Post on 23-Dec-2015
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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 instabilityLaurens Pluimers
Supervisors:
Dr.ir. W.M. van Spengen
Prof.dr.ir. A. van Keulen
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103
100
10-3
10-6
10-9
Micrometer(µm)
Nanometer(nm)
Picometer(pm)
Millimeter(mm)
Meter(m)
Kilometer(km)
Scaling
10-12
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Microscopes
Hair:40-80 µm
DNA:10-30 nm
Atoms:30-300 pm
Optical microscope
Resolution: 200nm
Resolution: 100pm
Source: andrew.cmu.edu
Atomic force microscope (AFM)
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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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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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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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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
Outline
Introduction Atomic Force Microscope (AFM)
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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
Outline
Introduction Atomic Force Microscope (AFM) Probe calibration
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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
Outline
Introduction Atomic Force Microscope (AFM) Probe calibration Electrostatic pull-in instability
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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
Outline
Introduction Atomic Force Microscope (AFM) Probe calibration Electrostatic pull-in instability Results of feasibility study
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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
Outline
Introduction Atomic Force Microscope (AFM) Probe calibration Electrostatic pull-in instability Results of feasibility study Conclusions & Recommendations
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Atomic Force MicroscopeWorking principle
Quadrant detectorLaser
Cantilever beam(probe)
Sample
Source: www.bruker.com
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Atomic Force MicroscopeWorking principle
Source: http://www.youtube.com/watch?v=fivhcWYEtkQ
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Atomic Force MicroscopeSetup: Optical beam deflection system
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Atomic Force MicroscopeAFM probe
20μmSource: www.absoluteastronomy.com
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Atomic Force MicroscopeImages
Topography image of metallic nanoparticles deposited on graphite
Source: www.oist.jp
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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 MicroscopeModes of operation
Imaging Topography scan
Force measurements Material properties
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Atomic Force MicroscopeMode of operation: Force measurementsMeasurement tip / sample interaction forces:
Atomic bonding Van der Waals forces Magnetic forces Chemical bonding
Probe
Sample
h
Source: www.bruker.com
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Atomic Force MicroscopeInteraction forces
Material A
Material B
Quadrant detector
Laser
Probe
Fint
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Atomic Force MicroscopeInteraction forces
x
y
“Force” imageMaterial A
Material B
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Atomic Force MicroscopeProbe calibration
k
Fint
x
Hooke’s lawFint=k·x
Probe
LaserQuadrant detector
k=spring constant
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Probe calibrationAdded mass
M
x
Hooke’s law
k
Mgxk
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Probe calibrationEuler-Bernoulli beam theory
t
Lb
Cantilever base
3
34EbtL
k Young's modulusE
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Probe calibrationOther 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 calibrationNew 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 calibrationNew 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
V
u=d0 u
Probe
Counter electrode
DC voltage source
Pull-in point
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Electrostatic Pull-in Instability
Top view cantilever beam
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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
Electrostatic Pull-in Instability
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Probe calibration Electrostatic pull-in instability
20
30
0.562 r piLbVk
d
Lb
d0
0 Permittivity of free space
Dielectric constantr
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20
30
0.562 r piLbVk
d
32/3 2/3
0 2 1
30.562
r p pLb V Vk
d
Probe calibration EPI: differential gap method
Vp1
V V
Vp2
Δd
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EPI probe calibration Experimental setup
Variables: Differential gap
(Δd) Pull-in voltage
(Vpi) Length (L) Width (b)
32/3 2/30 2 1
30.562
r p pLb V Vk
d
Accuracy: 5 -15 %
Model
Source: www.bruker.com
AFM system
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EPI probe calibration Experimental setup
XYZ stage
Variables: Differential gap (Δd)
XYZ stage
Source: www.bruker.com
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EPI probe calibration Experimental setup
Variables: Differential gap (Δd) Pull-in voltage (Vpi)
Source: www.bruker.com
XYZ stage
Counter electrode
XYZ stage
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EPI probe calibration Experimental setup
Variables: Differential gap (Δd) Pull-in voltage (Vpi)
Source: www.bruker.com
Counter electrode
XYZ stageXYZ stage
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EPI probe calibration Experimental setup
Variables: Differential gap (Δd) Pull-in voltage (Vpi) Length (L) Width (b)
Source: www.bruker.com
Counter electrode
XYZ stage
Aspheric lens
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EPI probe calibration Calibration mode
Source: www.bruker.com
Variable: Pull-in voltage (Vpi)
Source: www.bruker.com
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EPI probe calibration Width scan
x
Source: www.bruker.com
Variable: Width (b)
Source: www.bruker.com
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EPI probe calibration Length scan
y
Source: www.bruker.com
Variable: Length (L)
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
Optical path
Laser
Aspheric lens
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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ResultsWidth scan
Width
Position stage [µm]
QD
ou
tpu
t [V
]
Width scan EPI
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ResultsLength scan
Length
Position stage [µm]
QD
ou
tpu
t [V
]
Length scan EPI
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ResultsLength/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 ±0.33 1.32 ±0.5
Error [%] 0.23 0.28
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ResultsCalibration test probe
Probe Spring constant k [N/m] Δk [%]
NanoWorld EPI
1 (compliant)
0.17
2 (stiff) 46
0.143 16.2
15.38 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 beam
My model 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 calibration using the probe’s electrostatic pull-in instabilityQuestions?
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Extra sheetWidth scan
Width
Position stage [µm]
QD
ou
tpu
t [V
]
Width scan EPI
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Extra sheetWidth scan
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Laser + Lens
Quadrant detector
Laser beam
Width cantilever beam
Extra sheetWidth scan
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Extra sheetExtended model