 Farads

a

a

C N q

N

/ /V V C C Total range spin vector = 2S+1

2.8/ /

a

S SN

Thermal fluctuations give Gaussians:

1/3

6( )N

a

T eVN

2.8( )S

a

T eVN

10WIN

Variability

731/ (6 / ) ~ 10a oNN C eV T 2

2.8 / ~ 10a oSN eV T

or a linear length of 77 nm or a linear size of 1.6 nm

Charge Spin

Room Temperature.

Quantum fluctuations of the projection of the Spin

Quantum fluctuations of charge

Qu

antu

m flu

ctuatio

ns o

f the T

otal S

pin

Ovchinnikov and Wang, APL 2008

• High enough energy

• Collective particles

11WIN11

Spintronics for low power – Spin as a state variable

1exp( )

B

E

r k T

BE g B

eB m

e

2

For Single Spin

Bmin155 Tesla –Not practical!

E=2 B B = 1.157×10-4 eV at 1 T)

2 . 2 BE B N B For N Spins

ln BE k T r

ln 2 if independentlyBE Nk T

~ ln if collectively BE k T r

Datta, APL 90, 093503(2007)

~ ln per variable BE k T rSingle electron or collective variables should be used to satisfy thermal stability and power dissipation requirements

12WIN

Summary Comparison of Electronic, Spin and Optical State Computing

Electronic

Spin

Optical

3kBT

70kBT

3600kBT

1 nm

20 nm

7 nm

Mechanism Energy Size

Lower bound(Impractical Limit)

Practical limit ~3-5 nm

Practical limit >20 nm

Practical limit >90 nm

Victor Zhirnov

Independent electrons

13WIN

Summary Comparison of Electronic, Spin and Optical State Computing

Electronic

Spin

Optical

3kBT

3kBT

3600kBT

1 nm

20 nm

2 nm

Mechanism Energy Size

Lower bound(Impractical Limit)

Practical limit~20~70 nm

Practical limit ~2~7 nm

Practical limit >90 nm

Correlated electrons

14WIN

Spin Logic Devices

3-terminal

Spin Waves

Spin Valves/Spin Torque

Magnetic Cellular Automata

Sugahara- Tanaka

Phase modulation/Amplification/Superposition

Parallel

Anti-Parallel

0

RAP

I1

I2

I3

output

Spin FET

15WIN

Spin Wave Bus -- Spin-Based Logic Device and transfer of information (Phasetronics)

Three terminal device(three MOS with a common ferromagnetic film)

Two inputs – One output

The input is provided by a Source -Drain current pulse - ISD

The output is the inductive voltage between two nearest source ( or drain) contacts - VSS

16WIN

Experiment – Spin wave Propagation

Signal/Pulse Generator

circulator Oscilloscope50 GHz

100 nm NiFe

Time resolved inductive voltage measured

Quartz or Semiconductor Substrate

SiO2

ACPS line

ACPS line

Y

Z

X

nm

50m

2m

Magnetic Film

17WIN

Prominent modulation by weak (10 50 Gauss) magnetic field Prominent modulation by weak (10 50 Gauss) magnetic field

0 50 100 150 200 250 300

External m agnetic fie ld (O e)

Am plitude changes (dB)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Fre

qu

en

cy (

GH

z)

-4dB

-3dB

-2dB

-1dB

0dB

1dB

2dB

3dB

4dB

0 50 100 150 200 250 300

External magnetic field (Oe)

Phase sh ift (D egree)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Fre

qu

ne

cy (

GH

z)

-35D eg

-25D eg

-15D eg

-5D eg

5D eg

15D eg

25D eg

35D eg

45D eg

Experimental Data – SW transport in CoFe film

M. Bao, J-Y Lee, A Khitun, K. L Wang, D. W. Lee and S. Wang, 3-D mapping of spin wave propagation in CoFe thin film, (2007).

M. Bao, J-Y Lee, A Khitun, K. L Wang, D. W. Lee and S. Wang, 3-D mapping of spin wave propagation in CoFe thin film, (2007).

