lukas worschechlukas worschech technische physik ... summer school 2011...model for explanation...

Energy harvesting in nanoelectronic devices Lukas WorschechLukas Worschech

Technische Physik, Universität Würzburg, Germany

Lukas Worschech, NiPS summer school 2011, Perugia, 01.-05.08.2011

Energy harvesting with nanoelectronics

• Energy harvesting: Energy provider+Transducer+Rectifier

• Nonlinearities in nanoelectronics: Quantum effects, reduced screening, many devices, bits per volumeUlt i i t i d i it S ll i l t• Ultra-miniaturized circuits: Small signal-to-noise ratios (SNR) & feedback between different devices are unavoidable

• Is it possible to exploit ambient noise and• Is it possible to exploit ambient noise and feedback action for electronic applications


Outline• Nanoelectronic semiconductor electronic

devices– Technologygy– Nonlinear nanoelectronic transport

• Magnetic field asymmetry in quantum wire• Magnetic field asymmetry in quantum wire• SR in a YBS as B field sensor• Y-branch as logic gate and GHz rectifier• Logic stochastic resonance in RTDsg


semiconductors

• Electronics: frequencies Hz – THz• Optoelectronics: wavelengths 0.2 – 100 µmp g µ


Some electronic devices

• Transistors and memories

bitlinewordline

bitline

FET

today FLASHcapacitorDRAM


Electrostatics of FETs with nearby charges

g CQV

gq

Wq

g

Wq

gqWTg

CC

CC

CVVV

1)(


Heterostructures: Band gap engineering

Combination of different semiconductors with atomic precision

Growth techniques: e g Molecular beam epitaxy (MBE) Growth techniques: e.g. Molecular beam epitaxy (MBE)


GaAs/AlGaAs HEMT

Modulation-doped GaAs/AlGaAs heterostruktur (HEMT)

Mean free path: ~10µms @ 4,2K / 50 – 200nm @ RT


Structuring

Top-down route: lithography, etching,…

Bottom-up route: self-assembly, seeded growth,…p y, g ,

Different geometries: wires, dots, rings, splitters…Lukas Worschech, NiPS summer school 2011, Perugia, 01.-05.08.2011

Characteristic lengths• De Broglie wavelength: phldeBroglie /

• Fermi wavelength:FEEdeBroglieF ll |

kk • Mean free path: ek

me

ek

mpvlm

• Phase coherence length: mkThl 2/

L

a)

a) Diffusive

W

b)

)

)b) Coherentc) Ballistic

Wc)


Linear mesoscopic transportp p

• Conductance quantization in 1D wires1D wires

III LRRLT

22

TffEEdEhe

eVf

RL

Dv D

**/1*2

)(~ 1

eV )(~

TheVIG

22/

• Multi-terminal conductor:

h

Landauer-Büttiker formula

jijii TeI 2

jj

ijii Th

I


What is nano? A comparison: metals vs semiconductor

Metal:Gold film

H. Ohnishi et al., Nature 395, 780-782 (1998).

n = 2.3 x 1015/cm2

lF = 0.52 nm, EF=5.5 eVl ~ 1 10 nmlm ~ 1-10 nml~ 1-100 m

Semiconductor:2 dimensional electron gas (2DEG)

11 2n = 3.0 x 1011/cm2

lF = 46 nm, EF= 11 meVlm ~ 1-100 m T < 4 Km l~ 1-100 m


Quantum wire

• Electron wave propagation: each occupied subband t ib t ith 2 2/h t th d t contributes with 2e2/h to the conductance

conductance quantization7

8

3

4

5

6

G (2

e2 /h)

0

1

2

3

0,5 1,0 1,5-1

Vg (V)


Asymmetric scattering


Deterministic asymmetry


Stochastic resonance

SR k i l b• SR: weak signals can be amplified by fluctuations

• SR conditionsSR conditions– non-linear system (threshold)– Subthreshold signal– noise

• SR was introduced as model for explanation ofmodel for explanation of the periodic ocurrence of ice ages: Benzi, Parisi, SSutera, Vulpiani


