AFM for Measuring Surface Topography and Forces

Andreas Fery

ENB 2007 07.03.2007

• Scanning Probe : What is it and why do we need it ?

• AFM as a versatile tool for local analysis and manipulation

Dates

Course today 2* 1h with 15 min break

do it yourself AFM :

Tomorrow, starting 9:00 in AFM Lab in PCII

Scanning Probe : What is it an why do we need it

versus

IBM

How sensitive is an AFM ?

AFM-sensitivity translated to themacro-scale

Matterhorn = AFM tip

Ping Pong ball = moleculardimensions

Why should one try somethingso difficult ?

optical microscopy: the fraunhofer limit

a point source imagedby a lens of finite sizetransforms into an airydisc pattern due to diffraction

this sets a natural limit to theresolution of far field wave opticsdevices

2minλ≈∆x

solving the problem

1. usage of shorter wavelengthProblems: adsorption of the beam by glass for UV , the beam itself for x-Ray

2. usage of high speed electronsProblems: electron source, samples can only be observed in UHV, oxidation of the sample

3. Scanning techniquesProblems: long measurement time, UHV (for SEM), sample can be damaged due to probe sample interactions

Resolution of SPMs

the resolution of SPMs is determined by:

• the spatial dimension of the probe → the probe has to be small

• the distance probe-surface → the probe has to be a point probe

scanning probe microscopes are surface microscopes

The different types of SPM

• the nature of the interaction determines the property of the sample that is investigated

• the strength of the interaction used in SPM determines whether one observes or modifiesthe sample: SPM as a microscope or a tool

interaction

The different types of SPM

– STM: scanning tunnelling microscopy– SFM: scanning force microscopy– SNOM: scanning near-field optical microscopy

– SEM: scanning electron microscopy– SCM: scanning capacitance microscopy– SThM: scanning thermal microscopy– SICM: scanning ion conductance microscopy– SAM: scanning acoustic microscopy– …

the right tool for the right problem

the surface of a magneto-optic medium seen in AFM

the same part of the sampleimaged in MFM(Magnetic force microscopy)

AFM schematically

Sample

AFM-Probe mounted on springLaserdiode Mirror

Photodiode

Spring deflection detection

XYZ Piezo-Scanner

Sample - Probe displacement

Feedback MechanismFeedback

Piez

o

Substrate

P

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o

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o

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o

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o

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o

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o

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o

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Piez

o

Substrate

P

Substrate

Jump to Contact

Jump off contact

Hysteresis

Jump to Contact

Jump off Contact

Deflection-DisplacementCharacteristics

AFM-Tip Approaching and Retracting

Deflection as a function of the distance

Contact Region Non-Contact Region

Stable Contact Unstable

Very stablevery damagingshear forces

Too unstablebut would be less damaging

force-distance characteristics

AFM Imaging

Idea : Stay at the same separation by keeping tip-sampleInteractions constant while scanning the sample

z-Position controlled by feedbackxy-Position is scanned

Possible feedback parameters :

Spring deflection : Contact Mode

For vibrating tips : Amplitude of vibration

principle Contact mode

Example

DNA on a micasurface

molecular resolutionfor a nonconductingsample in air

Convolution Effects

One thing to keep in mind : convolution effect

„The smaller thing images the bigger thing“

The signal is always a convolution of sample topographyAnd tip topography

a bigger issue for AFM than for STMTips should be as sharp as possible (10nm standard)

Artifacts

DNA and debris PS „spheres“

How can you check if this is an artifact ??

Example : Surface Damage

Molecules are „swept“ out off the scanned Area

example : surface modification

using the possibility to exert forces with the afm:

nano- sculptures

recording friction

friction propertiescan be recordedby monitoringthe torsion of thecantilever

example LFM

hydrophobic and hydrophilic regions can beclearly destinguished inLFM

Methods Using Vibrating Tips

No permanent tip-sample contact

No shear forces

Tapping Mode, Intermittent Contact Mode And Non-Contact Mode are themost successful methods for pure imaging

Advantages :

Non-contact imaging possible

Feedback parameter : Amplitude

Dynamic AFM

Tip+cantilever can be described as harmonic oscillator

extFkxtxm =+

∂∂

2

2

( )tAF extext ωsin=

( ) ( )( )ωφωω += tAtx sin)(

wR : resonance-frequency

ww R

A(w) : Amplitude

F(w) : Phase Shift

mk

R =ω

Here :

Vibrating Tip and Surface Forces

extFkxtxm =+

∂∂

2

2

( ) extsurf FxFkxtxm =++

∂∂

2

2

Simple picture :

Long-range attractive forceSpring force

Simplify force(linear approx.)

A spring again,but k has decreased

An attractive force gradient results inan effective decrease of the spring constant

Effect on Vibration

Excitation frequency stays at wR , therefore :

Phase changes

A changes

Amplitude can serve as Feedback parameter

w

Phas

e-sh

ift

Am

plitu

de

Free vibration(no surface force)

w Ext = wR

Excitation frequ.equals res. frequ.

w ExtSurface influenced vibration

wR

k effectivelydecreases

mk

R =ω

example

soft ultrathin pattern on siliconwafer

(single molecular resolutionunder water)

Vibrating Tip Revisited: Phase Contrast

Chemically heterogeneous surface

Region 1F

D

Region 2F

D

Different surfaceforces Long-range

repulsiveLong-rangeattractive

Different Phase Shiftat same amplitude

w Rw R

Phase 1

Phase 2

Example Phase Contrast

Phase Image (right) shows Material Contrast Here : film of Diblockcopolymer mixture

(images courtesy M. Schneider / H. Schlaad)

AFM for Measuring Surface Topography and Forces II

Andreas Fery

ENB 2007 07.03.2007

• Force Spectroscopy : AFM for measuring forces

• Modern trends in AFM

Piez

o

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Piez

o

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P

Substrate

Jump to Contact

Jump off contact

Hysteresis

Jump to Contact

Jump off Contact

Deflection-DisplacementCharacteristics

AFM-Tip Approaching and Retracting

Simulating a measured curve

F

D

Piezo ext.

