Prof. N.-J. Wu

Prof. S. W. Hwang

Texas A&M Univ.　　Prof. L. B. Kish

Univ. of Warwick　　Prof. N. G. Stocks

JST ALCA

2

Stochastic Resonance

050100150200250300350

Now

ΔTe

mpe

ratu

re (

°C)

4

2

0

-2

-4

-6

-8

400

Old age

source: http://en.wikipedia.org/wiki/Milankovitch_cycles

Benzi et al., J. Phys. A, 14 1981.

Thousands of Years Ago

ice ice iceice

050100150200250300350400

Solar forcing, etc.3

paddlefishplankton

detectable area

Russell, Wilkens & Moss, Nature 402, 1999

Russell, Wilkens & Moss, Nature 402, 1999

Stochastic Resonance (SR)

Input

SR system

without noise with noise high noise

noise

response SR

linear system

6

threshold

output

input

noise

01 1

0

0

1

0 1 10

7

easy to use + low power + integration

Kosko's Gr. (Univ. Southern California)

S. Fauve and F. Heslot(École Normale Supérieure, France)

R. Benzi, et al. (Italian National Res. Council , Itary)

Mantegna and Spagnolo (Università di Palerm, Itary)

K. Wiesenfeld's Gr. (Georgia Inst. Tech.)

F. Moss's Gr. (University of Missouri)

Kasai and Asai (Hokkaido Univ.)

2003

1997

2008

1994

1993

1983

1982

2005

Semiconductor nanowire FET

Schmitt Trigger

Tunnel diode

pn junction

Carbon nanotube FET

Josephson junction

Climate change

Bio-system

Single electron device Amemiya & Asai's Gr. (Hokkaido Univ.)

F. Moss's Gr. (University of Missouri)

8

Y.-H. Shiau (Academia Sinica, China)1999 Gunn oscillator

VDS

FET

Input = gate, Output = drain current

Operating in subthreshold region + noise

GaAsnanowire

SchottkyWPG

500 nm

Vin

Voffset

whitenoise

output

W = 340 nmLG = 300 nm

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4VG (V)

I DS (μA

)

0

0.2

0.4

0.6

0.8

1

1.2

S = 102 mV/dec

RTVDS = 0.1 V

gm = 8 mS/mm

Vth = -0.4 V

VG

GaAs channel

AlGaAsbarrier

Schottky wrap gate(WPG)

GaAs-basednanowire

LNA

IDS

input

Transfer characteristic

9

FET

without noise with noise

0time (ms)

10 20 30

input

input + noise (Vrms = 0.2V)

output 5 nA

0time (ms)

10

5 nA

20 30

input

output

ΔVin = 0.05V

C1 =Vin ⋅ Iout − Vin Iout

Vin2 − Vin

2Iout

2 − Iout2

Measured waveformsInput-output correlation

nanowire FET

Vnoise rms (V)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Inpu

t-ou

tput

cor

rela

tion,

C1 Voffset = -0.7 V

N = 1

linear system

Vth= -0.45 V

Kasai and Asai, APEX 1 (2008)

10

Correlation coefficient (cross-correlation function)

C1 =Vin ⋅ Iout − Vin Iout

Vin2 − Vin

2Iout

2 − Iout2

-1 ≤ C1 ≤1SN

0.7

C1

0.9

0

0

-1

11

1

1

0.15

DC

noise

PDM

SR

12

-3 -2 -1 0 1 2 30

0.2

0.4

0.6

0.8

1.0

No

rmal

ized

pul

se d

ensi

tyInput amplitude, (Vin - Vth)/Vnoise

Gaussianwhite noisePDM

　Noise-induced linearization

FET SR

~ linear

erfc12

Vth-Vin

20.5 Vnoise

theory

Pulse density vs. Vin in FET

13

J. E. Levin & J. P. Miller, Nature 380 (1996) 165

ex. Shimozawa et al., J Comp Physiol A (1994)

0 0.2 0.4 0.6 0.8 1.00

40

80

120

160

Stimulus intensity (Vrms)

Mea

n fi

ring

rat

e (s

pik

es/s

ec) Cricket wind sensing

wind

noise

pulse trainsensory neuron

Neural pulse density vs. Input

Cricket wind sensing

14

10-10

10-9

10-8

10-7

10-6

10-5

I DS

(A)

