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


Introduction

Introduction

● Outline


● Realization



Experimental setup

Results

Conclusion


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


● Realization



Experimental setup

Results

Conclusion


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


● Realization



Experimental setup

Results

Conclusion


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


● History

● Description

● Forces

● Diffusion

● Activation energy

● Joule Heating


Experimental setup

Results

Conclusion



Introduction


● History

● Description

● Forces

● Diffusion


● Joule Heating


Experimental setup

Results

Conclusion


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


● History

● Description

● Forces

● Diffusion


● Joule Heating


Experimental setup

Results

Conclusion


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


● History

● Description

● Forces

● Diffusion


● Joule Heating


Experimental setup

Results

Conclusion


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


● History

● Description

● Forces

● Diffusion


● Joule Heating


Experimental setup

Results

Conclusion


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


● History

● Description

● Forces

● Diffusion


● Joule Heating


Experimental setup

Results

Conclusion


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


● History

● Description

● Forces

● Diffusion


● Joule Heating


Experimental setup

Results

Conclusion


Joule Heating

The power dissipated in the junction

P ∗ =v∗2

Rj

. (3)

increase the local temperature accelerating the process byfeedback mechanisms.

Introduction



● Quantization (1)


● Breaking phases

Experimental setup

Results

Conclusion



Introduction





● Breaking phases

Experimental setup

Results

Conclusion


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





● Breaking phases

Experimental setup

Results

Conclusion


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





● Breaking phases

Experimental setup

Results

Conclusion


Breaking phases

1. Bulk regime -> continuous resistance (diffusive regime)2. Intermediate steps3. QPC -> discrete resistance due to the size reduction

Introduction



Experimental setup

● Fabrication

● Geometry and sizes

● Four point measurement

● Feedback algorithm

Results

Conclusion


Experimental setup

Introduction



Experimental setup

● Fabrication




Results

Conclusion


Fabrication

■ The junctions (d)–> EBM

■ The connection pads–> Photolithography

Introduction



Experimental setup

● Fabrication




Results

Conclusion


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



Experimental setup

● Fabrication




Results

Conclusion


Four point measurement

Objective: reduce the error for the resistance measurement

Introduction



Experimental setup

● Fabrication




Results

Conclusion


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



Experimental setup

Results

● Electromigration

● Quantization

● Statistical occurence

● Gaps sizes

● Gaps sizes SEM (1)


● Critical power (1)


● Power feedback

Conclusion


Results

Introduction



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


Electromigration

A->B : ohmic responseB->C : controlled breakingC : break point

Introduction



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


Quantization

Instabilities:fluctuation between allowed atomic arrangements

Introduction



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


Statistical occurence

8 measurements were addedNon-integer value due to:■ To small number of measured junction8

■ Occurrence of non-integer value in Gold?

Introduction



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


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



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


Gaps sizes SEM (1)

Introduction



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


Gaps sizes SEM (2)

Introduction



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


Critical power (1)

v∗ =

√

P ∗

G(1 − GRs)(5)

■ Rs approximated asthe start resistance

■ fitting parameter P ∗

■ use least-squarealgorithm

Introduction



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


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



Experimental setup

Results


● Quantization


● Gaps sizes





● Power feedback

Conclusion


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



Experimental setup

Results

Conclusion

● Summary

● References

● Questions ?


Conclusion

Introduction



Experimental setup

Results

Conclusion

● Summary

● References

● Questions ?


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



Experimental setup

Results

Conclusion

● Summary

● References

● Questions ?


References

1. Wikipedia2. (CC-BY-SA) Patrick-Emil Zörner

http://www.wikipedia.org

Introduction



Experimental setup

Results

Conclusion

● Summary

● References

● Questions ?


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]

Technology

Breakjunction for molecular contacting