An Application of the Method of Images:

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An Application of the Method of Images Who
would have thought it?   David M. Schaefer,
Matthew Reames, Jeremy Robinson Towson
University   Donald Rimai NexPress
Inc.   Ronald Reifenberger, Brian Walsh Purdue
University Graduate School at U. of MD,
College Park
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Outline

• 1. What is The Method of Images?
• Atomic Force Microscopy
• Description of our experiment
• Analysis and Results

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Method of Images
Solving electrostatic problems involves solving
Laplaces Equation, assuming appropriate boundary
conditions.
?2 V 0
Uniqueness Theorem The solution to Laplaces
equation in some Region is uniquely determined if
the value of V is specified on all Boundaries of
the region
If we can guess at a solution to Laplaces eqn,
and it Satisfies all boundary conditions, then
it is THE solution.
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Classic Image Problem
Suppose a charge q is held a distance d above an
infinite grounded conducting plane. What is the
potential in this region?
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Scanning Probe Microscopy
I. Scanning Tunneling Microscope II Atomic Force
Microscope
Derivative Microscopes Kelvin Probe Capacitance M
agnetic Force Friction Force Electrochemical
General Operation of SPMs
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ATOMIC FORCE MICROSCOPE DESIGN
Diode Laser
Sample
AFM Image
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Nanotechnology Lab at Towson

• Two Commercial SPMs
• One Home built SPM

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Force Measurements with the AFM
Forces Van der Waals Electrostatic Adhesion Elas
tic Modulus Plasticity
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Our Experiment
Purpose To study electrostatic interactions and
charge transfer between micron
size particles and materials.
AFM Cantilever
Charged Particle (4.7 micron radius)
Surface
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Attachment of particles to the cantilever tip
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Particle Attachment
A picture captured by the CCD Camera shows how
the particle was maneuvered onto the tip. Once
the particle was picked up by one of the tungsten
tips and glue was applied to the cantilever tip
the particle was carefully moved onto the
cantilever tip.
When the particle is on the cantilever tip, a UV
light source is incident on the cantilever so the
glue will cure. Once cured, the final product is
a cantilever tip with a particle attached as
seen below
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How do you control the Charge on a Micron Size
Particle?
Photoconducting sphere and substrate
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Force Measurement Procedures

• 1. Charge the sphere
• Turn on UV Source, no sample voltage
• Apply a voltage to the sample
• E field induces a charge separation in sphere
• Turn off UV Source, locking in charge in sphere
• Set surface potential to zero

• 2. Perform Force measurement
• Sample is moved up to sphere until a specified
  force is obtained
• The sample then immediately is withdrawn to
  original position

• 3. Sphere is neutralized
• UV Light is turned on for 30 sec. (surface
  potential still 0)

4. Perform Force measurement
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Results
AMT 2
AMT 1
Initial Charging w/ V -20V. Slight long range
interaction observed.
Neutralization of charge. No long range
interaction observed.
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Results Force Curves
AMT 5 (V -58.64 V)
AMT 3 (V-39.06 V)
AMT 7 (V -78.20 V)
AMT 9 (V -97.8 V)
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Analysis of Long Range Attraction
Determining the position of image
Using Method of Images
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Long Range Interactions
Distance
nm
0
-25
AMF 9
-50
N
n
-75
e
c
r
o
F
-100
-125
-150
-175
0
100
200
300
400
Distance
nm
q3.5871910-16 C
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Long Range Interactions
q3.09070310-16 C
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Long Range Interactions
AMF 5
q2.186110-16 C
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Is the Charge Consistant with our Model?
If the charge, found by fitting our curves, is
correct, we would expect the charge to vary
linearly with the applied voltage.
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Conclusions

• A novel method of producing controllable amount
  of charge
• on a micron size particle has been produced.
• By fitting force curves with a simple theory
  based on the method
• of images, the charge on the sphere was
  determined.
• The charge follows a simple theory which predicts
  linearity in the
• charge vs. voltage plot, with the slope
  approximately as expected.
• These results have consequences for the
  contribution of electrostatics
• to adhesion of nanometer scale contacts.