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
• Ultimate limits
• 3. Components of an AFM
• Cantilever
• Deflection sensing
• Feedback
• Piezo scanners
• Image processing
• 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. Imaging artifacts
• 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
• otherwise Giessibl, APL 78, 123 (2001)

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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
• 2. Other limits
• - sensor shot noise
• - sensor back action
• - Heisenberg
• D.P.E. Smith RSI 66, 3191 (1995)

T4.5K
Arms amplitude
A2 kBT/k
Roseman Grutter, RSI 71, 3782 (2000)
Bottom line Under ambient conditions energy
resolution 10-24J ltlt 10-21J/molecule
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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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Deflection sensors
A

• A) Beam deflection
• B) Interferometry
• C) Piezoresisitive
• D) Piezoelectric

Meyer and Amer, APL53, 1045 (1988)
B
Rugar et al., APL 55, 2588 (1989)
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Feedback modes
z constant
F constant
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Piezoelectric scanners
(1)

• Properties
• 1. Hysterisis (non-linear)
• 2. Creep (history dependent)
• 3. Aging (regular recalibration)

(2)
Piezo tube
y
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Creating an image from the feedback signal
line scan
gray scale image
processed image
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Image processing
Beware of introducing image processing artifacts
! Understand and know what you are doing
Processing (here flatten) can remove them, but
can create new artifacts.
Raw data shows jumps in slow scan direction.
(Due to pointing instabilities of laser).
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Tip-sample approach

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

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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
Rubbed Nylon LCD alignment layer

• Diblock co-polymers used as self assembled etch
  mask

Meli, Badia, Grutter, Lennox, Nano Letters 2,
131 (2002)
Ruetschi, Grutter, Fuenfschilling and
Guentherodt, Science265, 512 (1994)
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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
Magnetic reversal studies by MFM particles size
90 x 240 x 10 nm X. Zhu (McGill)
hard disk floppy disk image
size 10 and 30 micrometers. M. Roseman (McGill)
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Capillary forces (water layer)

• Total force on cantilever
• sum of ALL forces
• 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

Can be LARGE (several 1-10 nN)
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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
Diblock co-polymer Normal forces Friction
Meli, Badia, Grutter, Lennox, Nano Letters 2,
131 (2002)
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Force Spectroscopy
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W(111) tip on Au(111)
Field ion microscope manipulation of atomic
structure of AFM tip

• 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
Induced contraction
elasticity contrast
topography
Cells stiffness increased
B. Smith, N. Durisic, P. Grutter, unpublished
HANKS buffer 1mM serotonin
HANKS buffer no serotonin
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DNA Unwinding
Anselmetti, Smith et. al. Single Mol. 1 (2000) 1,
53-58
AFM probe
Au surface
Nature - DNA replication, polymerization
Experiment - AFM force spectroscopy
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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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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

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)
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Imaging Artifacts
Blunt tip

• High resolution and double tip

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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)