Atomic force microscopy

1. Jiří Boldyš Atomic force microscopy

2. Outline • Motivation • Minisurvey of scanning probe microscopies • Imaging principles • Ideas about application of moment invariants • Alternative reconstruction approach • Image artifacts

3. Classification of blur kernel symmetries • n-fold circular symmetry (Cn symmetry) • Dihedral symmetry (Dn) • Radial symmetry

4. Common blurs • Atmospheric – radial symmetry • Out-of-focus – radial, cyclic or dihedral symmetry • Motion – central symmetry

5. What invariants we have • Model: g = f * h • I ( f ) = I ( g ) • Invariance x discriminability • Invariants to kernels with Cn and Dn symmetry • Potentially we can, we have not done that - arbitrary symmetry, arbitrary dimension

6. Other potential applications • