Noisy dynamics in nanoelectronic systems. Technische Physik, Universität Würzburg, Germany

Noisy dynamics in nanoelectronic systems Lukas Worschech Technische Physik, Universität Würzburg, Germany

Team Transport: FH F. Hartmann, SK S. Kremling, S. SGöpfert, L. LGammaitoni i Technology: M. Emmerling, S. Kuhn, T. Steinl, M. Kamp III V samples: III-V samples: C. Schneider, S. Höfling

Motivation: Stochastic resonance (SR), a noise enhanced information transfer process Stochastic resonance: Weak signals can be enhanced by fluctuations (for a review Ref.[1]) Ingredients: Noise Sub-threshold signal Non-linear system, e.g. bistable systems SR as model was introduced to explain the periodic recurrences of ice ages: Benzi, Parisi, i Sutera, Vulpiani [] SR has been found in various systems, e.g. in crayfish mechanoreceptors [3] [1] L. Gammaitoni et al., Stochastic resonance, Reviews of Modern Physics, Vol. 70, No. 1, January 1998 [] Benzi, R., G. Parisi, A. Sutera, and A. Vulpiani, 198, Tellus 34, 10. [3] Douglass, J. K., L. Wilkens, E. Pantazelou, and F. Moss, 1993, Nature (London) 365, 337.

Outline Nanoelectronic semiconductor electronic devices Technology Mesoscopic devices Nonlinear transport BL Motors Y-branch switch as half adder Quantum dot as a memory Resonant tunneling diode: Sensor, logic stochastic resonance Best detection strategy

semiconductors Electronics: frequencies Hz THz Optoelectronics: wavelengths 0. 100 µm

Heterostructures: Band gap engineering Combination of different semiconductors with atomic precision Growth techniques: e.g. Molecular beam epitaxy (MBE)

GaAs/AlGaAs HEMT Modulation-doped GaAs/AlGaAs heterostruktur (HEMT) Mean free path: ~10µms @ 4,K / 50 00nm @ RT

Structuring Top-down route: lithography, etching, Bottom-up route: self-assembly, seeded growth, Different geometries: wires, dots, rings, splitters

Characteristic lengths De Broglie wavelength: l debroglie h / p Fermi wavelength: l F l debroglie E E F p k k e k k Mean free path: l m v m e m e Phase coherence length: l h / mkt L a) Diffusive b) Coherent c) Ballistic a) b) c) W

Linear mesoscopic transport p p Conductance quantization in 1D wires 1D wires I I I L R R L T T f f E E de h e ev f R L D v D * * *1/ ) ( ~ 1 ev ) ( ~ T h e V I G / Multi-terminal conductor: h Landauer-Büttiker formula j ij i i T e I j j ij i i T h I

What is nano? A comparison: metals vs semiconductor H. Ohnishi et al., Nature 395, 780-78 (1998). Metal: Gold film n =.3 x 10 15 /cm l F = 0.5 nm, E F =5.5 ev l m ~110 1-10 nm l ~ 1-100 m Semiconductor: dimensional electron gas (DEG) n = 3.0 x 10 11 /cm l F = 46 nm, E F = 11 mev l m ~ 1-100 m T < 4 K l ~ 1-100 m

Quantum wire Electron wave propagation: each occupied subband contributes with e /h to the conductance 8 conductance quantization G (e /h) 7 6 5 4 3 1 0-1 0,5 1,0 1,5 V g (V)

Quantum ring Quantum oscillations: Aharonov-Bohm effect Magnetic field symmetry in linear mesocopic transport G(B)=G(-B) G(e /h 4, 4,0 ~ 3,8 3,6 h) 3,4 3, 3,0 A( r) dr h f r 59(0) nm e,8-0,06-0,04-0,0 0,00 0,0 0,04 0,06 B(T)

Conductor with 3 contacts 1 S S Current conservation symmetry 1 S S ij s ji s ij s ij T 1 r G G r Transmission matrix 1 1 1 1 1 1 1 1 1 r r r G r r G G r G r r G G r r G G r G G r T Switching parameter 1 1 r r ), ( 1 V V G g I-V curve 1 1 V V T I h e I I 3 3 V h I

Y-branch switch Stem and branches controlled by side gates

Non-linear transport via interaction Mesoscopic capacitance: Self-switching in a YBS 1 qd qg 1 Dqd / Cgd Dqd / Dqg C g b C D D b b g C D C lr b g C b lr g

YBS.00 1.75 V bias = 1.75 V 1.00 V 0.50 V V bl (V) 1.50 1.5 1.00 075 0.75 0.50 05 0.5 V br (V) Push-pull Mode: V gl + V gr = const (dv gl = -dv gr ) 0.00-0. -0.1 0.0 0.1 0. V g (V)

Dynamical gate operation in a YBS

Solar cell absorption rectifier Optical excitation of electron hole pair Separation by a p-n junction: asymmetry in the device structure Is it possible to generate a current in a symmetric structure?

