An Introduction to Atomic Force Microscopy Peter Grutter

An Introduction to Atomic Force Microscopy Peter Grutter Physics Department www. physics. mcgill. ca/~peter/ P. Grutter, Mc. Gill University

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 P. Grutter, Mc. Gill University 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, Mc. Gill 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, Mc. Gill University

Forces between atoms ‘Back of the envelope’: • Atomic energy scale: Ebond ~ 1 -4 e. V ~ 2 -6 • 10 -19 J • Typical bonding length: a ~ 0. 2 nm • Typical forces: F = E/a ~ 1 -3 n. N P. Grutter, Mc. Gill University Bonding energies: • Quantum mechanical (covalent, metallic bonds): 1 -3 n. N • Coulomb (dipole, ionic): 0. 1 -5 n. N • Polarization (induced dipoles): 0. 02 -0. 1 n. N J. Israelachvili ‘Intermolecular and Surface Forces’ Academic Press

P. Grutter, Mc. Gill University

Measuring forces Force: Dz F = k Dz spring constant k Harmonic oscillator: Force gradient F’ : f 2 = k /m F’= 2 k Df/f F’ acts like a spring in series: f 2 = (k+F’)/m P. Grutter, Mc. Gill University approximation good if d 2 V / dz 2 = constant for D z otherwise: Giessibl, APL 78, 123 (2001)

Atomic Force Microscope deflection sensor approach force sensor tip feedback sample scanner vibration damping Data acquisition P. Grutter, Mc. Gill University

The force sensor Microfabrication of integrated cantilevers with tips P. Grutter, Mc. Gill University

Spring constants k and resonant frequency f of cantilevers Spring constant k : W L t typical values: 0. 01 - 100 N/m Young’s modulus EY ~ 1012 N/m 2 Resonant frequency fo: typical values: 7 - 500 k. Hz P. Grutter, Mc. Gill University

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 P. Grutter, Mc. Gill University

Atomic Force Microscope deflection sensor approach force sensor feedback tip sample scanner vibration damping Data acquisition P. Grutter, Mc. Gill University

Deflection sensors A A) Beam deflection B) Interferometry C) Piezoresisitive Meyer and Amer, APL 53, 1045 (1988) D) Piezoelectric D B Giessibl, APL 73, 3956 (1998) Rugar et al. , APL 55, 2588 (1989) P. Grutter, Mc. Gill University

Atomic Force Microscope deflection sensor approach force sensor feedback tip sample scanner vibration damping Data acquisition P. Grutter, Mc. Gill University

Feedback modes F = constant P. Grutter, Mc. Gill University z = constant

Atomic Force Microscope deflection sensor approach force sensor feedback tip sample scanner vibration damping Data acquisition P. Grutter, Mc. Gill University

Piezoelectric scanners (1) Properties: 1. Hysterisis (non-linear) 2. Creep (history dependent) 3. Aging (regular recalibration) (2) Piezo tube +y +x -x P. Grutter, Mc. Gill University -y

Atomic Force Microscope deflection sensor approach force sensor feedback tip sample scanner vibration damping Data acquisition P. Grutter, Mc. Gill University

Creating an image from the feedback signal line scan gray scale image processed image P. Grutter, Mc. Gill University

Image processing Beware of introducing image processing artifacts ! Understand know what you are doing Raw data shows ‘jumps’ in slow scan direction. (Due to pointing instabilities of laser). P. Grutter, Mc. Gill University Processing (here ‘flatten’) can remove them, but can create new artifacts.

Imaging Artifacts ‘High’ resolution and double tip: P. Grutter, Mc. Gill University Blunt tip :

Atomic Force Microscope deflection sensor approach force sensor feedback tip sample scanner vibration damping Data acquisition P. Grutter, Mc. Gill University

Tip-sample approach • Dynamic range from mm to nm • Coarse & fine approach! • Many possibilities: 1. Piezo walkers 2. Lever arms P. Grutter, Mc. Gill University Fixed point Micrometer screw 1 Micrometer screw 2

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!? ! L/L = const T P. Grutter, Mc. Gill University const ~ 10 -5

The first AFM G. Binnig, Ch. Gerber and C. F. Quate, Phys. Rev. Lett. 56, 930 (1986) P. Grutter, Mc. Gill University

Repulsive Contact Forces Diblock co-polymers used as self assembled etch mask Meli, Badia, Grutter, Lennox, Nano Letters 2, 131 (2002) P. Grutter, Mc. Gill University Rubbed Nylon LCD alignment layer Ruetschi, Grutter, Fuenfschilling and Guentherodt, Science 265, 512 (1994)

Van der. Waals forces Fvd. W = AR/6 z 2 A…Hamaker const. R…Tip radius z…Tip - sample separation A depends on type of materials (polarizability). For most materials and vacuum A~1 e. V Krupp, Advances Colloidal Interface Sci. 1, 113 (1967) R~100 nm typical effective radius -> Fvd. W ~ 10 n. N at z~0. 5 nm P. Grutter, Mc. Gill University

Electrostatic forces Felectrostatic = p e 0 RU 2/ z U…Potential difference R…Tip radius z…Tip - sample separation R~100 nm typical effective radius U=1 V -> Felectrostatic ~ 5 n. N at z~0. 5 nm P. Grutter, Mc. Gill University Tans & Dekker, Nature 404, 834 (2000)

