single-electron devices interpreted by means of waiting time - - PowerPoint PPT Presentation

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single-electron devices interpreted by means of waiting time - - PowerPoint PPT Presentation

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videos are available on the powerpoint version, ask for it: vincent.talbo@gmail.com Frequency-dependent shot noise in single-electron devices interpreted by means of waiting time distributions Vincent Talbo, Javier Mateos, Toms Gonzlez

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Frequency-dependent shot noise in single-electron devices interpreted by means of waiting time distributions

Vincent Talbo, Javier Mateos, Tomás González

Department of Applied Physics University of Salamanca Spain

Sylvie Retailleau, Philippe Dollfus

Institute of Fundamental Electronics CNRS / University Paris-Sud France vtalbo@usal.es

videos are available on the powerpoint version, ask for it: vincent.talbo@gmail.com

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Introduction

COULOMB BLOCKADE AND APPLICATIONS

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From micrometric to nanometric

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3D - bulk 2D – quantum well 1D - nanowire 0D – quantum dot

  • discretization of energy levels
  • gap broadening with reduction of size
  • blue shift

size of the dot

ENERGY Density of states

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Applications in electronics

Granular floating gate FLASH memories

Multiple-tunnel junction FLASH memory

Deleruyelle, Microelec Eng., 2004

  • Writing through

nanocrystals

  • Writing/Reading

decoupled

grille de contrôle

source drain

grille flottante

COULOMB BLOCKADE

  • Tiwari, IEDM, 1995
  • Freescale

Single-Electron Transistor (SET)

Shin, APL, 2010

Thermoelectricity Double-Tunnel junction (DTJ) SHOT NOISE IN DTJ

Time Current

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Coulomb blockade

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double-tunnel junction: simple case of Coulomb blockade

Charging energy: (energy to bring to add an electron in the dot)

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SLIDE 6

COULOMB BLOCKADE

double-tunnel junction: simple case of Coulomb blockade

Charging energy: (energy to bring to add an electron in the dot)

Coulomb blockade

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SLIDE 7

Coulomb blockade

double-tunnel junction: simple case of Coulomb blockade

Charging energy: (energy to bring to add an electron in the dot)

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SLIDE 8

Coulomb blockade

double-tunnel junction: simple case of Coulomb blockade

Charging energy: (energy to bring to add an electron in the dot)

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SLIDE 9

Coulomb blockade

double-tunnel junction: simple case of Coulomb blockade

Charging energy: (energy to bring to add an electron in the dot)

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SLIDE 10

Coulomb blockade

COULOMB STAIRCASE

double-tunnel junction: simple case of Coulomb blockade

Charging energy: (energy to bring to add an electron in the dot)

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SLIDE 11

 Shot noise (SN): Consequence of charge granularity  more information of the electronic transport Between two electrodes: Poissonian transport  Comparison with Poissonian transport S ( f ) current spectral density at frequency f 2e <I> current spectral density of a Poissonian process

  • at f = 0, Fano factor

< 1 : sub-Poissonian noise = 1 : Poissonian noise > 1 : super-Poissonian noise

  • Behaviour at f = 0 already well understood

 

2 F S e I 

Shot Noise in double-tunnel junction

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  2

S f e I

Sub-Poissonian noise : Birk et al., Phys. Rev. Lett, 1995 Super-Poissonian noise in multi-levels QDs: W. Belzig, Phys. Rev. B, 2005 Shot Noise in double-tunnel junction: V. Talbo et al., Fluct. Noise Lett., 2012

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SENS Simulation

MODEL AND RESULTS

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SENS model – Single-Electron Nanodevice Simulation

Electronic structure of Si QDs( wave-function ψ, energy E)

  • 3D solver for Poisson and Schrödinger equations (geometry, bias,

number of electrons)

  • Hartree method, access to the electronic wave-function
  • delocalization of the wavefunction with bias

double-tunnel junction: J.Sée et al., IEEE TED, 2006 double-dot structure: A. Valentin et al., J. Appl. Phys., 2009 single-electron transistor: V. Talbo et al., IEEE TED, 2011