Dynamical gate operation in a YBS


Bistable selfswitching:Bistable selfswitching: depends on the bias voltage

YBS as amplifier and rectier logic operation


SR: Working principle

• self-gating leads to a bistableg gtransfer characteristic• the input and the working point

lt t t bi t blvoltages were set to bistableswitching controlled by noise • all measurements @ 20Kall measurements @ 20K

)sin()( 0, tVVtV ggg Input signal:

ggg

Weak periodic signal:

mVV 31 mVVg 3.1


SR: Signal traces

f = 0.1 Hz

f = 1 Hz

f = 1.8 Hz

At f = 1 Hz the noise dynamics follow directly the frequency of the external input forcing and a maximum synchronization is found.


Recording SR: Residence Time

For the unmodulated system with f = 0 Hz the residence time distribution decays exponentially with the inverse of thetime distribution decays exponentially with the inverse of the Kramer‘s rate

0.2

)exp()(,K

HL TTTN

(s)

KT0.1

NL

(T)

From fitting:

0 1 2 3 4 50.0

T (s)sTK )044.0502.0(

g

T (s)

KTT 2Time matching condition of SR: KTT 2Time matching condition of SR:



0.20.2f = 0.6 Hzf = 0.1 Hz• For f < fSR the residence time

0 1 2 30.0

0.1

0 2 4 60.0

0.1 distribution is strongly controlled by the noise

0.40.4

0 1 2 3T (s)

0 2 4 6

f = 2.4 Hzf = 1.8 Hz

T (s)

0.0

0.2

0.0

0.2 • For f > fSR odd multiples of the periodic forcing Tω occur:

0 1 2 30.0

T (s)0 1 2 3

0.0T (s)2/)12( TnTn



At the optimum frequency f = 1 Hz the residence time f fdistribution is almost perfectly restricted to the first peak.

0.4

(s)

0.2

NL

(T)

0 1 2 30.0

T (s)T (s)

The time scale condition of SR is fulfilled by tuning solely the frequency of the periodic forcingfrequency of the periodic forcing.


SR: Residence Time Distribution


Application: Magnetic field sensor

• Set the detector inSet the detector in the strongly noise activated regime• Magnetic field applied perpendicular to the motion ofto the motion of electrons either in or out of the plane

LHn

TT,1

p

ii

iLH

LHLH T

nT

1,

,,



0.700.75

Vbr,th • V decreases down

0 00.550.600.65

Vbarrier (V) -0,520 -0 514r

(V)

• Vbr decreases down to a magnetic field threshold Bth

• Transitions between

0 350.400.450.50

B

0,514 -0,508 -0,502 -0,496 -0,490

Vb

B

the two states occur between ∆B

1 5

0.0 0.5 1.0 1.5 2.0 2.5 3.00.35 B ,

B (T)

Bth

0.62

0.64

0 5

1.0

1.5

r,th

(V)

Bth

(T)The magnetic-field induced

switching is associated with

-0.52 -0.51 -0.50 -0.49

0.600.0

0.5V

br

B

a scattering asymmetry at the boundaries

Vbarrier (V)



3 0

s)2.53.0

ime

(s

1.52.0 TH TL

ence

ti

0 51.0

resi

de

0.00.5

mea

n r

0 10 20 30 40 50 60

m

B (mT)B (mT)



1.5 Measurement

0 51.01.5 Measurement

Simulation

)

Linear Fit• Output is a linear function of B around ∆T = 0 s

0 50.00.5

T

(s)

• Target signal independent iti it

-1.0-0.5 sensitivity

0 10 20 30 40 50 60-1.5

B ( T)

cBTBT 0)(B (mT)

cBTBS

)(B


Y-branch as ballistic rectificationRectification due to junctions:

• pn-junction• pn junction

• Metal-semiconductor junction

Y-branch junction: no geometrical asymmetry!