18WIN

General Concept and Some Results

0 50 100 150 200 250 300

External m agnetic fie ld (O e)

Am plitude changes (dB)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Fre

qu

en

cy (

GH

z)

-4dB

-3dB

-2dB

-1dB

0dB

1dB

2dB

3dB

4dB

Experimental data on amplitude and phase modulation for the structure with 100nm CoFe film in the frequency range

(0.5 6 GHz) and magnetic field range (0 350G)

Prominent power (8dB/20G) and phase modulation ( 60Deg/10G) in the specific frequency regions

Experimental data on amplitude and phase modulation for the structure with 100nm CoFe film in the frequency range

(0.5 6 GHz) and magnetic field range (0 350G)

Prominent power (8dB/20G) and phase modulation ( 60Deg/10G) in the specific frequency regions

“AND”, “OR”, “NOT” gates

Maj

19WIN

detectionInput 1 Input 2

In-Phase Out-of-Phase

In Phase: AmplificationOut of Phase: Cancellation

Prototype Three-Terminal Device

A. Khitun, M. Bao, Y. Wu, J-Y Kim, A. Hong, A. Jacob, K. Galatsis, and K. L. Wang, Logic Devices with Spin Wave Buses – an Approach to Scalable Magneto-Electric Circuitry, Proceeding of MRS, (in press), 2008

A. Khitun, M. Bao, Y. Wu, J-Y Kim, A. Hong, A. Jacob, K. Galatsis, and K. L. Wang, Logic Devices with Spin Wave Buses – an Approach to Scalable Magneto-Electric Circuitry, Proceeding of MRS, (in press), 2008

Logic state - spin wave phase Spin wave interferometer Phase control by the direction of

current in the excitation loop Only two phases 0 and

Logic state - spin wave phase Spin wave interferometer Phase control by the direction of

current in the excitation loop Only two phases 0 and

0 100 200 300 400 500 600 700 8000

2

4

6

8

10

12 Frequency = 3GHzIn-phaseOut of phase

Out

put V

olta

ge (

mV

)

Magnetic Field (Oe)

20WIN

Mitigating eddy current losses in nanoscale devices

0.0 0.5 1.0 1.5 2.0

15

20

25

30

35

0.1

1

10

100

Eddy current losses

"Insulator"

Dispersion

Fre

quen

cy, G

Hz

k, waves/micron

Dec

ay le

ngth

, mic

rons

Continuous metallic

Insulating film

Eddy current losses severely damp spin waves in a metallic film.

0.1 TCoFe; 100 nm

Ferrite (Fe3O4)

0.0 0.5 1.0 1.5 2.0

15

20

25

30

35

0.1

1

10

100

Dispersion

4 m

2 m

Fre

quen

cy, G

Hz

k, waves/micron

Wide film8 m

Dec

ay le

ngth

, mic

rons

Continuous metallic

2, 4, or 8 m

Eddy current loss can be reduced by laminations.

CoFe; 100 nm

Jim Allen – UCSB

Fig. (1) Fig. (2)

21WIN

Prototype Device by Kostylev et al:

2D Graph 2

Spin wave frequency, GHz

7.095 7.100 7.105 7.110 7.115 7.120 7.125

Inte

rfer

omet

er o

utpu

t si

gnal

am

plitu

de,

dB-40

-35

-30

-25

-20

-15

-10

-5

=0.8=0

f0

Umin

U

I, A

/

Kostylev, M.P., et al., Spin-wave logical gates. APL, 2005. 87(15): p. 153501-1-3.Kostylev, M.P., et al., Spin-wave logical gates. APL, 2005. 87(15): p. 153501-1-3.

Logic state - spin wave amplitude Spin wave interferometer Phase modulation by magnetic field Gradual phase shift control up to 2.5

Logic state - spin wave amplitude Spin wave interferometer Phase modulation by magnetic field Gradual phase shift control up to 2.5

22WIN

Follow-up work by T. Schneider et al.

T. Schneider, A.A. Serga, B. Leven, B. Hillebrands, R.L. Stamps and M.P. Kostylev, Realization of spin-wave logic gates, APL, 92, 0022505, 2008T. Schneider, A.A. Serga, B. Leven, B. Hillebrands, R.L. Stamps and M.P. Kostylev, Realization of spin-wave logic gates, APL, 92, 0022505, 2008

The same device structure as for the prototype (Kostylev et al.) Logic state - spin wave amplitude Phase modulation by magnetic field (Input current 1200mA XNOR, NAND logic gates demonstrated