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SENS model – Single-Electron Nanodevice Simulation

Electronic structure of Si QDs( wave-function ψ, energy E)

  • 3D solver for Poisson and Schrödinger equations (geometry, bias,

number of electrons)

  • Hartree method, access to the electronic wave-function

Tunnel transfer rates Γ(Bias, Temperature) from wave functions

  • weak coupling
  • Fermi golden rule and Bardeen formalism
  • decrease (increase) of Γin (Γout) with as consequence of

delocalization of the wavefunction with bias Electronic characteristics

  • Monte-Carlo algorithm: probability to find N electrons in the

dot(P(N))

  • and / or master equation, linked with Korotkov formalism for

noise

  • negative differential conductance when Γin (N) < Γout(N+1)

double-tunnel junction: J.Sée et al., IEEE TED, 2006 double-dot structure: A. Valentin et al., J. Appl. Phys., 2009 single-electron transistor: V. Talbo et al., IEEE TED, 2011

tunnel transfer rates (108 s-1) Γout(N) Γin(N) bias (V) current (pA) bias (V) 14/07/2015

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Results

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15 Ø = 10 nm hS = 1.2 nm hD = 1.8 nm T = 0 K

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Results – Sub-Poissonian case

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  • remains sub-Poissonian with frequency

Monte – Carlo simulation

1st electron in excess 2nd electron in excess

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Results – Super-Poissonian “bunching”

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  • remains super-Poissonian with frequency

Monte – Carlo simulation

1st electron in excess 2nd electron in excess 3rd electron in excess 4th electron in excess

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Results – Near-Poissonian (F = 1.01)

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Where this specific dynamics is coming from ?

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3-state case

CORRELATIONS AND WAITING TIME DISTRIBUTIONS

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Results

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Monte – Carlo simulation

frequency (Hz) spectral density / 2e<I> time lag (s) autocorrelation function (pA)

1st electron in excess 2nd electron in excess

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How to understand the behaviour of auto-correlation functions ?

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tunnel events through source: 01 and 12

partial AUTO-CORRELATIONS C01-01 C12-12 + partial CROSS-CORRELATIONS C01-12 C12-01 = total auto-correlation CII Probabilities of 01 and 12 peaks WAITING TIME DISTRIBUTIONS WT01-01 WT12-12 WT01-12 WT12-01

12 tunnel events through source time 01 WT01-01 WT01-12 WT12-01 WT12-12

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Electron Waiting Times in Mesoscopic Conductors

  • M. Albert, G. Haack, C. Flindt, and M. Büttiker
  • Phys. Rev. Lett. 2012
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Cross-correlations C01-12 and C12-01

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Monte – Carlo simulation

Prob01-12 = Prob12-01 = 23 %

time lag (s) autocorrelation function (pA) waiting time distribution (μs-1)

  • 2 tunnel events (drain side) between 12 and 01
  • WTD = 0 at short times
  • Negative correlation C12-01
  • No tunnel event between consecutive 01 and

12

  • Poissonian WTD (maximum at 0)
  • High correlation C01-12 at low times

01-12 12-01

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Auto-correlations C12-12 and C01-01

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Monte – Carlo simulation

  • one tunnel event between consecutive peaks
  • WTD = 0 at short times, increases after
  • negative correlation at low times,

increasing later

  • P12-12 is not high enough for C12-12 to remain

negative when WTD increases Prob12-12 = 43 % , Prob01-01 = 12 %

time lag (s) autocorrelation function (pA) waiting time distribution (μs-1)

ORIGIN OF SPECIFIC DYNAMICS

01-12 01-01 12-12 12-01

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Conclusion

The time-dependent physics of electronic transport in double- tunnel junction Obtained from SENS simulator: tunnel transfer rates Understood through the study of the link between: auto- and cross-correlations, probabilities and waiting time distributions High-majority of a given tunnel event: negative correlation

  • Equality of tunnel events: positive correlation
  • "in between": specific dynamics, going from negative to positive

correlation

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Thank you !

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