V (Y)r

0 05

0,00

V (X)l V (X AND Y)s-0,10

-0,05

Vs (V

)

V r

V s-0,15

Experiment Theory:

diffusive ballistic

V l-0,4 -0,2 0,0 0,2 0,4

Vxy (V)


Y-branch as ballistic rectification

V Vdiffusive Transport

Vl Vr

-0,05

0,00

-0,10

Vs (V

)

V s

Quasi-ballistic Transport

-0,4 0,0 0,4

-0,15 diffusive ballistic

, , ,Vxy (V)


YBS nonlinearity used for a compact adder

Half-Adder: binary addition with carry bit

h bl

y y

S h

X Y Z C

Truth table

X & = AND

Scheme

X Y Z C

H H L H

&XY C

= XOR=

H L H L

L H H L

Z=

L L L L> 10 FETs + i t tinterconnects


Nanoelectronic Half-Adder

• planar Half-Adder is basedon ballistic Y-junctionson ballistic Y junctions

• Inputs: x and y x g

• Outputs: c and z

Working point: s

lv sr• Working point: s

• Control: v

yc z

100 nm

L. Worschech et al., Appl. Phys. Lett. 83, 2462 (2003)


ModelModel

control of Vz via Vc: gate

a) Injection of electronsc zc

sl r

b) Gating

N t l t !

c zz

VVVs

R

c

No external gate!

Self induced switching

VzVc Vdg


0.1s

gate

l r

0.0 Vs = 0.1 V

Vz (V

)c zz

VVVs

R=10M

c

0 1 V

-0.1Vd = 0.1 V

VzVc Vd

-0.1 V -0.3 V -0.2 V

-0.4 -0.2 0.0 0.2 0.4Vc (V)

• Self switching N-shaped Vz (Vc)-characteristics

• Definition of the working point via Vsg p s


y c zy

x

Vx

c

s

gate

l r

0 10Vs = -0.3 V

VZ

(L H)(H H)(H L)

VC y c zy z

VzVc Vd

VsVy

R

c

0.05

0.10

V)

Z

0.1C

V)

d

0.00

Vz (

V

0.0

Vou

t (V

-0.05• Push-Pull-Mode:Vx + Vy= 0.3 V

• Push-Pull-Mode:Vx + Vy= 0.3 V

1 50 0 75 0 00 0 75 1 50

-0.1

-0.6 -0.3 0.0 0.3Vc (V)

• Rectification: Vc < (Vx + Vy)/2 • Self induced Switching: M shaped V characteristic

• Rectification: Vc < (Vx + Vy)/2 • Self induced Switching: M shaped V characteristic

-1.50-0.75 0.00 0.75 1.50Vx -Vy (V)

M-shaped Vz-characteristicM-shaped Vz-characteristic


V g Demonstration of logic function at RT:

T = 4.2 K T = 50 K T = 300 Ky c zy

x

z

Vx

Vs

c

s

g

l r

e o s a o o og c u c o a

0,00

0,10

z (V

)

y c zy zVz

Vc

V

Vy

R

c

-0,10

Vz

0 00

Vd

-0,50

-0,25

0,00

Vc (

V) X Y Z C

H H L HH L H L

(LL)

(HL)

(LH

)(H

H)

(HH

)(L

H)

(HL)

(LL)

(HH

)(L

H)

(HL)

(LL)

-0,75

H L H LL H H LL L L L Logic inputs (XY)L L L L


Dynamic properties of rectification

0,0

room temperature

V)

-0,5

VS (

V

1 1 1 AND Address Level

)

-1,0-1

01 -1-1 1

-1 -1

VS (

V)

-1,0 -0,5 0,0 0,5 1,0

V (V)


Microwave rectification: energy harvesting

2VV 2VcVs f

assuming3T ballistic cavity

)2

sin( 1~ tfVV

with

yA. N. Jordan, Markus Büttiker, PRB 2009 2

)2cos( 122 tfVcVcV ec 1~ )2

cos(22 ~~ tVVVs

F

c2

~


High Frequency SetupHigh Frequency Setup

S-Parameter

2at detectedpower microwaveS1 into injectedpower microwave

de ec edpowec ow ve21 S


Frequency doubling

-70 f2 = 100 MHz

Bm)Injection Detection

-70

-90

-80P 2 (dB

IS

V = 0S

IS

V = 0S

j

-80

P 2 (dB

m) -1,0 -0,5 0,0

V (V)

