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An Introduction to Atomic Force Microscopy
Peter Grutter Physics Department P. Grutter, McGill University
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Outline 1. Introduction 2. Magnitude of forces van der Waals 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
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P. Grutter, McGill University
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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 P. Grutter, McGill University
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Forces between atoms ‘Back of the envelope’: Atomic energy scale:
Ebond ~ 1-4 eV ~ 2-6 • J Typical bonding length: a ~ 0.2 nm Typical forces: F = E/a ~ 1-3 nN Bonding energies: Quantum mechanical (covalent, metallic bonds): 1-3 nN Coulomb (dipole, ionic): nN Polarization (induced dipoles): nN J. Israelachvili ‘Intermolecular and Surface Forces’ Academic Press P. Grutter, McGill University
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P. Grutter, McGill University
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Measuring forces Force: F = k Dz Force gradient F’ : F’= 2k Df/f D z
approximation good if d2V / dz2 = constant for D z otherwise: Giessibl, APL 78, 123 (2001) D z spring constant k Harmonic oscillator: f2 = k /m F’ acts like a spring in series: f2 = (k+F’)/m P. Grutter, McGill University
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Atomic Force Microscope
deflection sensor approach force sensor tip feedback sample vibration damping scanner Data acquisition P. Grutter, McGill University
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The force sensor Microfabrication of inte-grated cantilevers with tips
P. Grutter, McGill University
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Spring constants k and resonant frequency f of cantilevers
Spring constant k : typical values: N/m Young’s modulus EY ~ 1012 N/m2 Resonant frequency fo: typical values: kHz W L t P. Grutter, McGill University
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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: P. Grutter, McGill University
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Atomic Force Microscope
deflection sensor approach force sensor tip feedback sample vibration damping scanner Data acquisition P. Grutter, McGill University
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Deflection sensors A) Beam deflection B) Interferometry
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 P. Grutter, McGill University
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Atomic Force Microscope
deflection sensor approach force sensor tip feedback sample vibration damping scanner Data acquisition P. Grutter, McGill University
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Feedback modes F = constant z = constant P. Grutter, McGill University
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Atomic Force Microscope
deflection sensor approach force sensor tip feedback sample scanner vibration damping Data acquisition P. Grutter, McGill University
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Piezoelectric scanners
(1) 1. Hysterisis (non-linear) Properties: (2) 2. Creep (history dependent) 3. Aging (regular recalibration) +y -x +x -y Piezo tube P. Grutter, McGill University
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Atomic Force Microscope
deflection sensor approach force sensor tip feedback sample vibration damping scanner Data acquisition P. Grutter, McGill University
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Creating an image from the feedback signal
gray scale image line scan processed image P. Grutter, McGill University
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Understand and know what you are doing
Image processing Beware of introducing image processing artifacts ! Understand and know what you are doing Raw data shows ‘jumps’ in slow scan direction. (Due to pointing instabilities of laser). Processing (here ‘flatten’) can remove them, but can create new artifacts. P. Grutter, McGill University
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Imaging Artifacts ‘High’ resolution and double tip: Blunt tip :
P. Grutter, McGill University
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Atomic Force Microscope
deflection sensor approach vibration damping force sensor tip feedback sample scanner Data acquisition P. Grutter, McGill University
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Tip-sample approach Dynamic range from mm to nm
Micrometer screw 1 Micrometer screw 2 Fixed point Dynamic range from mm to nm Coarse & fine approach! Many possibilities: 1. Piezo walkers 2. Lever arms P. Grutter, McGill University
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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 P. Grutter, McGill University
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G. Binnig, Ch. Gerber and C.F. Quate, Phys. Rev. Lett. 56, 930 (1986)
The first AFM G. Binnig, Ch. Gerber and C.F. Quate, Phys. Rev. Lett. 56, 930 (1986) P. Grutter, McGill University
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Repulsive Contact Forces
Diblock co-polymers used as self assembled etch mask Rubbed Nylon LCD alignment layer Ruetschi, Grutter, Fuenfschilling and Guentherodt, Science 265, 512 (1994) Meli, Badia, Grutter, Lennox, Nano Letters 2, 131 (2002) P. Grutter, McGill University
