1 challenge the future feasibility study for afm probe calibration using the probe’s electrostatic...

1Challenge the future

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


103

100

10-3

10-6

10-9

Micrometer(µm)

Nanometer(nm)

Picometer(pm)

Millimeter(mm)

Meter(m)

Kilometer(km)

Scaling

10-12


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)




Outline

Introduction Atomic Force Microscope (AFM)




Outline

Introduction Atomic Force Microscope (AFM) Probe calibration




Outline

Introduction Atomic Force Microscope (AFM) Probe calibration Electrostatic pull-in instability




Outline

Introduction Atomic Force Microscope (AFM) Probe calibration Electrostatic pull-in instability Results of feasibility study




Outline

Introduction Atomic Force Microscope (AFM) Probe calibration Electrostatic pull-in instability Results of feasibility study Conclusions & Recommendations


Atomic Force MicroscopeWorking principle

Quadrant detectorLaser

Cantilever beam(probe)

Sample

Source: www.bruker.com


Atomic Force MicroscopeWorking principle

Source: http://www.youtube.com/watch?v=fivhcWYEtkQ


Atomic Force MicroscopeSetup: Optical beam deflection system


Atomic Force MicroscopeAFM probe

20μmSource: www.absoluteastronomy.com


Atomic Force MicroscopeImages

Topography image of metallic nanoparticles deposited on graphite

Source: www.oist.jp


Recap

What is an Atomic Force Microscope (AFM)?

“Feeling” the sample surface with probe Optical beam deflection system Resolution ~100pm

√


Atomic Force MicroscopeModes of operation

Imaging Topography scan

Force measurements Material properties


Atomic Force MicroscopeMode of operation: Force measurementsMeasurement tip / sample interaction forces:

Atomic bonding Van der Waals forces Magnetic forces Chemical bonding

Probe

Sample

h



Atomic Force MicroscopeInteraction forces

Material A

Material B

Quadrant detector

Laser

Probe

Fint


Atomic Force MicroscopeInteraction forces

x

y

“Force” imageMaterial A

Material B


Atomic Force MicroscopeProbe calibration

k

Fint

x

Hooke’s lawFint=k·x

Probe

LaserQuadrant detector

k=spring constant


Probe calibrationAdded mass

M

x

Hooke’s law

k

Mgxk


Probe calibrationEuler-Bernoulli beam theory

t

Lb

Cantilever base

3

34EbtL

k Young's modulusE


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


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

√


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


Probe calibrationNew calibration method

Based on probe’s Electrostatic Pull-in Instability (EPI)

EPI Probe calibration using EPI Experimental setup


Electrostatic Pull-in Instability

V

u=d0 u

Probe

Counter electrode

DC voltage source

Pull-in point



Top view cantilever beam


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



Probe calibration Electrostatic pull-in instability

20

30

0.562 r piLbVk

d

Lb

d0

0 Permittivity of free space

Dielectric constantr


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


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


AFM system



XYZ stage

Variables: Differential gap (Δd)

XYZ stage




Variables: Differential gap (Δd) Pull-in voltage (Vpi)


XYZ stage

Counter electrode

XYZ stage



Variables: Differential gap (Δd) Pull-in voltage (Vpi)


Counter electrode

XYZ stageXYZ stage



Variables: Differential gap (Δd) Pull-in voltage (Vpi) Length (L) Width (b)


Counter electrode

XYZ stage

Aspheric lens


EPI probe calibration Calibration mode


Variable: Pull-in voltage (Vpi)



EPI probe calibration Width scan

x


Variable: Width (b)



EPI probe calibration Length scan

y


Variable: Length (L)



Probe calibration Experimental setup

Optical path

Laser

Aspheric lens

Quadrant detector


Results

Performance check: Differential gap (Δd) Pull-in voltage (Vpi) Length (L) Width (w)

Calibration test probe


ResultsWidth scan

Width

Position stage [µm]

QD

ou

tpu

t [V

]

Width scan EPI


ResultsLength scan

Length


QD

ou

tpu

t [V

]

Length scan EPI


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


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 %


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


Recomendations

Increase accuracy by improving model Include fringing field effects Tapered end

beam beam

My model Reality


Recommendations



Recommendations


Cantilever beam


Recommendations


New model in progress


Feasibility study for AFM probe calibration using the probe’s electrostatic pull-in instabilityQuestions?


Extra sheetWidth scan

Width


QD

ou

tpu

t [V

]

Width scan EPI


Laser + Lens

Quadrant detector

Laser beam

Width cantilever beam



Extra sheetExtended model

1 challenge the future feasibility study for afm probe calibration using the probe’s electrostatic...

Documents

instability slide

future feasibility study

pm slide

future recap

van keulen slide

future microscopes hair

atomic bonding van

pm source