Feasibility
study
Feasibility study
for for
AFMAFM
probeprobe
calibration
calibration
using
the probe’s
using the probe’s
electrostatic
pull-in instability
Laurens Pluimers pull-in instability
electrostatic
Supervisors:
Dr.ir. W.M. van Spengen
Prof.dr.ir. A. van Keulen
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Kilometer(km)
Scaling
Meter(m)
Millimeter(mm)
103
Micrometer(µm)
100
Nanometer(nm)
10-3
Picometer(pm)
10-6
10-9
10-12
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Microscopes
Optical microscope
Hair:
40-80 µm
Resolution: 200nm
Atomic force
microscope (AFM)
DNA:
10-30 nm
Atoms:
30-300 pm
Source: andrew.cmu.edu
Resolution:
100pm
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Feasibility study for AFM probe calibration
using the probe’s electrostatic pull-in instability
Feasibility study for AFM probe
calibration using the probe’s
electrostatic pull-in instability
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4
Feasibility study for AFM probe calibration
using the probe’s electrostatic pull-in instability
Feasibility study for AFM probe
calibration using the probe’s
electrostatic pull-in instability
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5
Feasibility study for AFM probe calibration
using the probe’s electrostatic pull-in instability
Feasibility study for AFM probe
calibration using the probe’s
electrostatic pull-in instability
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6
Feasibility study for AFM probe calibration
using the probe’s electrostatic pull-in instability
Feasibility
study for AFM probe
Outline
calibration using the probe’s
 Introduction Atomic Force Microscope (AFM)
electrostatic pull-in instability
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7
Feasibility study for AFM probe calibration
using the probe’s electrostatic pull-in instability
Feasibility
study for AFM probe
Outline
calibration using the probe’s
 Introduction Atomic Force Microscope (AFM)
pull-in instability
electrostatic
Probe calibration
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8
Feasibility study for AFM probe calibration
using the probe’s electrostatic pull-in instability
Feasibility
study for AFM probe
Outline
calibration using the probe’s
 Introduction Atomic Force Microscope (AFM)
pull-in instability
electrostatic
Probe calibration

Electrostatic pull-in instability
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9
Feasibility study for AFM probe calibration
using the probe’s electrostatic pull-in instability
Feasibility
study for AFM probe
Outline
calibration using the probe’s
 Introduction Atomic Force Microscope (AFM)
pull-in instability
electrostatic
Probe calibration


Electrostatic pull-in instability
Results of feasibility study
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10
Feasibility study for AFM probe calibration
using the probe’s electrostatic pull-in instability
Feasibility
study for AFM probe
Outline
calibration using the probe’s
 Introduction Atomic Force Microscope (AFM)
pull-in instability
electrostatic
Probe calibration



Electrostatic pull-in instability
Results of feasibility study
Conclusions & Recommendations
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Atomic Force Microscope
Working principle
Laser
Quadrant detector
Cantilever
beam(probe)
Sample
Source: www.bruker.com
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Atomic Force Microscope
Working principle
Source: http://www.youtube.com/watch?v=fivhcWYEtkQ
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Atomic Force Microscope
Setup: Optical beam deflection system
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Atomic Force Microscope
AFM probe
20μm
Source: www.absoluteastronomy.com
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Atomic Force Microscope
Images
Source: www.oist.jp
Topography image of metallic nanoparticles deposited on graphite
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Recap
What is an Atomic Force Microscope (AFM)?



√
“Feeling” the sample surface with probe
Optical beam deflection system
Resolution ~100pm
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Atomic Force Microscope
Modes of operation
 Imaging

Topography scan
 Force measurements

Material properties
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Atomic Force Microscope
Mode of operation: Force measurements
Measurement tip / sample interaction forces:




Atomic bonding
Van der Waals forces
Magnetic forces
Chemical bonding
Probe
h
Sample
Source: www.bruker.com
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Atomic Force Microscope
Interaction forces
Laser
Quadrant
detector
Probe
Material A
Material B
Fint
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Atomic Force Microscope
Interaction forces
y
x
Material A
Material B
“Force” image
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Atomic Force Microscope
Probe calibration
Quadrant
detector
Laser
Probe
k
x
Hooke’s law
Fint=k·x
k=spring constant
Fint
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Probe calibration
Added mass
x
k
Hooke’s law
k
M
Mg
x
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Probe calibration
Euler-Bernoulli beam theory
Cantilever base
L
t
b
k
Ebt 3
4 L3
E  Young's modulus
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Probe calibration
Other calibration methods
Method
Accuracy
Disadvantages
Added mass
15-25%
Destructive, slow
Euler-Bernoulli
beam theory
20-40%
Inaccurate, slow
Nano-Force Balance
0.4%
External equipment,
expensive
Thermal tune
20%
Only compliant beams
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Recap
Why do you need to calibrate the probe?