The same device structure as for the prototype (Kostylev et al.) Logic state - spin wave amplitude Phase modulation by magnetic field (Input current 1200mA XNOR, NAND logic gates demonstrated

23WIN

Speed of Operation Internal delay time = propagation distance/group

velocityPropagation distance: ~ (submicron)

Group velocity: gr= d/dk (~ 107 cm/s )Delay time ~ 10-100 ps

0.0 0.5 1.0 1.5 2.0-15

-12

-9

-6

-3

0

3

6

9

12

15Subtracted H=0 from H=50 Oe

Osc

illo

scop

e O

utpu

t (m

V)

Time (ns)

Experimental Data:100nm CoFe film, RT

Propagation distance: 2Group velocity: ~105 m/s or 107cm/s

Experimental Data:100nm CoFe film, RT

Propagation distance: 2Group velocity: ~105 m/s or 107cm/s Current device: 1 ns

Ultimate limit: <10 ps

The fundamental limit for device operation speed – limited spin wave group velocity.

operation speed by the scaling down the signal propagation distance (submicron)

The fundamental limit for device operation speed – limited spin wave group velocity.

operation speed by the scaling down the signal propagation distance (submicron)

24WIN

Numerical modeling: Multifunctional MagnetoElectric Cell

Sang-Koog Kim, Sung-Chul Shin, and Kwangsoo No Seoul National University, IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004

Sang-Koog Kim, Sung-Chul Shin, and Kwangsoo No Seoul National University, IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004

effeff HmHmdt

md

21

pulsess

eff HeemM

Km

M

AH

)(

22 22

m - the unit magnetization vector Ms - the saturation magnetization - the gyro-magnetic ratio - the phenomenological Gilbert coefficient

Landau-Lifshitz-Gilbert formalism Landau-Lifshitz-Gilbert formalism

A - the exchange constantK - the uniaxial anisotropy constante - the unit vector along with the uniaxial direction Hpulse - the pulse field

V

M

25WIN

Spin Wave Modulation by Electric Field

R. Ramesh (Berkeley)

S. Wang (Stanford)

Modulation via the exchange bias coupling in FM/MF structure

Modulation via the exchange bias coupling in FM/MF structure

K. Wang (UCLA)

Work Integrated by Ajey P. Jacob (Intel)

26WIN

Magnetic Nanofabric: Spin Wave multibit processor

Piezoelectric

Ferromagnetic Film

Silicon Substrate

Modulator fn

ACPS Line (input f1,f2,f3,…fn)

ME Cell fn

ACPS Line (output f1,f2,f3,…fn)

Silicon Oxide Silicon Oxide

…

Input (f1,f2,f3,…fn)

Output (f1,f2,f3,…fn)

VC (f1) VC (f2) VC (fn)

Equivalent circuit

27WIN04/10/23

PAGE 27

Magnetic Nanofabrics:- Spin Wave device’s building blocks- A. Khitun, M. Bao and K. L. Wang (UCLA)

B a s i c E l e m e n t / S y m b o l S t r u c t u r e S c h e m a t i c s

C o n v e r t e r

V o l t a g e - t o - S p i n W a v e

S p i n W a v e - t o - V o l t a g e

S e m i c o n d u c t o r S u b s t r a t e ( e . g . S i )

F e r r o m a g n e t i c F i l m ( e . g . C o F e )

extH

V o l t a g e I n p u t

I n s u l a t o r ( e . g . S i O 2 )

S p i n W a v e O u t p u t

S e m i c o n d u c t o r S u b s t r a t e ( e . g . S i )

I n s u l a t o r ( e . g . S i O 2 )

S p i n W a v e s I n p u t

I n d u c t i v e V o l t a g e O u t p u t = -t

S p i n W a v e M o d u l a t o r

S e m i c o n d u c t o r S u b s t r a t e

F e r r o m a g n e t i c F i l m

mH

I m

I n s u l a t o r

C o n d u c t i n g W i r e

V G

S i l i c o n S u b s t r a t e

F e r r o m a g n e t i c F i l m ( e . g . C o F e , N i F e )

F e r r o e l e c t r i c ( e . g . P Z T )

M e ta l g a te

M a g n e t o e l e c t r i c C e l l ( M E )

( e . g . P i e z o e l e c t r i c - P i e z o m a g n e t i c )