Yes! If the nonlinear noise is asymmetric: Transport as a consequence of state-dependent diffusion Diffusion constants: Double well potential with minima located at A and D. D is the energetic favorable point D with D < A. Consider two temperatures at the slopes T hot and T cold with T hot >T cold. For systems subject to thermal noise, the Boltzmann factor is V exp( ) kt M. Büttiker, Z. Phys. B 68, 161 (1987). R. Landauer, J. Stat. Phys. 53, 33 (1988). For systems with mobility µ subject to drift and state dependent diffusion the Boltzmann factor is with exp( (q))

Transport as a consequence of state-dependent diffusion M. Büttiker, Z. Phys. B 68, 161 (1987). Ya. M. Blanter and M. Büttiker, Phys. Rev. Lett. 81, 4040-4044 (1998). I ov E T L T E 0 exp( )sin( ) T 0 1 0 0 I With: T E0 exp( )sin( ) T 1 mt 0 0

Y-branch as ballistic rectification Rectification due to junctions: pn-junction Metal-semiconductor junction Y-branch junction: no geometrical asymmetry! V (Y) r 0,00 V l (X) V s (X AND Y) V r V s (V) -0,05 005-0,10 V s -0,15 Experiment Theory: diffusive ballistic -0,4-0, 0,0 0, 0,4 V l V xy (V)

Y-branch as ballistic rectification diffusive Transport V l V r 0,00-0,05 V s (V) -0,10 Quasi-ballistic Transport -0,15 diffusive ballistic V s -0,4 0,0 0,4 V xy (V)

YBS nonlinearity used for a compact adder Half-Adder: binary addition with carry bit Truth table X Y Z C H H L H Sh Scheme X & = AND Y & C = = XOR H L H L L H H L = Z L L L L > 10 FETs + interconnects t

Nanoelectronic Half-Adder planar Half-Adder is based on ballistic Y-junctions Inputs: x and y x g Outputs: c and z Working point: s Control: v v y c l z r 100 nm s L. Worschech et al., Appl. Phys. Lett. 83, 46 (003)

Model control of V z via V c : gate a) Injection of electrons l r s b) Gating No external gate! V c c R z V s V z Self induced switching V d

V g Demonstration o of logic ogc function at RT: V x x V y y c z y c z V c l R V d r V z s V s z (V) V z 0,10 0,00 T = 4. K T = 50 K T = 300 K -0,10 X Y Z C H H L H H L H L L H H L V c (V) 000 0,00-0,5-0,50-0,75 (HH) (LH) (HL) (LL) (HH) (LH) (HL) (LL) L L L L Logic inputs (XY) (HH) (LH) (HL) (LL)

Positioned QDs

SET by positioning of QDs in a wire M. Stopa, Harvard 0,0 G/G 0 0,01 000 0,00 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0 1,1 1, V g (V) Coulomb oscillations due to charging of island with single electrons Coulomb-Diamond used to extract capacitances, charging energy > 10 mev

Memory: threshold shift of read-out transistor 7,5 5,0,5 0,0 17,5 V th I d (A A) 15,0 1,5 10,0 7,5 5,0,5 0,0-1 0 1 3 4 V g (V) Schaltspannung V W V g CWq 1 C g Q Cgq C C Wq gq

Resonant-tunneling diode fast operation ~THz negative differential resistance ballistic operation at room temperature

RTD operation

Logic operation with RTD mesas V (mv) 00 150 100 50 0 split RTD diameter: 600nm 0,00 0,5 0,50 0,75 1,00 1,5 1,50 V dc (V)

Noise-activated switching Ultra-miniaturized circuits: Small signal-to-noise ratios (SNR) & feedback between different devices are unavoidable Subtle strategy: exploit ambient noise and feedback action for electronic applications

No thermal transconductance limit ultra small switching voltages

Logic RTD gates V ac = 3 mv V ac = 4.5 mv V ac = 5 mv V 1 = V = 0 mv == Log. input I = I 1 +I =0+0=0