V o V-V /2o V o V-V /2o

f2 = 2f1f1

P

-902nd harmonic

0 5 10 15 20

2nd harmonic

f2 (GHz)f


Microwave generates a DC current

10-3

10-2

T = 300 Kf = 10 GHz0,4

f1 = 10 GHz) 10-5

10-4

VC = -1 V

f = 10 GHz

)

0,2 10 dBm 8 dBm 6 dBm no microwave

I S (A

10-7

10-6

I S(A)

0,0 10-9

10-8

-0,1 0,0 0,1

V (V)-5 0 5 10 15

10-10VC = 0.3 V

P(dBm)V (V) P(dBm)


Resonant-tunneling diode

fast operation TH● fast operation ~THz● negative differential resistance

ballistic operation at room temperature● ballistic operation at room temperatureLukas Worschech, NiPS summer school 2011, Perugia, 01.-05.08.2011

RTD operation


Logic operation with RTD mesas

200

050

100150200

V (m

V) split RTDdiameter: 600nm

0,00 0,25 0,50 0,75 1,00 1,25 1,50Vdc (V)


No thermal transconductance limit ultra small switching voltagesNo thermal transconductance limit ultra small switching voltages


Logic RTD gates

Vac = 23 mV Vac = 25 mVVac = 24.5 mV

V1 = V2 = 0 mV == Log. input I = I1+I2=0+0=0


Logic RTD gates

Vac = 25 mV Vac = 26.5 mVVac = 26 mV

V1 = 0,2 V2 = 2,0 mV == Log. input I = I1+I2=1+0=0+1=1


Logic RTD gates

Vac = 26.5 mV Vac = 29 mVVac = 27.5 mV

V1 = V2 = 2 mV == Log. input I = I1+I2=1+1=2


Logic RTD gates

NOR

0 0 | 1NAND

0 0 | 10 0 | 11 0 | 00 1 | 0

0 0 | 11 0 | 10 1 | 1

1 1 | 0

transition from NOR to NAND opertation for

1 1 | 0

transition from NOR to NAND opertation for amplitude changes smaller than 1 mV


Logic stochastic resonance

Murali, K. , Sinha, S. , Ditto, W. , Bulsara, A. Phys. Rev. Lett. 102, 104101 (2009).

Murali, K., Rajamohamed, I. , Sinha, S. , Ditto, W. , and Bulsara, A. , Appl. Phys. L tt 95 194102 (2009)Lett. 95, 194102 (2009).

L. W., F. Hartmann,T. Y. Kim,S. Höfling,M. Kamp A Forchel J Ahopelto 2I Neri AKamp,A. Forchel,J. Ahopelto,2I. Neri,A. Dari, L. Gammaitoni, APL 2010


RTD as light sensor and light-programmable LSR

120 P=0nW P=0.1 nWGaussian Fit

60

80

100

Cou

nts

Gaussian Fit

91 90 89 88 87 86 85 840

20

40

-91 -90 -89 -88 -87 -86 -85 -84<VS> (mV)


SummarySu a y

• Introduction into different nanoelectronicdevices

• Nonlinear transport: rectification, bistableswitching

• Noise-induced switching, logic stochastic resonanceRoutes for energy harvesting in nanoelectronics• Routes for energy harvesting in nanoelectronics


For important contributions many thanks to

Transport:F H t S K li S Gö f t A D i LF. Hartmann, S. Kremling, S. Göpfert, A. Dari, L. Gammaitoni

Technology:M. Emmerling, S. Kuhn, T. Steinl, G. Heller, M. Kamp

III-V samples:C. Schneider, S. Höfling, A. Forchel


Acknowledgement

• Support via EU: SUBTLE & NANOPOWER

• Many thanks for your attention!Many thanks for your attention!


lukas worschechlukas worschech technische physik ... summer school 2011...model for explanation...

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