Breakjunction for molecular contacting
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Transcript of Breakjunction for molecular contacting
François Bianco, July 10, 2007 Break junction - p. 1/35
Break junction for molecular electronicsusing electromigration
François Bianco
Introduction
● Outline
● Idea and History
● Realization
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 2/35
Introduction
Introduction
● Outline
● Idea and History
● Realization
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 3/35
Outline
1. Long terms goal and interest of molecular electronics2. Electromigration process3. Breaking phases4. Quantization of the conductance
5. Experimental setup6. Results
■ Conductance quantization■ Electromigration process■ Gap size■ Critical power■ Feedback algorithm
7. Conclusion
Introduction
● Outline
● Idea and History
● Realization
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 4/35
Idea and History
Idea
■ Use molecule as building block for passive and activeelectronic components
■ Extend the Moore’s law beyond the foreseen limit of commonsilicon electronics
■ Access to new quantum effects
History
■ 1940 first theoretical explanation of charge transfer inmolecules
■ 1988 theoretical single-molecule field-effect transistor■ 1997 first measurement of a single molecule conductance
Introduction
● Outline
● Idea and History
● Realization
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 5/35
Realization
The first problem arising is the fabrication of molecular-scaleelectrical contacts. The use of:
■ Scanning tunneling microscope manipulation■ Atomic force microscope manipulation■ Mechanical break junction■ or Electromigration break junction
allows one to reach nanometer-spaced electrodes.
Introduction
Electromigration process
● History
● Description
● Forces
● Diffusion
● Activation energy
● Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 6/35
Electromigration process
Introduction
Electromigration process
● History
● Description
● Forces
● Diffusion
● Activation energy
● Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 7/35
History
■ Failure mechanism of small wires and electronics■ Discovered more than 100 years ago by Gerardin a French
scientist■ Became practical only in the 60s for electronics design■ 1968 James R. Black wrote his famous equation describing
the mean time before failure due to electromigration3
(CC-BY-SA) Patrick-Emil Zörner
Introduction
Electromigration process
● History
● Description
● Forces
● Diffusion
● Activation energy
● Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 8/35
Description
Electromigration (EM) is the ion mass flux driven by a highelectrical current density.
■ Due to collisions between the moving electrons and the ions■ Two types of failure:
◆ Open circuit◆ Short circuit
Introduction
Electromigration process
● History
● Description
● Forces
● Diffusion
● Activation energy
● Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 9/35
Forces
There is two forces acting on the ions
■ Electrostatics force due to the applied voltage Fe
■ Electron wind due to the momentum transfer from theelectrons to the ions Fp
~F = ~Fe − ~Fp. = Z∗e ~E (1)
Introduction
Electromigration process
● History
● Description
● Forces
● Diffusion
● Activation energy
● Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 10/35
Diffusion
The migration of ions takes place where the symmetry isbroken like at:
■ the grain boundaries■ the surface■ or within the lattice at high temperature
Introduction
Electromigration process
● History
● Description
● Forces
● Diffusion
● Activation energy
● Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 11/35
Activation energy
Only the activated ions could participate to the diffusion, this isreflected by the temperature dependent diffusion coefficient:
D = D0e−EA
kT (2)
where EA is the activation energy.
Introduction
Electromigration process
● History
● Description
● Forces
● Diffusion
● Activation energy
● Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 12/35
Joule Heating
The power dissipated in the junction
P ∗ =v∗2
Rj
. (3)
increase the local temperature accelerating the process byfeedback mechanisms.
Introduction
Electromigration process
Conductance quantization
● Quantization (1)
● Quantization (2)
● Breaking phases
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 13/35
Conductance quantization
Introduction
Electromigration process
Conductance quantization
● Quantization (1)
● Quantization (2)
● Breaking phases
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 14/35
Quantization (1)
To get a theoretical explanation of the quantization use thefollowing steps
1. Solve the Schrödinger’s equation2. Assumption translation symmetry in y direction
3. Separate the wavefunction4. Plug the wavefunction into the current density
Contribution to the current density of the electron in mode nky
~jnky= −e
1
L|χn(x, z)|2
︸ ︷︷ ︸
ρ
~ky
m∗~ey
︸ ︷︷ ︸
~v
(4)
ρ charge carrier density, ~v the group velocity
Introduction
Electromigration process
Conductance quantization
● Quantization (1)
● Quantization (2)
● Breaking phases
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 15/35
Quantization (2)
The total current is the sum over ky and n.
■ Cross section determines the boundaries conditions■ Use the Pauli Exclusion Principle■ Possible n bellow the Fermi energy in the wire■ Conductance shows plateaus at integer multiples of the
conductance quantum G0 = 2e2
h.
