P. Grutter, McGill University An Introduction to Atomic Force Microscopy Peter Grutter Physics...

P. Grutter, McGill University

An Introduction to Atomic Force Microscopy

Peter Grutter

Physics Department

www.physics.mcgill.ca/~peter/


Outline1. Introduction

2. Magnitude of forces

How to measure forces

3. Components of an AFM

Cantilever

Deflection sensing

Feedback

Piezo scanners

Image processing & artifacts

Approach mechanisms

4. What forces?

Repulsive forces

van der Waals forces

Electrostatic forces

Magnetic forces

Capillary forces

5. Operation modes

Normal and lateral forces

Force spectroscopy

Modulation techniques

AC techniques

Dissipation

6. Ultimate limits

7. Summary


Scanning Tunneling Microscope (STM)

• Based on quantum mechanical tunneling current

• Works for electrically conductive samples

• Imaging, spectroscopy and manipulation possible

D. Eigler, IBM Almaden


Forces between atoms

Bonding energies:• Quantum mechanical

(covalent, metallic bonds): 1-3 nN

• Coulomb (dipole, ionic): 0.1-5 nN

• Polarization (induced dipoles): 0.02-0.1 nNJ. Israelachvili ‘Intermolecular and Surface Forces’ Academic Press

‘Back of the envelope’:• Atomic energy scale:

Ebond ~ 1-4 eV ~ 2-6 • 10-19 J

• Typical bonding length:a ~ 0.2 nm

• Typical forces:

F = E/a ~ 1-3 nN


Measuring forces

Force:

F = k z

Force gradient F’ :

F’= 2k ffapproximation good if

d2V / dz2 = constant for z

otherwise: Giessibl, APL 78, 123 (2001)

z

spring constant k

Harmonic oscillator:

f2 = k /m

F’ acts like a spring in series:

f2 = (k+F’)/m


Atomic Force Microscopedeflection sensor

approach

Data acquisition

scanner

feedback

force sensorforce sensor

tiptip

vibration damping

sample


The force sensor Microfabrication of inte-

grated cantilevers with tips


Spring constants k and resonant frequency f of cantilevers

Spring constant k :

typical values: 0.01 - 100 N/m

Young’s modulus EY ~ 1012 N/m2

Resonant frequency fo:

typical values: 7 - 500 kHz

W

L

t

3

3

4 L

wtEk Y

YE

L

tf

20 162.0


Calibration of cantilever spring constant k

Methods:• Thermal

Hutter and Bechoefer, RSI 64, 1068 (1993)

• Sader method (measure geometry)Sader RSI 66, 9 (1995)

• Reference spring method

M. Tortonese, Park Scientific

• Added massWalters, RSI 67, 3583 (1996)

Excellent discussion and references:www.asylumresearch.com/springconstant.asp


Atomic Force Microscopedeflection sensordeflection sensor

approach

Data acquisition

scanner

tipfeedback

force sensor

vibration damping

sample


Deflection sensors

A

Meyer and Amer, APL53, 1045 (1988)

A) Beam deflection

B

Rugar et al., APL 55, 2588 (1989)

B) Interferometry

C) Piezoresisitive

Giessibl, APL 73, 3956 (1998)

D

D) Piezoelectric



approach

Data acquisition

scanner

tipfeedbackfeedback

force sensor

vibration damping

sample


Feedback modesF = constant z = constant



approach

Data acquisition

tipfeedback

force sensor

vibration damping

samplesample

scannerscanner


Piezoelectric scannersProperties:

+y

-x +x

-y

Piezo tube

(2)

2. Creep (history dependent)

3. Aging (regular recalibration)

(1)

1. Hysterisis (non-linear)



approach

Data acquisitionData acquisition

scanner

tipfeedback

force sensor

vibration damping

sample


Creating an image from the feedback signal

line scan

gray scale image

processed image


Image processing

Raw data shows ‘jumps’ in slow scan direction. (Due to pointing instabilities of laser).

Beware of introducing image processing artifacts !Understand and know what you are doing

Processing (here ‘flatten’) can remove them, but can create new artifacts.


