An Introduction to Atomic Force Microscopy

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

2. 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 Outline

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. 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 Forces between atoms

7. D z spring constant k Harmonic oscillator: f2 = k/m F’ acts like a spring in series: f2 = (k+F’)/m Measuring forces Force: F = kDz Force gradient F’ : F’= 2k Df/f approximation good if d2V / dz2 = constant for D z otherwise: Giessibl, APL 78, 123 (2001)

8. Atomic Force Microscope deflection sensor approach force sensor tip feedback sample vibration damping scanner Data acquisition

9. The force sensor Microfabrication of inte-grated cantilevers with tips

10. W L t 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

11. 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. Atomic Force Microscope deflection sensor approach force sensor tip feedback sample vibration damping scanner Data acquisition

13. A) Beam deflection A B) Interferometry D) Piezoelectric Meyer and Amer, APL53, 1045 (1988) D B Giessibl, APL 73, 3956 (1998) Rugar et al., APL 55, 2588 (1989) Deflection sensors C) Piezoresisitive

14. Atomic Force Microscope deflection sensor approach force sensor tip feedback sample vibration damping scanner Data acquisition

15. z = constant Feedback modes F = constant

16. Atomic Force Microscope deflection sensor approach force sensor tip feedback sample scanner vibration damping Data acquisition

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

18. Atomic Force Microscope deflection sensor approach force sensor tip feedback sample vibration damping scanner Data acquisition

19. gray scale image processed image Creating an image from the feedback signal line scan

20. 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). Image processing Beware of introducing image processing artifacts ! Understand and know what you are doing

21. Blunt tip : ‘High’ resolution and double tip: Imaging Artifacts

22. Atomic Force Microscope deflection sensor approach vibration damping force sensor tip feedback sample scanner Data acquisition

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

24. 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 = constDT const ~ 10-5

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

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

27. Van derWaals forces FvdW = AR/6z2 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

28. 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)

29. 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)

30. 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

31. Magnetic reversal studies by MFM particles size 90 x 240 x 10 nm X. Zhu (McGill) Magnetic Force Microscopy Tracks on hard disk floppy disk image size 10 and 30 micrometers. M. Roseman (McGill)

32. Total force on cantilever = sum of ALL forces Tip Water Surface Can be LARGE (several 1-10 nN) Capillary forces (water layer) 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

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

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

36. Field ion microscope manipulation of atomic structure of AFM tip W(111) tip on Au(111) Cross et al. PRL 80, 4685 (1998) Schirmeisen et al, NJP 2, 29.1 (2000)

37. Site specific chemical interaction potential: Si(111) 7x7 Lantz, Hug, Hoffmann, van Schendel, Kappenberg, Martin, Baratoff, and Guentherodt , Science 291, 2580 (2001)

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

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

40. 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]

41. Typical forces and length scales Gaub Research Group, Munchen

42. 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: Loading Rate Dependent Unbinding: Good review: Evans, E. Annu. Rev. Biophys. Biomol. Struct. 2001. 30:105-28.

43. 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)

44. Modulation techniques Concept: modulate at frequency fmodand use e.g. lock-in detection. • Elasticity • Viscoelasticity • Kelvin probe • Electrical potential • Piezoresponse • …. Carbon fibers in epoxy matrix, 40 micrometer scan Digital Instruments

45. 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

46. Anczykowski et al., Appl. Phys. A 66, S885 (1998) 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.

47. 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 • 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

48. 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 << 10-21J/molecule

49. 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. AFM providesimaging, spectroscopyand manipulationcapabilities in almost any environment: ambient, UHV, liquid at temperatures rangingfrom mK - 900K withatomic resolution and sensitivity (at least in some cases)