Rest position

Def

lect

ion

Piezo ext.

Det. Deflection

F

D

Piezo ext. Def

lect

ion

Piezo ext.

F

D

Def

lect

ion

Piezo ext.

F

D

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lect

ion

Piezo ext.

Instability !

unstable

stable

F

D

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lect

ion

Piezo ext.

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D

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lect

ion

Piezo ext.

F

D

Def

lect

ion

Piezo ext.

F

D

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lect

ion

Piezo ext.

Instability

Def

lect

ion

Piezo ext.

F

D

Impact of the spring constant on stability

B. Cappella and G. Dietler, "Force-distance curves by atomic force microscopy", Surface Science Reports, 34, 1-+, (1999)

Impact of the spring constant on stability 2

B. Cappella and G. Dietler, "Force-distance curves by atomic force microscopy", Surface Science Reports, 34, 1-+, (1999)

From raw data to force-distance

1) Photodetector signal [V]

2) Piezo displacement [m] Distance probe-surface [m]

Interaction force [N]

1) : a) get sensitivity from force-deflection characteristic of hard sample( photodiode signal [V] -> deflection [nm] )

b) determine spring constant( deflection [nm] -> force [N] )

2) : a) use calibrated Piezo / measure displacementb) subtract/add cantilever deflection from piezo position

added mass effect

J. P. Cleveland, S. Manne, D. Bocek and P. K. Hansma, Review of Scientific Instruments,64, 403-405, (1993)

added mass effect 2

J. P. Cleveland, S. Manne, D. Bocek and P. K. Hansma, "A Nondestructive Method forDetermining the Spring Constant of Cantilevers forScanning Force Microscopy", Review of Scientific Instruments, 64, 403-405, (1993)

thermal noise spectrum

J. L. Hutter and J. Bechhoefer, "Calibration of Atomic-force microscopy tips", Rev. Sci. Instrum., 64, 1868, (1993)

Two worlds

I have measured that myAFM tip is attracted with15 nN force at 10 nm distance

Experimentalist

I have calculated that 2 infinite half spaces of this material shouldhave an interaction energy/area of 1J/m2 at this distance

Theoretician

How can we build a bridge from one to the other ??

A bridge

)(2)(21

21 DWRR

RRDF+

= π

2R2

2R1

D

infinite half space

infinite half space

D

F(D) : interaction Force W(D) : interaction energyper area

Derjaguin relation :

valid for all forces, as longas R >> range of force

Typical AFM cantilevers

Here : radius of tip R notmuch bigger than typicalinteraction ranges

Colloidal Probe AFM

A typical protein for single moleculeexperiments : Titin

His-Tag to allow for easy

purificationMultiple repeats of TI I27

free SH allows for attachment to

gold surfaces

The AFM ExperimentThe AFM Experiment

Pulling chains off the surface

ksp

v

Force = ksp × Deflection

Stage Position = v × Time

Pulling chains off the surface

Pulling chains off the surface

Pulling chains off the surface

Pulling chains off the surface

Pulling chains off the surface

Pulling chains off the surface

Pulling chains off the surface

statistical variation:

to few unfolding events :not the full protein is stretched

to many unfoldingevents, more than 1 protein

statistics over many pulls

to compensate for that, statistics over many pulls is necessary

from this the „typical“ curve is obtained

what does the peak force mean ?

influence of additionalcoupling to spring :

the force is rate dependent

Fo

rce

(N)

• Unfolding proteins by AFM is a kinetic measurement: average unfolding force depends on pulling speed.

• Average unfolding rates can be estimated by Monte-Carlo simulation or by extrapolation.

Forc

e (N

)

physically meaningful single moleculeexperiments

* average over many experiments to extract the typical set of unfoldinglengths and forces

• do this for different pulling speeds

• compare to molecular dynamics calculations

Real-life Cantilevers

Real-life cantilevers are damped harmonic oscillators

extFkxtxm =+

∂∂

2

2

Ideal, no damping

extFkxtx

txm =+

∂∂

−∂∂ β2

2Real, damping force proportional to speed

Damping broadens the resonance peak, limiting sensitivity

ω

A

50% ofmax. ampl.

ωRes

Damping is characterized by the Q-Factor(Quality Factor)

∆ ω

ωω∆

= RQ Typical Q-factors are between100 and 1000

Q-switching : tuning the resonance

extFkxtx

txm =+

∂∂

−∂∂ β2

2

( )tAF extext ωsin=Usually with

Now, use additional external force coupled to speed, compensating damping

( )txtAF extext ∂

∂−= βωsin Damping force compensated !!

ω

A

ω

A

In theory much better for imaging, in practise sometimes

Q>10000possible

„Supertips“

carbon nanotubes as a try to get the „perfect“ tip (no convolution problem)

Combination AFM - microscopy

general problem in deformation measurements :

only force (indentation) accessible

for (mechanically) complex objectsnot suffcient

methods that combine force-deformation withshape information !

combination RICM - AFM

Combination of force and deformationmeasurements

inter-ferometry

example : buckling process

Setup

Acknowledgement

H. Heinzelmann

Marc Nolte

because they made so nice presentations concerning SPMwhere I could pinch graphics, animation, …