Blunt tip :

Imaging Artifacts

‘High’ resolution and double tip:



approachapproach

vibration vibration dampingdamping

Data acquisition

scanner

tipfeedback

force sensor

sample


Tip-sample approach

• Dynamic range from mm to nm

• Coarse & fine approach!

• Many possibilities:

1. Piezo walkers

2. Lever arms

Micrometer screw 1

Micrometer screw 2

Fixed point


Touching the microscope (e.g. sample, cantilever) will change its temperature T. Shining light on it too! Cantilever has a mass of ~ 1 ng, and thus a VERY small heat capacity.

And finally: thermal drift!

So what!?!

L/L = const T const ~ 10-5


The first AFM

G. Binnig, Ch. Gerber and C.F. Quate, Phys. Rev. Lett. 56, 930 (1986)


Repulsive Contact Forces

Diblock co-polymers used as self assembled etch mask

Meli, Badia, Grutter, Lennox, Nano Letters 2, 131 (2002)

Rubbed Nylon LCD alignment layer

Ruetschi, Grutter, Fuenfschilling and Guentherodt,Science 265, 512 (1994)


Van derWaals forces

FvdW = AR/6z2

A…Hamaker const.R…Tip radiusz…Tip - sample separation

A depends on type of materials (polarizability). For most materials and vacuum A~1eV

Krupp, Advances Colloidal Interface Sci. 1, 113 (1967)

R~100nm typical effective radius

-> FvdW ~ 10 nN at z~0.5 nm


Electrostatic forces

Felectrostatic = RU2/ z

U…Potential differenceR…Tip radiusz…Tip - sample separation

R~100nm typical effective radiusU=1V

-> Felectrostatic ~ 5 nN at z~0.5 nm Tans & Dekker, Nature404, 834 (2000)


Chemical forces

FMorse = Ebond/z • (2e-(z-) - e-2(z-))

Ebond …Bond energy

…decay length radius…equilibrium distance

Other popular choice: 12-6 Lennard Jones potential

Si(111) 7x7

Lantz et al, Science 291, 2580 (2001)


Magnetic Forces

Fmagntic = mtip • Hsample

Comprehensive review: Grutter, Mamin and Rugar, in‘Scanning Tunneling Microscopy II’Springer, 1991

Melting of flux lattice in Nb

Images stray field and thus very useful

in the magnetic recording industry, but

also in science.

Roseman & Grutter, unpublished


Magnetic Force Microscopy

hard disk floppy disk

image size 10 and 30 micrometers. M. Roseman (McGill)

Magnetic reversal studies by MFM

particles size 90 x 240 x 10 nmX. Zhu (McGill)

Tracks on


Capillary forces (water layer)

There is always a water layer on a surface in air!

Fcapillary = 4 R cos

…surface tension, ~10-50 mJ/m2

…contact angle

Surface

Water

Tip

Can be LARGE (several 1-10 nN)

Total force on cantilever =

sum of ALL forces


Different operation modes

• Imaging (DC)• Lateral or frictional forces• Force spectroscopy (F(z), snap-in, interaction potentials,

molecular pulling and energy landscapes)

• Modulation techniques (elasticity, electrical potentials, …)

• AC techniques (amplitude, phase, FM detection, tapping)

• Dissipation


DC Imaging, lateral forces

Meli, Badia, Grutter, Lennox, Nano Letters 2, 131 (2002)

Diblock co-polymer:Normal forces Friction


Force SpectroscopySnap in condition: k < F’

For meaningful quantitative

analysis, k > stiffness of molecule

a

a

water

force

distance


W(111) tip on Au(111)

Cross et al. PRL 80, 4685 (1998)Schirmeisen et al, NJP 2, 29.1 (2000)

Field ion microscope manipulation

of atomic structure of AFM tip


Site specific chemical interaction potential: Si(111) 7x7

Lantz, Hug, Hoffmann, van Schendel, Kappenberg, Martin, Baratoff, and Guentherodt , Science 291, 2580 (2001)


AFM Elasticity Maps of Smooth Muscle Cells

HANKS bufferno serotonin

topography

elasticity contrast

HANKS buffer1M serotonin

induced contraction

cells stiffness increased

B. Smith, N. Durisic, B. Tolesko, P. Grutter, unpublished


DNA “Unwinding”

