Phelim Bradley            Quantised         Conductance in Self-         Breaking Nanowires      Mentor: John MacHale     ...
2                                                              Contents• Quantised Conductance• Feedback controlled Electr...
3                                               Quantised Conductance• When the wire length is less than the Fermi Wavelen...
4                                                          Motivation• To understand the fabrication and properties of nan...
5.                                                                      Feedback Controlled Electromigration  • Electromig...
7                                                                                     Self-Breaking Regime• At room temper...
Variation in Traces  Pt                                             Au•Data from John MacHale Tyndall.•40 Gold traces, 91 ...
What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from indiv...
Single levels•Single stableplateau•Usually singleGaussian histogram– normal distribution.•Little or no finestructure inhis...
Step Traces•Conductance Plateuas•Staircase like drops in conductance ~G0•Structure in the histogram                       ...
Multi-Level Systems•   Multi-level systems can be                       [4] Halbritter, A., L. Borda, and A. Zawadowski, S...
n-Level systems•   Both “slow and fast” n-level systems•   Slow = transition rate between the two states can be of the ord...
Previous Research•   Mechanically controllable break junctions (MCBJ)•   Slowly stretch the wire and measure conductance t...
Diffusion argument• Based on the MCBJ data it would be nice to assume each atom  gives a contributions of G0 to the conduc...
Orbital Contributions and Shell Effects•Below are theoretical models for contributions of given orbitals totransmission.•C...
What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from indiv...
Histogram Analysis• Fit multiple  Gaussians to  histogram.• Isolate position and  size of a quantum  conductance  channel....
Difficulties in Histogram analysis.• Fine structure of  histograms varied  hugely so finding a  consistent fitting  regime...
What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from indiv...
Histogram Conductance Levels•Distribution of peak conductance levels.•Shows lots of structure Pt 4-5Go and in tunnelling r...
Overview of histogram Analysis• Can see evidence of recurring levels.                                                     ...
What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from indiv...
Cumulative Histogramwww.tyndall.ie
What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from indiv...
Correlation Analysis                               Slide adapted from presentation by Prof. Halbritter, Budapest Universit...
Correlation AnalysisPlatinum                    Gold           www.tyndall.ie
Is there actually correlation?•   Ran n-1 correlation analysis.                                    www.tyndall.ie
What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from indiv...
Au vs Pt• Pt more stable as expected.  – Pt ~1% break (1/90) Au 40% (16/40) break  – Pt ~40% (37/90) Au 55% (22/40) enter ...
What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from indiv...
Typical behaviour?• Predicting the behaviour of an individual trace is extremely  difficult.• Can only really give a stati...
Summary and Future Research•Evolution of conductance in self-breaking nanowires is a complexstatistical process.•Diffusion...
Questions?Questions?             www.tyndall.ie
Differential Histogram Analysis•   Enables to distinguish “fast” and    “slow” n-level states.•   Both would show similar ...
Conductance Level JumpsPlatinum                    Gold           www.tyndall.ie
Outlierswww.tyndall.ie
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Quantised Conductance in Self Breaking Nanowires

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PY4116 Final Report Presentation.
Phelim Bradley
March 21 2012

Published in: Technology, Education
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  • The equivilant unit of resistance quantisation R0=h/e2 is called the Von Kiltzing constant after Klaus Von Kiltzing who received the nobel prize for the first experimental evidence of conductance quantisation in 1980.
  • Note plateuas and jumps. Ramp up voltage The force on the adatoms is caused by the electronic wind through the hot neck [2]. The electromigration occurs at critical power dissipation P*=I*2/G in the neck of the bridge [3]. The voltage across the gap is increased until a 4% (for R < 1 kΩ) or 8% (R>1kΩ) increase in R is observed [see Figure 1]. Then, the voltage is dropped and the process is repeated. In this way the voltage is kept at a critical level for electromigration to occur. TEM images of FCEM nanogaps show well-defined facets, and as such show that melting is avoided.
  • However, it is possible for values of less then G0 to be seen before the tunnelling regime due to fractional contributions from conducting channels with transmission probabilities less than one i.e. non-ballistic channels. It has been shown that conductance plateaus in this regime can form at values which do not correspond to integer multiples of G0
  • Note that the histograms will look the same
  • Note majic numbers found in van ruitenbeek paperIn low temperature investigations of quantum conductance the atoms are frozen in certain configurations with preferred conductance values for this configuration. However, in room temperature (as considered in this project) atomic mobility plays a large role and atoms can self-organise to find the most stable configuration. As such, preferred conductance in our data reflects preferred stable radii, as opposed to preferred conductance for a frozen configuration as in the case of low temperature experiments
  • Note the lack of evidence of stable levels from area under histogram, this is an artifact of the fitting rather then a real result.Note small statistical size.Note peaks with contributions from multiple levels.
  • AS expected PT more stable.Gold has more fine strucrure, higher number of peaks on average with larger distribution. PT has narrower distribution and lower average.Also note the differences earlier on with regards prefered levels.
