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

2. P. Grutter, McGill 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 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

3. P. Grutter, McGill University

4. Scanning Tunneling Microscope (STM) Based on quantum mechanical tunneling current Works for electrically conductive samples Imaging, spectroscopy and manipulation possible D. Eigler, IBM Almaden

5. 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 nN J. Israelachvili ‘Intermolecular and Surface Forces’ Academic Press ‘Back of the envelope’: Atomic energy scale: E bond ~ 1-4 eV ~ 2-6 10 -19 J Typical bonding length: a ~ 0.2 nm Typical forces: F = E/a ~ 1-3 nN

6. P. Grutter, McGill University

7. Measuring forces Force: F = k  z Force gradient F’ : F’= 2k  f  f approximation good if d 2 V / dz 2 = constant for  z otherwise: Giessibl, APL 78, 123 (2001)  z spring constant k Harmonic oscillator: f 2 = k /m F’ acts like a spring in series: f 2 = (k+F’)/m

8. P. Grutter, McGill University Atomic Force Microscope deflection sensor approach Data acquisition scanner feedback force sensor force sensortip vibration damping sample

9. P. Grutter, McGill University The force sensor Microfabrication of inte- grated cantilevers with tips

10. 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 E Y ~ 10 12 N/m 2 Resonant frequency f o : typical values: 7 - 500 kHz W L t

11. P. Grutter, McGill 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

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

13. 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

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

15. P. Grutter, McGill University Feedback modes F = constantz = constant

16. P. Grutter, McGill University Atomic Force Microscope deflection sensor approach Data acquisition tip feedback force sensor vibration damping samplescanner

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

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

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

20. P. Grutter, McGill University 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.

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

22. P. Grutter, McGill University Atomic Force Microscope deflection sensor approachvibrationdamping Data acquisition scanner tip feedback force sensor sample

23. 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

24. P. Grutter, McGill University 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

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

26. P. Grutter, McGill University 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)

27. P. Grutter, McGill University Van derWaals forces F vdW = AR/6z 2 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 -> F vdW ~ 10 nN at z~0.5 nm

28. P. Grutter, McGill University Electrostatic forces F electrostatic =   RU 2 / z U…Potential difference R…Tip radius z…Tip - sample separation R~100nm typical effective radius U=1V -> F electrostatic ~ 5 nN at z~0.5 nm Tans & Dekker, Nature404, 834 (2000)

29. P. Grutter, McGill University Chemical forces F Morse = E bond /z (2e -  (z-  ) - e -2  (z-  ) ) E bond …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)

30. P. Grutter, McGill University Magnetic Forces F magntic = m tip  H sample 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

31. 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 nm X. Zhu (McGill) Tracks on

32. P. Grutter, McGill University Capillary forces (water layer) There is always a water layer on a surface in air! F capillary = 4  R  cos   …surface tension, ~10-50 mJ/m 2  …contact angle Surface Water Tip Can be LARGE (several 1-10 nN) Total force on cantilever = sum of ALL forces

33. P. Grutter, McGill University 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

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

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

36. P. Grutter, McGill University 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

37. 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)

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

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

40. P. Grutter, McGill University DNA Structural Transitions AFM Force Spectroscopy in TRIS Buffer 300 450600 750 800 400 0 Duplex poly(dG-dC) B-S Transition ~ 70 pN Melting Transition ~ 300 pN 50 75 100 125 800 400 0 Force [pN] Duplex poly(dA-dT) B-S Transition ~ 40 pN Simulation data from Lavery and Lebrun 1997. B S ssDNA Elasticity Model Molecular Extension [nm]

41. P. Grutter, McGill University Typical forces and length scales Gaub Research Group, Munchen

42. P. Grutter, McGill University 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.

43. 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 of energy barriers and thus is a direct measure of the energy landscape in conformational space. Evans, Annu. Rev. Biophys. Biomol. Struct., 30, 105 (2001)

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

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

46. P. Grutter, McGill University 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 )

47. 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

48. 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) A 2 = k B T/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 -24 J << 10 -21 J/molecule

49. P. Grutter, McGill University 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)

50. 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)

51. 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)