www.tyndall. ie Phelim Bradley Quantised Conductance in Self-Breaking Nanowires Mentor: John MacHale Supervisor: Dr. Aidan Quinn
Jun 14, 2015
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Phelim Bradley
Quantised Conductance in Self-Breaking
Nanowires
Mentor: John MacHale
Supervisor: Dr. Aidan Quinn
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• 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.
Contents
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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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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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• 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)
Feedback Controlled Electromigration5.
[1.] Rous, P.J., Driving force for adatom electromigration within mixed Cu/Al overlayers on Al(111). J. Appl. Phys., 2001. 89: p. 4809.
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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.
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).
• 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.
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Pt Au
Variation in Traces
• Data from John MacHale Tyndall.• 40 Gold traces, 91 Platinum. ~15000 data points per trace.
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• 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?
What we want to know?
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Single levels
• Single stable plateau
• Usually single Gaussian histogram – normal distribution.
• Little or no fine structure in histogram
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Step Traces
• Conductance Plateuas
• Staircase like drops in conductance ~G0
• Structure in the histogram
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Multi-Level Systems
• Multi-level systems can be viewed as a double potential 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.
[4] Halbritter, A., L. Borda, and A. Zawadowski, Slow two-level systems in point contacts. Advances in Physics, 2004. 53(8): p. 939-1010.
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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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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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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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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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• 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?
What we want to know?
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Histogram Analysis
• Fit multiple Gaussians to histogram.
• Isolate position and size of a quantum conductance channel.
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• 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.
Difficulties in Histogram analysis.
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• 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?
What we want to know?
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Gold Platinum
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.
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• Can see evidence of recurring levels.
Overview of histogram Analysis
Au
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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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Cumulative Histogram
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• 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?
What we want to know?
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Correlation Analysis
i
j
i
j
i
j
Positive correlationPlateaus at both bin i and j
Or no plateaus at i or j
i
j
Negative correlation
A plateau at i or jbut not both
Independent
Anticorrelated
Ni and Nj
Correlated
Every bin is correlated with itself, the diagonal
Ci,i = 1
Slide adapted from presentation by Prof. Halbritter, Budapest University
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GoldPlatinum
Correlation Analysis
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• Ran n-1 correlation analysis.
Is there actually correlation?
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• 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?
What we want to know?
www.tyndall.ie
• 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
Au vs Pt
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• 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?
What we want to know?
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• Predicting the behaviour of an individual trace is extremely difficult.
• Can only really give a statistical evaluation of the life time of a state.
Typical behaviour?
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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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Questions?
Questions?
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• 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
Differential Histogram Analysis
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Conductance Level Jumps
GoldPlatinum
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Outliers