  • Previously, the Lorenztian distributions of differential histograms have shown shoulders on the cumulative histogram. We have shown that these shoulders emerge from a subset of the traces showing strong shoulders due to FMLS.
  • Note sharp peak in most probable transition.
  • Quantised Conductance in Self Breaking Nanowires

    1. 1. Phelim Bradley Quantised Conductance in Self- Breaking Nanowires Mentor: John MacHale Supervisor: Dr. Aidan Quinnwww.tyndall.ie
    2. 2. 2 Contents• Quantised Conductance• Feedback controlled Electromigration.• MCBJ and previous research.• Analysis of self-breaking region of nanobridges.• Degree of variability in traces.• Isolation of the contribution from individual conductance channels.• Preferred and stable conductance levels.• Favorable transitions.• Differences between Au and Pt. www.tyndall.ie
    3. 3. 3 Quantised Conductance• When the wire length is less than the Fermi Wavelength, quantised conductance can be observed. The wire behaves like an electron wave guide with each ballistic channel contributing a maximum conductance:• However, this does not necessarily mean that the conductance will be an integer multiple of G0.• A quantum channel with transmission T<1 contributes < G0 www.tyndall.ie
    4. 4. 4 Motivation• To understand the fabrication and properties of nanoscale metallic structures.• Vital importance in next generation of sub 10nm electronics.• Intellectual pursuit of understanding the quantum world. www.tyndall.ie
    5. 5. 5. Feedback Controlled Electromigration • Electromigration is the transport of material due to the electronic wind force.[1] • Occurs at a critical power dissipation in the neck.[2]“Unzipping” of bridge via FCE-assisted diffusion, Strachan et al.,Phys. Rev. Lett. 100, 056805 (2008) [1.] Rous, P.J., Driving force for adatom electromigration within mixed Cu/Al overlayers on Al(111). J. Appl. Phys., 2001. 89: p. 4809. www.tyndall.ie
    6. 6. 7 Self-Breaking Regime• At room temperature is can be high enough to break the bridge entirely without even applying a bias once the conductance has fallen below a certain value• When the conductance reaches a certain level is unstable even when the current is reduced to 0.• Gold (Au) nanobridges with diameters – ~5G0 can be stable on the order of days. – ~20G0 can be stable for months. [2]• In Platinum (Pt) the activation energy is higher so self breaking at room temperature is uncommon. [3]• A tunnelling regime is entered once G falls below G0 accompanied by formation of a nanogap. 2. Strachan, D.R., et al., Clean electromigrated nanogaps imaged by transmission electron microscopy. Nano Letters, 2006. 6(3): p. 441-444. 3.Van der Zant, H.S.J., et al., Room-temperature stability of Pt nanogaps formed by self-breaking. Applied Physics Letters, 2009. 94(12). www.tyndall.ie
    7. 7. Variation in Traces Pt Au•Data from John MacHale Tyndall.•40 Gold traces, 91 Platinum. ~15000 data points per trace. www.tyndall.ie
    8. 8. What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from individual conductance channels?• Are there preferred conductance levels?• Which levels are more stable?• Are there favourable transitions?• Differences between Au and Pt.• Is there a “Typical Behaviour”?• If so, what is it and can we describe the outliers? www.tyndall.ie
    9. 9. Single levels•Single stableplateau•Usually singleGaussian histogram– normal distribution.•Little or no finestructure inhistogram www.tyndall.ie
    10. 10. Step Traces•Conductance Plateuas•Staircase like drops in conductance ~G0•Structure in the histogram www.tyndall.ie
    11. 11. Multi-Level Systems• Multi-level systems can be [4] Halbritter, A., L. Borda, and A. Zawadowski, Slow two-level viewed as a double potential systems in point contacts. Advances in Physics, 2004. 53(8): p. 939-1010. with an energy difference Δ between the two (or more) configurations. [4]• A group of atoms can have a transmission between these two states either by tunnelling or at higher temperatures thermal excitation over the barrier .A two-level system as a double well potential withan energy difference between the two positions,and a tunnelling probability T for crossing thebarrier between the two metastable states. W andd denote the width of the barrier and the distancebetween the minima, respectively. www.tyndall.ie
    12. 12. n-Level systems• Both “slow and fast” n-level systems• Slow = transition rate between the two states can be of the order of seconds or longer. Tunnelling case.• Fast = oscillations between metastable states at a rate faster or equal to the measuring rate www.tyndall.ie
    13. 13. Previous Research• Mechanically controllable break junctions (MCBJ)• Slowly stretch the wire and measure conductance throughout.• Mostly low temperature ~4K experiments.• Frozen atomic configurations. Halbritter, A., S. Csonka, et al. (2002). "Connective neck evolution and conductance steps in hot point contacts." Physical Review B 65(4). www.tyndall.ie
    14. 14. Diffusion argument• Based on the MCBJ data it would be nice to assume each atom gives a contributions of G0 to the conductance.• However, we can see in individual trace histograms peaks at non integer multiples of Go with structure - 0.1G0 www.tyndall.ie
