P. Grutter, McGill University
An Introduction to Atomic Force Microscopy
Peter Grutter
Physics Department
www.physics.mcgill.ca/~peter/
P. Grutter, McGill University
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
P. Grutter, McGill University
Scanning Tunneling Microscope (STM)
• Based on quantum mechanical tunneling current
• Works for electrically conductive samples
• Imaging, spectroscopy and manipulation possible
D. Eigler, IBM Almaden
P. Grutter, McGill University
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
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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
P. Grutter, McGill University
Atomic Force Microscopedeflection sensor
approach
Data acquisition
scanner
feedback
force sensorforce sensor
tiptip
vibration damping
sample
P. Grutter, McGill University
The force sensor Microfabrication of inte-
grated cantilevers with tips
P. Grutter, McGill University
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
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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 massWalters, RSI 67, 3583 (1996)
Excellent discussion and references:www.asylumresearch.com/springconstant.asp
P. Grutter, McGill University
Atomic Force Microscopedeflection sensordeflection sensor
approach
Data acquisition
scanner
tipfeedback
force sensor
vibration damping
sample
P. Grutter, McGill University
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
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Atomic Force Microscopedeflection sensor
approach
Data acquisition
scanner
tipfeedbackfeedback
force sensor
vibration damping
sample
P. Grutter, McGill University
Atomic Force Microscopedeflection sensor
approach
Data acquisition
tipfeedback
force sensor
vibration damping
samplesample
scannerscanner
P. Grutter, McGill University
Piezoelectric scannersProperties:
+y
-x +x
-y
Piezo tube
(2)
2. Creep (history dependent)
3. Aging (regular recalibration)
(1)
1. Hysterisis (non-linear)
P. Grutter, McGill University
Atomic Force Microscopedeflection sensor
approach
Data acquisitionData acquisition
scanner
tipfeedback
force sensor
vibration damping
sample
P. Grutter, McGill University
Creating an image from the feedback signal
line scan
gray scale image
processed image
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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.
P. Grutter, McGill University
Atomic Force Microscopedeflection sensor
approachapproach
vibration vibration dampingdamping
Data acquisition
scanner
tipfeedback
force sensor
sample
P. Grutter, McGill University
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
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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
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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)
Rubbed Nylon LCD alignment layer
Ruetschi, Grutter, Fuenfschilling and Guentherodt,Science 265, 512 (1994)
P. Grutter, McGill University
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
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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)
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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)
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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
P. Grutter, McGill University
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
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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
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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
Meli, Badia, Grutter, Lennox, Nano Letters 2, 131 (2002)
Diblock co-polymer:Normal forces Friction
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Force SpectroscopySnap in condition: k < F’
For meaningful quantitative
analysis, k > stiffness of molecule
a
a
water
force
distance
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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)
Field ion microscope manipulation
of atomic structure of AFM tip
P. Grutter, McGill University
Site specific chemical interaction potential: Si(111) 7x7
Lantz, Hug, Hoffmann, van Schendel, Kappenberg, Martin, Baratoff, and Guentherodt , Science 291, 2580 (2001)
P. Grutter, McGill University
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
P. Grutter, McGill University
DNA “Unwinding”
Nature - DNA replication,polymerization
AFM probe
Au surfaceExperiment - AFM force
spectroscopy
Anselmetti, Smith et. al. Single Mol. 1 (2000) 1, 53-58
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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]
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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.
P. Grutter, McGill University
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)
P. Grutter, McGill University
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
P. Grutter, McGill University
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
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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.
Anczykowski et al., Appl. Phys. A 66, S885 (1998)
P. Grutter, McGill University
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
P. Grutter, McGill University
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
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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)
P. Grutter, McGill University
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)