presentation final 掲載用 - 国立情報学研究所 ... · 2010.08.19...

2010.08.19 量子情報サマースクール (NTT 山口) Slide-#1

NTT 物性科学基礎研究所

山口浩司

ナノ機械構造の物理と応用- ナノ機械計算の可能性 -


Thermodynamics of Computing - - -

What is the minimum energy required to carry out a computation ?

The computation can actually be done with no minimal loss of energy !!

If your computer is reversible, the energy loss could be made as small as you want.

The energy cost comes in the step of erasure of the information; E = kTlog2 per one bit.

C. H. Bennett, R. Landauer etc.


http://www.zyvex.com/nanotech/mechano.htmland Nanotechnology, 4, 114 (1993)

“0” “1”

)0(,)( 42 bbxaxxV

no stress (a > 0)

critical stress (a ~ 0)

large stress (a<0)


Bistable MEMS memory using buckled beams

B. Charlot et al. J. Micromech. Microeng. 18, 045005 (2008)

D. Roodenburg et al. Appl. Phys. Lett. 94, 183501 (2009)


Micro/Nanomechanical Resonators

Mechanical resonators

Ultrasensitive Force/Mass Detection- Displacement detection up to femtometer scale (UCSB)- Zeptogram mass sensing (Caltech)- Single spin sensing (IBM)

Logic Applications- Bistability in nonlinear Duffing resonators (Boston, APL 2004)- Mechanical XOR by coupled resonators (Caltech, Science 2007)

S. C. Masmanidis et al. Science

D. Rugar et al. Nature

fres

Beam resonator

Frequency

Vibr

atio

n En

ergy

Qff 0

0f )cos(/)(

)(222

0222

0

0

tQ

ftx

tFxmdtdx

Qm

dtxdm cos2

00

2

2

Equation of motion

f0 : 100Hz -1GHz, Q: 103 -106


+ + +

- --

Strain-voltage transduction

GaAs- --

+ ++ -

+

-

+

-

+GaAs [001]

[110]

Piezoelectric effect in Zinc Blende structure

Ga As

[110]


Strain-voltage transduction

GaAs- --

+ ++ -

+

-

+

-

+GaAs [001]

[110]

Electrical actuation, detection and frequency control

2DEG




Strain-voltage transduction-

+

-

+

-

+

GaAs

-

+

-

+

-

+GaAs

Electrical actuation, detection and frequency control

[001]

[110]

- --+ + 2DEG


Fabricated device (top view)

beamGate 1

2DESGate 2

Gate 3

100 m

Gate 1: Application of AC voltage Actuation through bending moment

Gate 2: Measurement of generated voltage Beam-motion detection

Gate 3: Application of DC voltage Resonance frequency modulation

～

Output

fres

Piezoelectric mechanical resonator

Applied AC voltage induces the vibration.（fres ~ 140 kHz, amplitude: 10 nmrms）

Motion


Fabricated device (top view)

beamGate 1

2DESGate 2

Gate 3

100 m

Gate 1: Application of AC voltage Actuation through bending moment

Gate 2: Measurement of generated voltage Beam-motion detection

Gate 3: Application of DC voltage Resonance frequency modulation

～

Output

fres

Gate 3 bias voltage (V)

Gat

e 1

actu

atio

n fr

eque

ncy

(kH

z)

0 4 0 2 0 0 0 2 0

f0 /Vgate1 = 28.4 HzV-1

0 V 300 nV137.96

137.97

137.98

0.4 0.2 0.0 - 0.2 0.00

0.05

0.10

0.15

0.20

0.25

0.30

100 Vrms

700 Vrms

Am

plitu

de (

V)

Gate 1 actuation frequency (Hz)

Q = 115000Sx

1/2 = 2.5×10-10 mHz-1/2

137.846 137.850 137.854

0.3

0.2

0.1

0.0

Gat

e 2

outp

ut v

olta

ge (

V)

I. Mahboob and H. Y., Appl. Phys. Lett. 92, 173109 (2008)

2.5K

Piezoelectric mechanical resonator


Parametric actuation of mechanical resonance

fact = 2 fres


beamGate 1

2DESGate 2

Gate 3

Lock-inAmp.

Ref

.

Detection

Parametric actuation

fact

AC actuation

~fact /2

fact = 2 fres



Frequency response for parametric actuation

0)()]2sin(2)(1[ 220

102

2

txttxm

dtdQm

dtdm

damping Non-linearity


fixedspring cst.