S p l i t t e r / C o m b i n e r

I n p u t A

I n p u t B

I n p u t

O u t p u t

O u t p u t A

O u t p u t B

1 m

5 0 n m

( a )

( b )

( c )

( d )

(1) (2)

28WIN

  Physical Parameter Estimated Range

Energy per bit Spin wave energy 1kT – 100kT

(Hext ~ 100Oe, VSW: 0.1um2 - 0.01um2)

Energy to excite spin wave

a) External magnetic field (e.g. coil)b) Internal excitation (e.g. spin

torque)

Energy to create a magnetic field

a)

102kT – 104kT

(M/M ~0.01, ~107 rad/s/Oe, Z~50Ohm, ~ 10-12s)

h: 1um – 10nm Ref.1

Number of functions without restoration (amplification)

Spin wave coherence length /wavelength 100-1000(L ~ 50um@RT) : 100nm-10nm

Signal restoration energyElectromagnetic coupling 102kT-105kT

- magnetoelectric coupling range from 10 to 1000 mV/(cm Oe) Ref.2

Signal propagation speed Spin wave group velocity 106 cm/s - 107cm/s

(function of film thickness)

Time delay Propagation length/Spin wave velocity 0.05ns-1nsd range from 1um to 100nm

Scaling factor and Defect Tolerance

Spin wavelength

10nm - 100nm(insensitive to defects with size << )

Operation frequency Spin wave frequency

1GHz - 200GHz (NiFe, CoFe) Ref.3,4

(depends on the material structure)

SWextSW VMHE 0

/L

2

2CV

Q

fEdiss

SW Logic Efficiency Estimates

kvg

gvd /

exts

extextloop

Zh

M

MZIE

22

2 2

jjijii HE

1) Khitun A., Nikonov D.E., Bao M., Galatsis K., and Wang K.L., Feasibility study of logic circuits with spin wave bus. Nanotechnology 18, p. 465202, 2007.2) Eerenstein, W., N.D. Mathur, and J.F. Scott, Multiferroic and magnetoelectric materials. Nature, 2006. 442(17): p. 759-65. 3) Covington, M., T.M. Crawford, and G.J. Parker, Time-resolved measurement of propagating spin waves in ferromagnetic thin films. Physical Review Letters, 002. 89(23): p. 237202-1-4.4) Vasiliev S.V., Kruglyak V.V.,Sokolovskii M.L., and Kuchko A.N., Spin wave interferometer employing a local nonuniformity of the effective magnetic field , JOURNAL OF APPLIED PHYSICS 101, p. 113919 (2007).

1) Khitun A., Nikonov D.E., Bao M., Galatsis K., and Wang K.L., Feasibility study of logic circuits with spin wave bus. Nanotechnology 18, p. 465202, 2007.2) Eerenstein, W., N.D. Mathur, and J.F. Scott, Multiferroic and magnetoelectric materials. Nature, 2006. 442(17): p. 759-65. 3) Covington, M., T.M. Crawford, and G.J. Parker, Time-resolved measurement of propagating spin waves in ferromagnetic thin films. Physical Review Letters, 002. 89(23): p. 237202-1-4.4) Vasiliev S.V., Kruglyak V.V.,Sokolovskii M.L., and Kuchko A.N., Spin wave interferometer employing a local nonuniformity of the effective magnetic field , JOURNAL OF APPLIED PHYSICS 101, p. 113919 (2007).

29WIN

Spin Wave Logic Devices

Experimentally demonstrated devices:M.P. Kostylev, A.A. Serga, T. Schneider, B. Leven, B. Hillebrands, Spin-wave logical

gates. APL, 87(15): p. 153501-1-3, 2005.

T. Schneider, A.A. Serga, B. Leven, B. Hillebrands, R.L. Stamps and M.P. Kostylev, Realization of spin-wave logic gates, APL, 92, 0022505, 2008

A. Khitun, M. Bao, Y. Wu, J-Y Kim, A. Hong, A. Jacob, K. Galatsis, and K. L. Wang, Logic Devices with Spin Wave Buses – an Approach to Scalable Magneto-Electric Circuitry, Proceeding of MRS, (in press), 2008

Ferromagnetic resonance controlled by electric field:

A.A. Semenov, S.F. Karmanenko, V.E. Demidov, B.A. Kalinikos, S. Grinivasan, A.N. Slavin, J.V. Mantese, Ferrite-ferroelectric layered structures for electrically and magnetically tunable microwave resonators. APL 88, 033503, 2006.