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Van derWaals forces FvdW = AR/6z2 -> FvdW ~ 10 nN at z~0.5 nm
A…Hamaker const. R…Tip radius z…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 P. Grutter, McGill University
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Felectrostatic = p e0 RU2/ z
Electrostatic forces Felectrostatic = p e0 RU2/ z U…Potential difference R…Tip radius z…Tip - sample separation R~100nm typical effective radius U=1V -> Felectrostatic ~ 5 nN at z~0.5 nm Tans & Dekker, Nature404, 834 (2000) P. Grutter, McGill University
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FMorse = Ebond/z • (2e-k(z-s) - e-2k(z-s))
Chemical forces Si(111) 7x7 FMorse = Ebond/z • (2e-k(z-s) - e-2k(z-s)) Ebond …Bond energy k …decay length radius s…equilibrium distance Other popular choice: 12-6 Lennard Jones potential Lantz et al, Science 291, 2580 (2001) P. Grutter, McGill University
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Melting of flux lattice in Nb
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
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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) P. Grutter, McGill University
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Capillary forces (water layer)
Total force on cantilever = sum of ALL forces Surface Water Tip Can be LARGE (several 1-10 nN) 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 P. Grutter, McGill University
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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 P. Grutter, McGill University
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DC Imaging, lateral forces
Meli, Badia, Grutter, Lennox, Nano Letters 2, 131 (2002) Diblock co-polymer: Normal forces Friction P. Grutter, McGill University
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Force Spectroscopy Snap in condition: k < F’ force
For meaningful quantitative analysis, k > stiffness of molecule distance a water a P. Grutter, McGill University
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W(111) tip on Au(111) Cross et al. PRL 80, 4685 (1998)
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) P. Grutter, McGill University
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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) P. Grutter, McGill University
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AFM Elasticity Maps of Smooth Muscle Cells
elasticity contrast HANKS buffer 1mM serotonin induced contraction cells stiffness increased topography HANKS buffer no serotonin B. Smith, N. Durisic, B. Tolesko, P. Grutter, unpublished P. Grutter, McGill University
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DNA “Unwinding” Experiment - AFM force spectroscopy
Anselmetti, Smith et. al. Single Mol. 1 (2000) 1, 53-58 AFM probe Au surface Experiment - AFM force spectroscopy Nature - DNA replication, polymerization P. Grutter, McGill University
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DNA Structural Transitions AFM Force Spectroscopy in TRIS Buffer
Duplex poly(dA-dT) Duplex poly(dG-dC) Simulation data from Lavery and Lebrun 1997. B 800 400 800 400 ssDNA Elasticity Model Melting Transition ~ 300 pN Force [pN] S B-S Transition ~ 70 pN B-S Transition ~ 40 pN Molecular Extension [nm] Molecular Extension [nm] P. Grutter, McGill University
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Typical forces and length scales
Gaub Research Group, Munchen P. Grutter, McGill University
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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 : P. Grutter, McGill University
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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) P. Grutter, McGill University
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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 P. Grutter, McGill University
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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 P. Grutter, McGill University
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Some words on Tapping™ Amount of energy dissipated
Anczykowski et al., Appl. Phys. A 66, S885 (1998) 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. P. Grutter, McGill University
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Dissipation The cantilever is a damped, driven, harmonic oscillator
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 eV per oscillation cycle Y. Liu and Grutter, J. Appl. Phys. 83, 7333 (1998) P. Grutter, McGill University
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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’ T=4.5K A…rms 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 << J/molecule P. Grutter, McGill University
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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
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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) P. Grutter, McGill University
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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) P. Grutter, McGill University
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