VDS = 0.1V

-1.5 -1 -0.5 0VG (V)

S=89mVsimulationexperiment

0

0.1

0.2

0.3

0.4

0.5

0.6 T = 293KWPGFET

0

0.1

0.2

0.3

0.4

0.5

0.6

0 50 100 150 200 250

WPGFET

0 100 200 300

Vnoise rms (mV)0 100 200 300

Vnoise rms (mV)

DC

SR

15

-1

0

1

2

3

4

5

1 1.5 2 2.5 3

TI CD40106BVDD

Schmitt Trigger

VDDTI TLC393

Comparator

VDD = 5.1 VVoffset = 0 VVin = 0.1 Vpp

1 kHz

VDD = 4 VVoffset = 3VVin = 0.8 Vpp

10 kHz-1

0

1

2

3

4

5

6

-0.2 -0.1 0 0.1 0.2

pp

Input (V) Input (V)

Out

put (

V)

Out

put (

V) 0.5 V0.02 V

Comparator

Schmitt Trigger16

Vnoise rms (mV) Vnoise rms (mV) In

put-

outp

ut c

orre

latio

n, C

1

Inpu

t-ou

tput

cor

rela

tion,

C1

Comparator Schmitt Trigger

amp = 0.02 Vpp

offset = -0.04 Vfrequency = 110 HzVDD = 5 V

amp = 0.2 Vpp

offset = 2 Vfrequency = 110 HzVDD = 4 V

Comp.

SchmittTrigger

linear

Comparator

Schmitt Trigger

17

Comparator Schmitt Trigger

Time (s)

Vnoise = 22 mV -8

-6

-4

-2

0

2

4

0 0.01 0.02 0.03Time (s)

output

inputinput

output

Vnoise = 110 mV

0

5

10

0 0.01 0.02 0.03

Comparator (PDM)

Schmitt Trigger (PWM)

18

(PDM) (PWM)

PDM PWM

1/f2

∫fout(t)•gin(t) dt ∫fout(t)•gin(t) dt＜

19

Collins et al., Nature 376 (1995)

input

output

FET

Kasai and Asai, APEX (2008)

interpretation implementation

21

FET

FET

SR in FET network　Conventional system　

22

FET

SR in FET network

Noise voltage (V)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

N = 128

32

16

8

N = 1

theoryInp

ut-

ou

tpu

t co

rrel

atio

n, C

1

averaging 128 x

32 x

16 x

8 x

1 shot

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Inpu

t-ou

tput

cor

rela

tion,

C1

Vnoise (V)

Linear system

Inp

ut-

ou

tpu

t co

rrel

atio

n, C

1 Noise voltage (V)

theory

Linear system

n>100： >0.7 23

24

device 2

device 1

threshold

Single device Summing network +uncorrelated noise

device 1device 2

Sensing

Communication

Processing

Required S/N

30 dB

15 dB

0 dB 1~10

10~100

100~1000

(S/N, BER)

# of FETs

25

0.0

0.2

0.4

0.6

0.8

1.0

Nor

mal

ized

cova

rianc

e

0.0 0.5 1.0 1.5 2.0Normalized noise intensity

0.0

0.2

0.4

0.6

0.8

1.0(b)

VN/Vpeak)(VN/V1/f

1/f noiseWhite noise

Soma et al., Phys. Rev. Lett., 91 (2003)

1/f ～

1/ƒ

1/ƒ2

white noise1/ƒ0

Nozaki et al., Phys. Rev. E, 60 (1999)

30

White: regular distribution by short correlation timeColored: swelled wave with long correlation time

1/f noise 1/f2 noiseWhite noise

1/ƒ1/ƒ2

Volta

ge (V

)

flat

noise floor

0 20 40 60 80

Time (ms)

100 1K 10K 100K

0 20 40 60 800 20 40 60 80

0

-20

-40

-60

-80

Pow

er s

pec

trum

den

sity

(dB

)

100 1K 10K 100K

Frequency (Hz)100 1K 10K 100K

0

0.2

-0.2

0.4

-0.4

Vnoise = 0.11 Vrms Vnoise = 0.138 Vrms Vnoise = 0.138 Vrms

Vnoise = 0.138 VrmsVnoise = 0.138 VrmsVnoise = 0.11 Vrms

(pink) (brown)