Chemical forces Si(111) 7 x 7 FMorse = Ebond/z • (2 e-k(z-s) - e-2 k(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, Mc. Gill University

Magnetic Forces Fmagntic = mtip • Hsample Melting of flux lattice in Nb Images stray field and thus very useful in the magnetic recording industry, but also in science. Comprehensive review: Grutter, Mamin and Rugar, in ‘Scanning Tunneling Microscopy II’ Springer, 1991 P. Grutter, Mc. Gill University Roseman & Grutter, unpublished

Magnetic Force Microscopy Tracks on Magnetic reversal studies by MFM particles size 90 x 240 x 10 nm X. Zhu (Mc. Gill) hard disk floppy disk image size 10 and 30 micrometers. M. Roseman (Mc. Gill) P. Grutter, Mc. Gill University

Capillary forces (water layer) Total force on cantilever = sum of ALL forces There is always a water layer on a surface in air! Fcapillary = 4 p R g cos g …surface tension, ~10 -50 m. J/m 2 …contact angle P. Grutter, Mc. Gill University Tip Water Surface Can be LARGE (several 1 -10 n. N)

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, Mc. Gill University

DC Imaging, lateral forces Diblock co-polymer: Normal forces Friction Meli, Badia, Grutter, Lennox, Nano Letters 2, 131 (2002) P. Grutter, Mc. Gill University

Force Spectroscopy Snap in condition: k < F’ For meaningful quantitative analysis, k > stiffness of molecule force distance a water a P. Grutter, Mc. Gill University

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) P. Grutter, Mc. Gill University

Site specific chemical interaction potential: Si(111) 7 x 7 Lantz, Hug, Hoffmann, van Schendel, Kappenberg, Martin, Baratoff, and Guentherodt , Science 291, 2580 (2001) P. Grutter, Mc. Gill University

AFM Elasticity Maps of Smooth Muscle Cells elasticity contrast topography HANKS buffer no serotonin induced contraction cells stiffness increased HANKS buffer 1 m. M serotonin B. Smith, N. Durisic, B. Tolesko, P. Grutter, unpublished P. Grutter, Mc. Gill University

DNA “Unwinding” Anselmetti, Smith et. al. Single Mol. 1 (2000) 1, 53 -58 AFM probe Nature - DNA replication, polymerization P. Grutter, Mc. Gill University Au surface Experiment - AFM force spectroscopy

DNA Structural Transitions AFM Force Spectroscopy in TRIS Buffer Duplex poly(d. A-d. T) Force [p. N] 800 Simulation data from Lavery and Lebrun 1997. B 400 Duplex poly(d. G-d. C) 800 S 400 ss. DNA Elasticity Model Melting Transition ~ 300 p. N B-S Transition ~ 70 p. N B-S Transition ~ 40 p. N 0 0 50 75 100 125 Molecular Extension [nm] P. Grutter, Mc. Gill University 300 450 600 750 Molecular Extension [nm]

Typical forces and length scales Gaub Research Group, Munchen P. Grutter, Mc. Gill University

Loading Rate Dependent Unbinding: • 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. Most probable unbinding force: Good. P. review: Annu. Rev. Biophys. Biomol. Struct. 2001. 30: 105 -28. Grutter, Evans, Mc. Gill E. University

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, Mc. Gill University

Modulation techniques Concept: modulate at frequency fmod and use e. g. lock-in detection. • Elasticity Carbon fibers in epoxy matrix, 40 micrometer scan Digital Instruments P. Grutter, Mc. Gill University • • Viscoelasticity Kelvin probe Electrical potential Piezoresponse • ….

AC techniques Change in resonance curve can be detected by: f • Lock-in (A or ) * A • FM detection ( f and Adrive) Albrecht, Grutter, Horne and Rugar J. Appl. Phys. 69, 668 (1991) f 1 f 2 f 3 P. Grutter, Mc. Gill University (*) used in Tapping™ mode

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. Anczykowski et al. , Appl. Phys. A 66, S 885 (1998) P. Grutter, Mc. Gill University NOT necessarily less power dissipation than repulsive contact AFM.

Dissipation The cantilever is a damped, driven, harmonic oscillator Dissipation due to non-conservative tipsample interactions such as: • Inelastic tip-sample interactions • Adhesion hysterisis • Joule losses • Magnetic dissipation due to domain wall oscillations. Sensitivity better than 0. 019 e. V per oscillation cycle Y. Liu and Grutter, J. Appl. Phys. 83, 7333 (1998) P. Grutter, Mc. Gill University

Ultimate limits of force sensitivity 1. Brownian motion of cantilever! A…rms amplitude T=4. 5 K A 2 = k. BT/k 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) P. Grutter, Mc. Gill University Roseman & Grutter, RSI 71, 3782 (2000) Bottom line: Under ambient conditions energy resolution ~ 10 -24 J << 10 -21 J/molecule

Outlook AFM provides imaging, spectroscopy and manipulation capabilities in almost any environment: ambient, UHV, liquid at temperatures ranging from m. K - 900 K with atomic resolution and sensitivity (at least in some cases) P. Grutter, Mc. Gill University