    15. 15. Orbital Contributions and Shell Effects•Below are theoretical models for contributions of given orbitals totransmission.•Calculations done at 0K•Long chain = contributions dominated by single orbital.•Short chain = contributions from many orbitals. Pauly, F., M. Dreher, et al. (2006). "Theoretical analysis of the conductance histograms and structural properties of Ag, Pt, and Ni nanocontacts." Physical Review B 74(23): 235106. www.tyndall.ie
    16. 16. What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from individual conductance channels?• Are there preferred conductance levels?• Which levels are more stable?• Are there favourable transitions?• Differences between Au and Pt.• Is there a “Typical Behaviour”?• If so, what is it and can we describe the outliers? www.tyndall.ie
    17. 17. Histogram Analysis• Fit multiple Gaussians to histogram.• Isolate position and size of a quantum conductance channel. www.tyndall.ie
    18. 18. Difficulties in Histogram analysis.• Fine structure of histograms varied hugely so finding a consistent fitting regime without over constraining the fits was non-trivial.• Some of the traces had particularly complex structure and fitting large number of Gaussians to involved minimising large search space. www.tyndall.ie
    19. 19. What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from individual conductance channels?• Are there preferred conductance levels?• Which levels are more stable?• Are there favourable transitions?• Differences between Au and Pt.• Is there a “Typical Behaviour”?• If so, what is it and can we describe the outliers? www.tyndall.ie
    20. 20. Histogram Conductance Levels•Distribution of peak conductance levels.•Shows lots of structure Pt 4-5Go and in tunnelling regime.•Some indictation of preferred values visible. Gold Platinum www.tyndall.ie
    21. 21. Overview of histogram Analysis• Can see evidence of recurring levels. Au www.tyndall.ie
    22. 22. What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from individual conductance channels?• Are there preferred conductance levels?• Which levels are more stable?• Are there favourable transitions?• Differences between Au and Pt.• Is there a “Typical Behaviour”?• If so, what is it and can we describe the outliers? www.tyndall.ie
    23. 23. Cumulative Histogramwww.tyndall.ie
    24. 24. What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from individual conductance channels?• Are there preferred conductance levels?• Which levels are more stable?• Are there favourable transitions?• Differences between Au and Pt.• Is there a “Typical Behaviour”?• If so, what is it and can we describe the outliers? www.tyndall.ie
    25. 25. Correlation Analysis Slide adapted from presentation by Prof. Halbritter, Budapest University Positive correlation Negative correlationPlateaus at both bin i and j A plateau at i or j Or no plateaus at i or j but not both Every bin is correlated with itself, the diagonal Ci,i = 1 j j Ni and Nj Correlated i i Independenti i Anticorrelated j j www.tyndall.ie
    26. 26. Correlation AnalysisPlatinum Gold www.tyndall.ie
    27. 27. Is there actually correlation?• Ran n-1 correlation analysis. www.tyndall.ie
    28. 28. What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from individual conductance channels?• Are there preferred conductance levels?• Which levels are more stable?• Are there favourable transitions?• Differences between Au and Pt.• Is there a “Typical Behaviour”?• If so, what is it and can we describe the outliers? www.tyndall.ie
    29. 29. Au vs Pt• Pt more stable as expected. – Pt ~1% break (1/90) Au 40% (16/40) break – Pt ~40% (37/90) Au 55% (22/40) enter tunneling regime. – Gold tends to have more peaks in a trace. Gold Platinum www.tyndall.ie
    30. 30. What we want to know?• Can we give an idea of the expected degree of variability?• Can we isolate contributions from individual conductance channels?• Are there preferred conductance levels?• Which levels are more stable?• Are there favourable transitions?• Differences between Au and Pt.• Is there a “Typical Behaviour”?• If so, what is it and can we describe the outliers? www.tyndall.ie
    31. 31. Typical behaviour?• Predicting the behaviour of an individual trace is extremely difficult.• Can only really give a statistical evaluation of the life time of a state. www.tyndall.ie
    32. 32. Summary and Future Research•Evolution of conductance in self-breaking nanowires is a complexstatistical process.•Diffusion model 1G0=1atom too simple. Lots of interesting sub-structure.•Can identify indications of preferred levels and transitions.•Further Research•Apply some of this analysis to pre-break data.•Correlation beyond just conductance-conductance•Physical model to explain “magic numbers” – potentially orbitalcontributions www.tyndall.ie
    33. 33. Questions?Questions? www.tyndall.ie
    34. 34. Differential Histogram Analysis• Enables to distinguish “fast” and “slow” n-level states.• Both would show similar histograms.• Fast will have multi “level” differential histograms.• Slow will have close to Lorentzian differential histograms www.tyndall.ie
    35. 35. Conductance Level JumpsPlatinum Gold www.tyndall.ie
    36. 36. Outlierswww.tyndall.ie
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