An Introduction to Atomic Force Microscopy

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An Introduction to Atomic Force Microscopy

• Peter Grutter
• Physics Department
• www.physics.mcgill.ca/peter/

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Outline

• 1. 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

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Scanning Tunneling Microscope (STM)

• Based on quantum mechanical tunneling current
• Works for electrically conductive samples
• Imaging, spectroscopy and manipulation possible

D. Eigler, IBM Almaden
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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 nN
• J. 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

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Measuring forces

• Force
• F k Dz
• Force gradient F
• F 2k Df/f
• approximation good if
• d2V / dz2 constant for D z
• otherwise Giessibl, APL 78, 123 (2001)

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Atomic Force Microscope
deflection sensor
approach
force sensor tip
feedback
sample
vibration damping
scanner
Data acquisition
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The force sensor

• Microfabrication of inte-grated cantilevers
  with tips

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Spring constants k and resonant frequency f of
cantilevers

• Spring constant k
• typical values 0.01 - 100 N/m
• Youngs modulus EY 1012 N/m2
• Resonant frequency fo
• typical values 7 - 500 kHz

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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 mass
• Walters, RSI 67, 3583 (1996)
• Excellent discussion and references
• www.asylumresearch.com/springconstant.asp

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Atomic Force Microscope
deflection sensor
approach
force sensor
tip
feedback
sample
vibration damping
scanner
Data acquisition
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Deflection sensors
C) Piezoresisitive
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Atomic Force Microscope
deflection sensor
approach
force sensor
tip
feedback
sample
vibration damping
scanner
Data acquisition
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Feedback modes
F constant
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Atomic Force Microscope
deflection sensor
approach
force sensor
tip
feedback
sample scanner
vibration damping
Data acquisition
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Piezoelectric scanners

• Properties

3. Aging (regular recalibration)
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Atomic Force Microscope
deflection sensor
approach
force sensor
tip
feedback
sample
vibration damping
scanner
Data acquisition
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Creating an image from the feedback signal
line scan
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Image processing
Beware of introducing image processing artifacts
! Understand and know what you are doing
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Imaging Artifacts
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Atomic Force Microscope
deflection sensor
approach vibration damping
force sensor
tip
feedback
sample
scanner
Data acquisition
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Tip-sample approach

• Dynamic range from mm to nm
• Coarse fine approach!
• Many possibilities
• 1. Piezo walkers
• 2. Lever arms

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And finally thermal drift!

• 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.

So what!?!
DL/L const DT const 10-5
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The first AFM

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

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Repulsive Contact Forces

• Diblock co-polymers used as self assembled etch
  mask

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

• FvdW AR/6z2
• AHamaker const.
• RTip radius
• zTip - sample separation
• A depends on type of materials
  (polarizability). For most materials and vacuum
  A1eV
• Krupp, Advances Colloidal Interface Sci. 1,
  113 (1967)
• R100nm typical effective radius
• -gt FvdW 10 nN at z0.5 nm

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Electrostatic forces

• Felectrostatic p e0 RU2/ z
• UPotential difference
• RTip radius
• zTip - sample separation
• R100nm typical effective radius
• U1V
• -gt Felectrostatic 5 nN at z0.5 nm

Tans Dekker, Nature404, 834 (2000)
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Chemical forces
Si(111) 7x7

• FMorse Ebond/z (2e-k(z-s) - e-2k(z-s))
• Ebond Bond energy
• k decay length radius
• sequilibrium distance
• Other popular choice
• 12-6 Lennard Jones potential

Lantz et al, Science 291, 2580 (2001)
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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
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Magnetic Force Microscopy
Tracks on
hard disk floppy disk image
size 10 and 30 micrometers. M. Roseman (McGill)
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Capillary forces (water layer)

• There is always a water layer on a surface in
  air!
• Fcapillary 4p R g cos?
• g surface tension, 10-50 mJ/m2
• ? contact angle

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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

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DC Imaging, lateral forces
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Force Spectroscopy
Snap in condition k lt F
For meaningful quantitative analysis, k gt
stiffness of molecule
force
distance
a
water
a
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W(111) tip on Au(111)

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

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Site specific chemical interaction potential
Si(111) 7x7
Lantz, Hug, Hoffmann, van Schendel, Kappenberg,
Martin, Baratoff, and Guentherodt , Science 291,
2580 (2001)
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AFM Elasticity Maps of Smooth Muscle Cells
elasticity contrast
topography
HANKS buffer no serotonin
B. Smith, N. Durisic, B. Tolesko, P. Grutter,
unpublished
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DNA Unwinding
Anselmetti, Smith et. al. Single Mol. 1 (2000) 1,
53-58
Nature - DNA replication, polymerization
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DNA Structural TransitionsAFM Force
Spectroscopy in TRIS Buffer
Duplex poly(dA-dT)
Duplex poly(dG-dC)
Simulation data from Lavery and Lebrun 1997.
B
800 400 0
800 400 0
ssDNA Elasticity Model
Melting Transition 300 pN
Force pN
S
B-S Transition 70 pN
B-S Transition 40 pN
50 75 100 125
300 450 600 750
Molecular Extension nm
Molecular Extension nm
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Typical forces and length scales
Gaub Research Group, Munchen
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Loading Rate Dependent Unbinding
Good review Evans, E. Annu. Rev. Biophys.
Biomol. Struct. 2001. 30105-28.
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F(z) as a function of pulling speed
Allows the determination of energy barriers and
thus is a direct measure of the energy
landscape in conformational space.
Clausen-Schaumann et al., Current Opinions in
Chem. Biol. 4, 524 (2000)
Merkel et al., Nature 397, (1999)
Evans, Annu. Rev. Biophys. Biomol. Struct., 30,
105 (2001)
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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
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AC techniques

• Change in resonance curve can be detected by
• Lock-in (A or ?)
• FM detection (?f and Adrive)
• Albrecht, Grutter, Horne and Rugar
• J. Appl. Phys. 69, 668 (1991)
• () used in Tapping mode

?f
?A
f1 f2 f3
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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.

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Dissipation

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

• The cantilever is a damped, driven, harmonic
  oscillator

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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

T4.5K
Arms amplitude
A2 kBT/k
Roseman Grutter, RSI 71, 3782 (2000)
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 ltlt 10-21J/molecule
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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)

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• 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)

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• 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)