Nature - DNA replication,polymerization

AFM probe

Au surfaceExperiment - AFM force

spectroscopy

Anselmetti, Smith et. al. Single Mol. 1 (2000) 1, 53-58


DNA Structural TransitionsAFM Force Spectroscopy in TRIS Buffer

300 450 600 750

800

400

0

Duplex poly(dG-dC)

B-S Transition ~ 70 pN

Melting Transition ~ 300 pN

50 75 100 125

800

400

0

For

ce [p

N]

Duplex poly(dA-dT)

B-S Transition ~ 40 pN

Simulation data from Lavery and Lebrun 1997.

B

S

ssDNA Elasticity Model

Molecular Extension [nm] Molecular Extension [nm]


Typical forces and length scales

Gaub Research Group, Munchen


Loading Rate Dependent Unbinding:

Most probable unbinding force:

• Ligand-receptor dissociation forces and rates depend on the rate at which the bond is ruptured!!!• Distinct binding states can be identified from a force v.s. loading rate plot.

Good review: Evans, E. Annu. Rev. Biophys. Biomol. Struct. 2001. 30:105-28.


F(z) as a function of

pulling speed

Clausen-Schaumann et al., Current Opinions in Chem. Biol. 4, 524 (2000)

Merkel et al., Nature 397, (1999)

Allows the determination ofenergy barriers and thus is a direct measure of the energy landscape in conformational space.

Evans, Annu. Rev. Biophys. Biomol. Struct., 30, 105 (2001)


Modulation techniques

Concept: modulate at frequency fmod and use e.g. lock-in detection.

• Elasticity

• Viscoelasticity

• Kelvin probe

• Electrical potential

• Piezoresponse

• ….

Carbon fibers in epoxy matrix,40 micrometer scan Digital Instruments


AC techniques

Change in resonance curve can be detected by:

• Lock-in (A or ) *

• FM detection (f and Adrive)

Albrecht, Grutter, Horne and RugarJ. Appl. Phys. 69, 668 (1991)

(*) used in Tapping™ mode

f

A

f1 f2 f3


Some words on Tapping™

Amount of energy dissipated

into sample and tip strongly depends on operation conditions.

Challenging to

determine magnitude or sign of force.

NOT necessarily less

power dissipation than repulsive contact AFM.

Anczykowski et al., Appl. Phys. A 66, S885 (1998)


Dissipation

The cantilever is a damped, driven, harmonic oscillator

Magnetic dissipation due to domain wall oscillations. Sensitivity better than 0.019 eV per oscillation cycle

Y. Liu and Grutter, J. Appl. Phys. 83, 7333 (1998)

Dissipation due to non-conservative tip-sample interactions such as:• Inelastic tip-sample interactions• Adhesion hysterisis• Joule losses• Magnetic dissipation


Ultimate limits of force sensitivity

1. Brownian motion of cantilever!

thermal limits Martin, Williams, Wickramasinghe JAP 61, 4723 (1987)Albrecht, Grutter, Horne, and Rugar JAP 69, 668 (1991)

D. Sarid ‘Scanning Force Microscopy’

Roseman & Grutter, RSI 71, 3782 (2000)

A2 = kBT/k

A…rms amplitude T=4.5K

2. Other limits:- sensor shot noise- sensor back action- Heisenberg

D.P.E. Smith RSI 66, 3191 (1995)

Bottom line:Under ambient conditions energy resolution ~ 10-24J << 10-21J/molecule

QfkA

TBk

f

f Bo

023

0

2


Outlook

AFM provides imaging, spectroscopy and manipulation capabilities in almost any environment:

ambient, UHV, liquid

at temperatures ranging from mK - 900K

with atomic resolution and sensitivity

(at least in some cases)


AFM provides imaging, spectroscopy and manipulation capabilities in almost any environment:

ambient, UHV, liquid

at temperatures ranging from mK - 900K

with atomic resolution and sensitivity

(at least in some cases)

P. Grutter, McGill University An Introduction to Atomic Force Microscopy Peter Grutter Physics...

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