PY4116 Final Report Presentation. Phelim Bradley March 21 2012

1. Phelim Bradley
Quantised
Conductance in Self-
Breaking Nanowires
Mentor: John MacHale
Supervisor: Dr. Aidan
Quinn
www.tyndall.ie

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.
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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
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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.
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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. 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).
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7. Variation in Traces
Pt Au
•Data from John MacHale Tyndall.
•40 Gold traces, 91 Platinum. ~15000 data points per trace.
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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?
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9. Single levels
•Single stable
plateau
•Usually single
Gaussian histogram
– normal distribution.
•Little or no fine
structure in
histogram
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10. Step Traces
•Conductance Plateuas
•Staircase like drops in conductance ~G0
•Structure in the histogram
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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 with
an energy difference between the two positions,
and a tunnelling probability T for crossing the
barrier between the two metastable states. W and
d denote the width of the barrier and the distance
between the minima, respectively.
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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
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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).
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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
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15. Orbital Contributions and Shell Effects
•Below are theoretical models for contributions of given orbitals to
transmission.
•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.
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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. Histogram Analysis
• Fit multiple
Gaussians to
histogram.
• Isolate position and
size of a quantum
conductance
channel.
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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.
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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. 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
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21. Overview of histogram Analysis
• Can see evidence of recurring levels.
Au
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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. Cumulative Histogram
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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. Correlation Analysis
Slide adapted from presentation by Prof. Halbritter, Budapest University
Positive correlation Negative correlation
Plateaus 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
Independent
i
i Anticorrelated
j j
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26. Correlation Analysis
Platinum Gold
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27. Is there actually correlation?
• Ran n-1 correlation analysis.
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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. 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
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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. 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.
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32. Summary and Future Research
•Evolution of conductance in self-breaking nanowires is a complex
statistical 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 orbital
contributions
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33. Questions?
Questions?
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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
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35. Conductance Level Jumps
Platinum Gold
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36. Outliers
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