31

White noise 1/f noise 1/f2 noise

Vnoise = 214 mVrmsVnoise = 235 mVrms

12 mVrms 14 mVrms

Vpp = 50 mV

Vnoise = 214 mVrms

Input

Output

14 mVrms

0 20 40 60 80 100

Time (ms)0 20 40 60 80 100

Time (ms)0 20 40 60 80 100

Time (ms)

Voffset = 400 mV

White noise : Colored noise :

32

FET

white > 1/f > 1/f2　

0 100 200 3000

0.2

0.4

0.6

0.8

1.0

Vnoise (mVrms)

Inp

ut-o

utp

ut c

ross

cor

rela

tion,

C1 Voffset = 400 mV

white

1/f

1/f2

linear

33

Summing network integrating 7 FETs with different Vth

output

VDS

inputDC

offset

gate

nanowirechannel IDS

Kasai et al., APL (2010)

0

1

2

3

4

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

5

ΔVth = 0.3V

I DS (μA

)

7654321

RTVDS = 0.1 V

W

LG

WPG

GaAsnanowire

VG (V)

34

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

Inpu

t-ou

tput

cor

rela

tion,

C1

-0.4 V-0.3 V

-0.2 V

-0.1 V

Voffset = 0 V

N = 7

Vth = +80 mV

Uniform Vth

Noise voltage, Vnoise (mV rms)

averaging7 x

Uniform Vth FET network

Kasai et al., APL (2010)

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100Noise voltage, Vnoise (mV rms)

-0.4 V

-0.3 V

-0.2 V

-0.1 VVoffset = 0 V

N = 7

Vth = -180 ~ +82 mV

Inpu

t-ou

tput

cor

rela

tion,

C1

Varied Vth

averaging7 x

Varied Vth FET network

35

Vth

FET

in-out correlation coefficient in each FET

network outputinputunit output

threshold

output

VDS

inputDC

offset

gate

nanowirechannel IDS

=

FET output

36

Suprathreshold Stochastic Resonance

FIG. 1. A summing network of N threshold devices. Eachdevice is subject to the same signal but independent Gaussiannoise.

0 0.5 1 1.50

0.5

1

1.5

2

2.5

I (bi

ts)

N=31

N=1

N=2

N=15

N=7

N=3

σ

FIG. 2. Transmitted information using a Gaussian signalsource with a standard deviation sx . s � sh�sx and allui � 0. The data points are the results of a digital simulation ofthe network, and the solid lines were obtained by numericallyevaluating Eq. (2).

N. G. Stocks, Phys. Rev. Lett. 84 (2000) p.2310

•

37

T = 18ªCVDS = 0.05VW = 400nm

Vth = 0.16VS = 152 mV/dec

ΔVin=0.6V

output

Time (sec)

Noise = 0.5 V

0.3V

Time (sec)

Noise = 0

• FET

•

Response of FET network (N=8)

input

38

FET Suprathreshold SR

Vnoise (V)

Inp

ut-o

utp

ut c

orre

latio

n, C

1

Inp

ut-o

utp

ut c

orre

latio

n, C

1Vnoise (V)

VDS = 0.05VVoffset = 0.2V

Linear system FET network

averaging x 32

8

2

1

N = 32

82

1

Vth = 0.16VS = 152 mV/dec

• N ≥ 8 Suprathreshold SR

• • Vnoise ~ Vpp_input

39

electrode array

~ cm

sensoroutput

standard surface electrode size

summer

semiconductornanowire

gate

output

Stochastic Resonance FETparallel input

41

FET

THz wave

photocurrent, IPC

12

3

N

gate

0 100 200 3000

0.2

0.4

0.6

0.8

1

N = 100

10

1

VAC = 5mVVth-VGoff = 50mVβ = 0.03, K = 1

Temperature (K)T

Hz

VA

C -

I pc

corr

elat

ion

Kasai et al., OECC 2010

SR enables detection of weak THz in higher temp.

-1.6 -1.5 -1.4 -1.3 -1.2VG (V)

0

1

2

3

Cond

uctance (2e2/h)

Conductance

0

0.5

1

ΔI D

S (n

A)

T = 6K 2.54 THzPin = 13 mW

photocurrent

Calculated THz-photocurrent correlation

44