Preparation of breakjunction for molecular contacting based on electromigration.

1. François Bianco, July 10, 2007 Break junction - p. 1/35
Break junction for molecular electronics
using electromigration
François Bianco

2. Introduction
q Outline
q Idea and History
q Realization
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 2/35
Introduction

3. Introduction
q Outline
q Idea and History
q 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 electronics
2. Electromigration process
3. Breaking phases
4. Quantization of the conductance
5. Experimental setup
6. Results
s Conductance quantization
s Electromigration process
s Gap size
s Critical power
s Feedback algorithm
7. Conclusion

4. Introduction
q Outline
q Idea and History
q Realization
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 4/35
Idea and History
Idea
s Use molecule as building block for passive and active
electronic components
s Extend the Moore’s law beyond the foreseen limit of common
silicon electronics
s Access to new quantum effects
History
s 1940 first theoretical explanation of charge transfer in
molecules
s 1988 theoretical single-molecule field-effect transistor
s 1997 first measurement of a single molecule conductance

5. Introduction
q Outline
q Idea and History
q 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-scale
electrical contacts. The use of:
s Scanning tunneling microscope manipulation
s Atomic force microscope manipulation
s Mechanical break junction
s or Electromigration break junction
allows one to reach nanometer-spaced electrodes.

6. Introduction
Electromigration process
q History
q Description
q Forces
q Diffusion
q Activation energy
q Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 6/35
Electromigration process

7. Introduction
Electromigration process
q History
q Description
q Forces
q Diffusion
q Activation energy
q Joule Heating
Conductance quantization
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 7/35
History
s Failure mechanism of small wires and electronics
s Discovered more than 100 years ago by Gerardin a French
scientist
s Became practical only in the 60s for electronics design
s 1968 James R. Black wrote his famous equation describing
the mean time before failure due to electromigration3
(CC-BY-SA) Patrick-Emil Zörner

8. Introduction
Electromigration process
q History
q Description
q Forces
q Diffusion
q Activation energy
q 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 high
electrical current density.
s Due to collisions between the moving electrons and the ions
s Two types of failure:
x Open circuit
x Short circuit

9. Introduction
Electromigration process
q History
q Description
q Forces
q Diffusion
q Activation energy
q 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
s Electrostatics force due to the applied voltage Fe
s Electron wind due to the momentum transfer from the
electrons to the ions Fp
F = Fe − Fp. = Z∗
eE (1)

10. Introduction
Electromigration process
q History
q Description
q Forces
q Diffusion
q Activation energy
q 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 is
broken like at:
s the grain boundaries
s the surface
s or within the lattice at high temperature

11. Introduction
Electromigration process
q History
q Description
q Forces
q Diffusion
q Activation energy
q 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 is
reflected by the temperature dependent diffusion coefficient:
D = D0e
−EA
kT (2)
where EA is the activation energy.

12. Introduction
Electromigration process
q History
q Description
q Forces
q Diffusion
q Activation energy
q 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 by
feedback mechanisms.

13. Introduction
Electromigration process
Conductance quantization
q Quantization (1)
q Quantization (2)
q Breaking phases
Experimental setup
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 13/35
Conductance quantization

14. Introduction
Electromigration process
Conductance quantization
q Quantization (1)
q Quantization (2)
q 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 the
following steps
1. Solve the Schrödinger’s equation
2. Assumption translation symmetry in y direction
3. Separate the wavefunction
4. 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

15. Introduction
Electromigration process
Conductance quantization
q Quantization (1)
q Quantization (2)
q 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.
s Cross section determines the boundaries conditions
s Use the Pauli Exclusion Principle
s Possible n bellow the Fermi energy in the wire
s Conductance shows plateaus at integer multiples of the
conductance quantum G0 = 2e2
h .

16. Introduction
Electromigration process
Conductance quantization
q Quantization (1)
q Quantization (2)
q 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 steps
3. QPC -> discrete resistance due to the size reduction

17. Introduction
Electromigration process
Conductance quantization
Experimental setup
q Fabrication
q Geometry and sizes
q Four point measurement
q Feedback algorithm
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 17/35
Experimental setup

18. Introduction
Electromigration process
Conductance quantization
Experimental setup
q Fabrication
q Geometry and sizes
q Four point measurement
q Feedback algorithm
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 18/35
Fabrication
s The junctions (d)
–> EBM
s The connection pads
–> Photolithography

19. Introduction
Electromigration process
Conductance quantization
Experimental setup
q Fabrication
q Geometry and sizes
q Four point measurement
q 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 for
the voltage pads.
We build two junctions with two different geometries:
s Wire
s 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

20. Introduction
Electromigration process
Conductance quantization
Experimental setup
q Fabrication
q Geometry and sizes
q Four point measurement
q 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

21. Introduction
Electromigration process
Conductance quantization
Experimental setup
q Fabrication
q Geometry and sizes
q Four point measurement
q Feedback algorithm
Results
Conclusion
François Bianco, July 10, 2007 Break junction - p. 21/35
Feedback algorithm
Goals:
s EM in a controlled fashion
s to reach the latest conductance plateau
s and avoid a runaway of the EM
Implementation:
s Apply voltage ramps
s Control the evolution with different feedback mechanisms
x Resistance dR
x Normalized conductance G/G0
x Normalized breaking rate 1
R
∂R
∂t

22. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 22/35
Results

23. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 23/35
Electromigration
A->B : ohmic response
B->C : controlled breaking
C : break point

24. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 24/35
Quantization
Instabilities:
fluctuation between allowed atomic arrangements

25. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 25/35
Statistical occurence
8 measurements were added
Non-integer value due to:
s To small number of measured junction8
s Occurrence of non-integer value in Gold?

26. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q 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

27. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 27/35
Gaps sizes SEM (1)

28. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 28/35
Gaps sizes SEM (2)

29. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q Power feedback
Conclusion
François Bianco, July 10, 2007 Break junction - p. 29/35
Critical power (1)
v∗
=
P∗
G(1 − GRs)
(5)
s Rs approximated as
the start resistance
s fitting parameter P∗
s use least-square
algorithm

30. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q 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
s Feedback mechanism not adapted
s No good approximation for the series resistance
s Wrong idea for the fitting

31. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
q Electromigration
q Quantization
q Statistical occurence
q Gaps sizes
q Gaps sizes SEM (1)
q Gaps sizes SEM (2)
q Critical power (1)
q Critical power (2)
q 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.

32. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
q Summary
q References
q Questions ?
François Bianco, July 10, 2007 Break junction - p. 32/35
Conclusion

33. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
q Summary
q References
q Questions ?
François Bianco, July 10, 2007 Break junction - p. 33/35
Summary
Break junction
s EM process observed
s Quantization of
conductance seen
Feedback
s Need to detect sooner the
break point
s No able to detect the EM
but avoid a runaway of the
process

34. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
q Summary
q References
q Questions ?
François Bianco, July 10, 2007 Break junction - p. 34/35
References
1. Wikipedia
2. (CC-BY-SA) Patrick-Emil Zörner

35. Introduction
Electromigration process
Conductance quantization
Experimental setup
Results
Conclusion
q Summary
q References
q Questions ?
François Bianco, July 10, 2007 Break junction - p. 35/35
Questions ?
Science has explained nothing; the more we know the more
fantastic the world becomes and the profounder the
surrounding darkness. [Aldous Leonard Huxley]
The important thing is not to stop questioning. [Albert Einstein]