√
To determine the exact interaction forces
between tip and sample
Bonding forces
Material properties
Disadvantages other methods
 Need for new method
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Probe calibration
New calibration method
Based on probe’s Electrostatic Pull-in Instability (EPI)
Inventor: Prof.dr.ir. F. van Keulen
Improvements:




Wide range of cantilever beams (k= 0.1 – 50 N/m)
Non-destructive
Integrated system in AFM
Fast and easy to use
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Probe calibration
New calibration method
Based on probe’s Electrostatic Pull-in Instability (EPI)
 EPI
 Probe calibration using EPI
 Experimental setup
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Electrostatic Pull-in Instability
Pull-in point
V
Probe
Counter
electrode
DC voltage source
u=d0
u
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Electrostatic Pull-in
Instability
Top view cantilever beam
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Electrostatic Pull-in Instability




Non-linear behaviour of the cantilever
beam
Elastic restoring forces are linear
Electrostatic forces are quadratic
Main advantage: well defined instability
point(pull-in)  measurement
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Probe calibration
Electrostatic pull-in instability
k  0.562
L
 0 r LbV pi2
d 03
 0  Permittivity of free space
 r  Dielectric constant
b
d0
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Probe calibration
EPI: differential gap method
k  0.562
 0 r LbV
d
3
0
2
pi
k  0.562
 0 r Lb V
2/ 3
p2
d
V

2/ 3 3
p1
3
Vp2
p1
Δd
V
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EPI probe calibration
Experimental setup
Model
k  0.562
AFM system
 0 r Lb Vp2/2 3  Vp2/1 3 
3
d 3
Variables:
 Differential gap (Δd)
 Pull-in voltage (Vpi)
 Length (L)
 Width (b)
Accuracy: 5 -15 %
Source: www.bruker.com
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EPI probe calibration
Variables:
 Differential gap (Δd)
Experimental setup
XYZ stage
XYZ stage
Source: www.bruker.com
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EPI probe calibration
Experimental setup
Variables:
 Differential gap (Δd)
 Pull-in voltage (Vpi)
Counter
electrode
XYZ stage
XYZ stage
Source: www.bruker.com
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EPI probe calibration
Experimental setup
Variables:
 Differential gap (Δd)
 Pull-in voltage (Vpi)
Counter
electrode
XYZ stage
XYZ stage
Source: www.bruker.com
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EPI probe calibration
Experimental setup
Variables:
 Differential gap (Δd)
 Pull-in voltage (Vpi)
 Length (L)
 Width (b)
Aspheric lens
Counter
electrode
XYZ stage
Source: www.bruker.com
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EPI probe calibration
Calibration mode
Variable:
 Pull-in voltage (Vpi)
Source: www.bruker.com
Source: www.bruker.com
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EPI probe calibration
Width scan
Variable:
 Width (b)
x
Source: www.bruker.com
Source: www.bruker.com
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EPI probe calibration
Length scan
Variable:
 Length (L)
y
Source: www.bruker.com
Source: www.bruker.com
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EPI probe calibration
Experimental setup
Source: www.bruker.com
Source: www.bruker.com
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Probe calibration
Experimental setup
Aspheric lens
Optical path
Laser
Quadrant
detector
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Probe calibration
Experimental setup
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Probe calibration
Experimental setup
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Probe calibration
Experimental setup
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Probe calibration
Experimental setup
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Probe calibration
Experimental setup
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Results
Performance check:
 Differential gap (Δd)
 Pull-in voltage (Vpi)
 Length (L)
 Width (w)
Calibration test probe
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Results
Width scan
QD output [V]
Width scan EPI
Width
Position stage [µm]
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Results
Length scan
QD output [V]
Length scan EPI
Length
Position stage [µm]
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Results
Length/Width scan
Width [µm]
Length[µm]
EPI
50.59
±0.15
467.34
±0.40
Bruker WL
50.71
±0.3
466.02
±0.3
Error [µm]
0.12
Error [%]
0.23
±0.33
1.32
±0.5
0.28
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Results
Calibration test probe
Probe
Spring constant k [N/m]
NanoWorld
1 (compliant)
2 (stiff)
0.17
46
Δk [%]
EPI
0.143
15.38
16.2
66.6
Requirement: Accuracy 5 -15 %
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Conclusions
Performance check:
 EPI method can be implemented as integrated
system
Calibration test probe:
 EPI calibration method is able to determine the
spring constant of AFM probes
 Accuracy system not within requirements
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Recomendations
Increase accuracy by improving model
 Include fringing field effects
 Tapered end
beam
My model
beam
Reality
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Recommendations
Increase accuracy by improving model
 Include fringing field effects
 Tapered end
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Recommendations
Increase accuracy by improving model
 Include fringing field effects
 Tapered end
Cantilever beam
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Recommendations
Increase accuracy by improving model
 Include fringing field effects
 Tapered end
New model in progress
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Feasibility study for AFM probe
Questions?
calibration
using the probe’s
electrostatic pull-in instability
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Extra sheet
Width scan
QD output [V]
Width scan EPI
Width
Position stage [µm]
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Extra sheet
Width scan
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Extra sheet
Laser + Lens
Width scan
Laser beam
Width cantilever beam
Quadrant detector
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Extra sheet
Extended model
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