A.A. Semenov, S.F. Karmanenko, V.E. Demidov, B.A. Kalinikos, S. Grinivasan, A.N. Slavin, J.V. Mantese, Ferrite-ferroelectric layered structures for electrically and magnetically tunable microwave resonators. APL 88, 033503, 2006.

Spin wave modulation using multiferroics:

NoneNone

30WIN

Magnetic Logic - Cellular Automata

NAND gates form the building blocks for circuits inside your computer

31WIN

=

Current state-of-the-art: the majority logic gate. Imre et al, Science 311, 205 (2006)

Logic Gates using MQCA

32WIN

Instability of bits

Energy (normalized) vs. θ

0° is unstable

33WIN

Vertical Lines

The Problem – stray fields cause vertical bits to flip first The Solution – Add stabilizing bits to left and right

34WIN

10 01 1100

The B-gate (NAND function)

D. Carlton, UCB

35WIN

=

these gates can be linked together to do logic...

D. Carlton, UCB

36WIN

Nano magnet Switching speed

Direct observation of spin transfer switching by x-ray microscopy.

Joachim Stöhr – SLACwith Yves Acremann

d) 8.6 ns e) 9.0 ns f) 9.6 ns

g) 12.0 ns h) 12.2 ns

i) 13.2 ns

a) 0 ns b) 0.15 ns

c) 0.6 ns

a

b

c

d ef

ih

gb

c

de f

g hh

i

Y. Acremann et al., PRL 96, 217202/1-4 (2006)

• 20 nm CoPt free layer• 5 nm Cu as a tunneling

layer • Fe as Fixed layer

37WIN 37

Spin FET

-3000 -2000 -1000 0 1000 2000 3000

-2

-1

0

1

2

Mo

men

t (1

0-5em

u)

Field (Oe)

-3V -6V -12V -30V 0V 30V

MnGe on n-type Ge substrateField-Effect

Field Effect in DMS Confirmed

Ge

MnGe

Al2O3

Al

Al

JingJing Chen and KL Wang et al., App. Phys. Letts. 90, 012501 2007

Schematic Spin gain FET structure with a MnGe/SiGe quantum well.

Transistor with

Memory

38WIN

Molecular Building Blocks

Phase ChangeMolecular Motion Rotational Conformation

Physical Molecular Change

1 2 2~ exp ( )store b

tun

ma E

P

MEMORYMEMORY applications

2swb

mLt Lv E

LOGIC applications

39WIN

Metal carborane molecules“electronic switching”

Atomic Scale: 90 rotation Cu(II) Cu(I)

Molecular Rotation - metallacarboranes

“ON” “OFF”

Rotor

Stator

Tetrahedral Square planar

-10 -5 0 5 10

-1.5x10-3

-1.0x10-3

-5.0x10-4

0.0

5.0x10-4

1.0x10-3

Cu

rre

nt

de

ns

ity

(A

/cm

2)

Voltage (V)

Cu(I)(dmp)(phen-Si)PF6

SiO O

OSi

O OO

N N

NOO

NHHN

Cu(I)

N N

-10 -5 0 5 10

-1.5x10-3

-1.0x10-3

-5.0x10-4

0.0

5.0x10-4

1.0x10-3

Cu

rre

nt

de

ns

ity

(A

/cm

2)

Voltage (V)

Cu(I)(dmp)(bisp-Si)PF6

SiO O

O

Ph2P PPh2

Cu(I)

N N

I-V characteristics

• Negative differential resistance due to tunneling through molecular rotor

• Hysteresis due to rotation

LUMO

HOMO

EF

MetalEc

Ev

EF

P+ Si

5.2eV4.6eV

4.1eV

40WIN40

Acknowledgments

V Zhirnov and R Cavin A Jacob, J Allen, A Khitun, I Ovchinnikov, M Bao H Ohno, Tanaka, and K Ando All the FENA, WIN & CNSI participants All students, postdoctoral fellows, Faculty and

visitors as well as collaborators around the world

Support: DARPA, SRC, NSF, Marco, NERC, ARO, AFOSR, ONR, and many industrial companies

Support: DARPA, SRC, NSF, Marco, NERC, ARO, AFOSR, ONR, and many industrial companies