Introduction
Electromigration process
Conductance quantization
● Quantization (1)
● Quantization (2)
● Breaking phases
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 16/35
Breaking phases
1. Bulk regime -> continuous resistance (diffusive regime)2. Intermediate steps3. QPC -> discrete resistance due to the size reduction
Introduction
Electromigration process
Conductance quantization
Experimental setup
● Fabrication
● Geometry and sizes
● Four point measurement
● Feedback algorithm
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 17/35
Experimental setup
Introduction
Electromigration process
Conductance quantization
Experimental setup
● Fabrication
● Geometry and sizes
● Four point measurement
● Feedback algorithm
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 18/35
Fabrication
■ The junctions (d)–> EBM
■ The connection pads–> Photolithography
Introduction
Electromigration process
Conductance quantization
Experimental setup
● Fabrication
● Geometry and sizes
● Four point measurement
● Feedback algorithm
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 19/35
Geometry and sizes
The connectors are designed for minimizing the resistance forthe voltage pads.
We build two junctions with two different geometries:
■ Wire■ Bowtie
Device Geometry Length (nm) Width (nm) Thickness (nm)
1 & 2 wire 500 70 30
3 & 4 wire 500 75 30
7 & 8 wire 400 80 30
02 bowtie - 100 30
Introduction
Electromigration process
Conductance quantization
Experimental setup
● Fabrication
● Geometry and sizes
● Four point measurement
● Feedback algorithm
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 20/35
Four point measurement
Objective: reduce the error for the resistance measurement
Introduction
Electromigration process
Conductance quantization
Experimental setup
● Fabrication
● Geometry and sizes
● Four point measurement
● Feedback algorithm
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 21/35
Feedback algorithm
Goals:
■ EM in a controlled fashion■ to reach the latest conductance plateau■ and avoid a runaway of the EM
Implementation:
■ Apply voltage ramps■ Control the evolution with different feedback mechanisms
◆ Resistance dR◆ Normalized conductance G/G0
◆ Normalized breaking rate 1
R∂R∂t
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 22/35
Results
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 23/35
Electromigration
A->B : ohmic responseB->C : controlled breakingC : break point
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 24/35
Quantization
Instabilities:fluctuation between allowed atomic arrangements
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 25/35
Statistical occurence
8 measurements were addedNon-integer value due to:■ To small number of measured junction8
■ Occurrence of non-integer value in Gold?
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 26/35
Gaps sizes
The sizes were approximated from SEM pictures.Size Number Yield
< 10 nm 7 23%
10 − 20 nm 5 17%
20 − 50 nm 1 7%Low yields:Feedback take too long to detect the break point (0.1 to 1 s)Reorganization of the atoms the surface
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 27/35
Gaps sizes SEM (1)
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 28/35
Gaps sizes SEM (2)
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 29/35
Critical power (1)
v∗ =
√
P ∗
G(1 − GRs)(5)
■ Rs approximated asthe start resistance
■ fitting parameter P ∗
■ use least-squarealgorithm
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 30/35
Critical power (2)
Geometry Mean critical power (µW ) Standard deviation (µW )
Wire 147 27
Bowtie 158 42■ Feedback mechanism not adapted■ No good approximation for the series resistance■ Wrong idea for the fitting
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
● Electromigration
● Quantization
● Statistical occurence
● Gaps sizes
● Gaps sizes SEM (1)
● Gaps sizes SEM (2)
● Critical power (1)
● Critical power (2)
● Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 31/35
Power feedback
Feedback do not step down the voltage at a constant value :
Conclusion:Feedback only prevents a runaway EM but is not able to detect
it.
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
● Summary
● References
● Questions ?
François Bianco, July 10, 2007 Break junction - p. 32/35
Conclusion
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
● Summary
● References
● Questions ?
François Bianco, July 10, 2007 Break junction - p. 33/35
Summary
Break junction
■ EM process observed■ Quantization of
conductance seen
Feedback
■ Need to detect sooner thebreak point
■ No able to detect the EMbut avoid a runaway of theprocess
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
● Summary
● References
● Questions ?
François Bianco, July 10, 2007 Break junction - p. 34/35
References
1. Wikipedia2. (CC-BY-SA) Patrick-Emil Zörner
Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
● Summary
● References
● Questions ?
François Bianco, July 10, 2007 Break junction - p. 35/35
Questions ?
Science has explained nothing; the more we know the morefantastic the world becomes and the profounder thesurrounding darkness. [Aldous Leonard Huxley]
The important thing is not to stop questioning. [Albert Einstein]