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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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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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