Logic RTD gates V ac = 5 mv V ac = 6 mv V ac = 6.5 mv V 1 = 0, V =,0 mv == Log. input I = I 1 +I =1+0=0+1=1

Logic RTD gates V ac = 6.5 mv V ac = 7.5 mv V ac = 9 mv V 1 = V = mv == Log. input I = I 1 +I =1+1=

Logic RTD gates NOR 00 1 0 1 0 0 0 1 0 1 1 0 NAND 00 1 0 1 0 1 0 1 1 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. 10, 104101 (009). Murali, K., Rajamohamed, I., Sinha, S., Ditto, W., and Bulsara, A., Appl. Phys. Lett. 95, 19410 (009). L. W., F. Hartmann,T. Y. Kim,S. Höfling,M. Kamp,A. Forchel,J. Ahopelto,I. Neri,A. Dari, L. Gammaitoni, APL 010

Stochastic resonance : A short introduction L. Gammaitoni et al., Stochastic resonance, Reviews of Modern Physics, Vol. 70, No. 1, January 1998 Overdamped motion of a Brownian particle in a bistable potential in the presence of noise and periodic forcing. with x V `( x) A0 V 1 cos( t ) ( t) 1 4 4 ( x) x x Noise-induced hopping between the local equilibrium states with the Kramers rate 1 V r K exp( D The time-scale matching condition for stochastic resonance: T T K )

Stochastic resonance in resonant tunneling diodes: Exploiting noise & nonlinearity RTD is bistable with stable outputs I H = 800 µa and I L = 70 µa. Works @ RT PVR ~ 3 Noise induced switching between the two stable states appear. Time scale T k is given by the inverse of the Kramer s rate.

Recording of SR: Spectral response <V> versus the noise power added to the device For P noise <P SR no spectral component at f = 500 Hz is found. For P noise > P SR the spectral component at f = 500 Hz is still apparent. At the optimum noise level P SR, the spectral amplitude reaches a maximum value and is decreasing apart from P SR.

Stochastic resonance: Time trace signals P noise = nw P noise = 3 nw noise P noise = 11 nw At P noise = 3 nw the output follows almost perfectly the input signal!!

YBS: Residence time magnetic field detector The input and the working point voltages set the condition of the Y-branch switch. Self-gating leads to a bistable transfer characteristic. Noise induced oscillations occur All measurements @ 0K. Input signal: V g ( t) V g 0 V sin( ), g t Weak periodic signal: V g 1. 1 3mV

Magnetic field sensors based on the residence time difference in electron waveguides The detector in biased in the strongly noise activated regime. Switching between V H and V L solely controlled by the internal noise. Magnetic field is applied perpendicular to the motion of electrons. Measure the time spent in each of the two stable states: n H, L 1 T H T H, L nh, L i1 T T H i, L Output of the detector is the residence time difference: T H T L i

Vb br (V) Magnetic field sensors based on the residence time difference in electron waveguides 0.75 0.70 V br,th 065 0.65 0.60 Vbarrier (V) 0.55-0,50-0,514 050 0.50-0,508 0.45-0,50 0.40-0,496 0.35 B B th -0,490 0.0 0.5 1.0 1.5.0.5 3.0 B (T) The magnetic-field induced switching (between V H and V L ) is associated with an interplay between a scattering asymmetry at the boundaries. [1] Increasing magnetic field: The output V br decreases linearly down to a magnetic field threshold B th. Transitions between the two stable states occur within a magnetic field range B. The output V br changed its stable state from V br = V H to V br = V L. Vbr r,th (V) [1] D. Hartmann et al., PHYSICAL REVIEW B 78, 113306 (008). 15 1.5 0.64 1.0 0.6 05 0.5 0.60 0.0-0.5-0.51-0.50-0.49 Vbarrier (V) Bth B (T)

mean res sidence ti ime (s) 3.0.5 1.5 1.0 0.5 0.0 Magnetic field sensors based on the residence time difference in electron waveguides.0 TH TL 0 10 0 30 40 50 60 B (mt) T (s) 1.5 Measurement 1.0 Simulation Linear Fit 0.5 0.0-05 0.5-1.0-1.5 0 10 0 30 40 50 60 B (mt) The residence time T H (high state) is decreasing and T L (low state) is increasing with increasing B. Output T is a linear function of the magnetic field around the symmetric point T = 0 s. Target signal (magnetic field) independent sensitivity. T ( B) T0 cb T S ( B) c B