Nonlinear Mathieu-equation




0)()]2sin(2)(1[ 220

102

2

txttxm

dtdQm

dtdm

Nonlinear Mathieu-equation

scscccccssss XXXXXQXXXXXXQX

22

0

1

0

22

0

1

0 4322,

4322

Rotating frame approximation: )cos()()sin()()( ttXttXtx cs



Simulation



Bi- and tri-stabilities in parametric resonator

No amplitude

Bi-stable

Tri-stable

Origin of bi-stability

0 phase phase


Hamiltonian in the rotating frame for parametric resonator

0)()]2cos(2)(1[ 22002

2

txttxm

dtdm

dtdm

420

220

2

41)2cos(21

21

2xmtxm

mpH

Canonical transformation by a time-dependent generator:

)sin()()cos()()(,/)]cos()()sin()([)( ttQttPmtpmttQttPtx

)(4

)(4

)(323~

),(),('

22220222 QPQPQPm

tFxpHQPH

)tan2/sin/tan2/(),,( 22 tQtxQmtxmtQxF

( = 0 )


0

P 0

Q

= 1.0 x /m0

0-phasestate

-phasestate

H’(P,Q)

M. Marthaler and M. I. DykmanPhys. Rev. A76, 010102 (2007)

= 0 = 0

)(4

)(4

)(323~

),(),('

22220222 QPQPQPm

tFxpHQPH

Hamiltonian in the rotating frame for parametric resonator

actuation amplitude increased

0

P 0

Q

= 0.2 x /m0

0

P 0

Q


“0” “1”

Analogies between buckled beams and parametrically-driven resonators

“0” “1” Driving stress: periodic

Threshold: yes ( / 0 ~ Q-1)

)0(,)( 42 bbxaxxV

a > 0 a ~ 0 a < 0

Driving stress: static

Threshold: yes (Euler’s condition)


0-phasestate

0

P 0

Q

-phasestate

beamGate 1

2DESGate 2

Gate 3

Lock-inAmp.

Detection

2fres

Parametricactuation ~

Noise

Estimation of Barrier Height

Noise-inducedTransition Noise-inducedTransition

Time

0-state

-state

0 0 0

Am

plitu

de (a

rb. U

nits

)

100 sec


Estimation of Barrier Height

Tres (s)

Cou

nts

in lo

g sc

ale

log

Rtr

ans

Pnoise-1 (10-6V-2Hz1)

Counts~exp(-RtransTres)

Rtrans~exp(-cEB/Pnoise)

Detuning f (Hz)

Bar

rier E

nerg

y E B

(pJ)

- Scaling law -EB ~ cf2

Time

0-state

-state

0 0 0

Am

plitu

de (a

rb. U

nits

)

100 sec

Tres

0-phasestate

Noise-inducedTransition Noise-inducedTransition

0

P 0

Q

-phasestate

M. Marthaler et al.PRA (2007)H. B. Chan et al., PRL (2007)


Symmetry Lifting

0-phasestate

0

P 0

Q

-phasestate

beamGate 1

2DESGate 2

Gate 3

Lock-inAmp.

Detection

2fres

~

NoisePhaseLocked

fres

~

P Q

0-state

-state


0-phasestate

0

P 0

Q

-phasestate

Symmetry Lifting Symmetry lifting amplitude

P Q

0-state

-state

The asymmetry of the double well potential can be electrically controlled.

I. Mahboob, C. Froitier, and H. Yamaguchi, Appl. Phys. Lett. 96, 213103 (2010)


Electromechanical implementation of Parametron

Triger Input(signal from prev. bit)

~

Lock-inAmp.

2fres


Output(signal to next bit)

fres

Phase lockedR

ef.

Bit storage and bit reset operation was realized in an equivalent way to the “Parametron”

~

I. Mahboob and H. Yamaguchi, Nature Nanotechnol. 3, 275 (2008)


“0” “1”

Similarity between buckled beams and parametrically-driven resonators

“0” “1”

Symmetry lifting: small lateral force

Symmetry lifting: small fres actuation

Driving stress: staticThreshold: yes (Euler’s condition)

Driving stress: periodicThreshold: yes ( / 0 ~ Q-1)

)0(,)( 42 bxbxaxxV

“1”


- built in 1957 in NTT- 4.6MHz operation frequency- 4,600 parametric resonator- used for practical calculation

Parametron computer (Musashino-1)


How to construct logic ? -- Controlled OR/AND --

Data input Data outputA

BC

10001110Data Output11001100C10101010B00001111A

B OR C B AND C

Concept of “Majority Voter”


Can we use it for energy-efficient mechanical logic systems ?

Power consumption

Operation speed and integration: Submicron-long resonators fres ~ several GHzGraphene resonators fres ~ 500GHz ?Integration density 1Gbits/cm2

Our device (250 x 90 x 1.4 m3) : Pmech ~ 0.1 pW/bit

][~ 223 LxmQfP actresmech

- Mechanical energy dissipation


Conclusion

We fabricated a GaAs/AlGaAs piezoelectric micromechanical resonator and demonstrated its possible applications.

- Effective strain-voltage transduction-Realizing of electromechanical Parametron-Non-degenerate parametric amplification-Multiple and parallel logic gates using f-conversion

Imran Mahboob (NTT)Charline Froitier (NTT/ESPCI)Emmanuel Flurin (NTT/ESPCI)Katsuhiko Nishiguchi (NTT)Akira Fujiwara (NTT)

Acknowledgements

Parametric resonators

Si nano-FET

presentation final 掲載用 - 国立情報学研究所 ... · 2010.08.19...

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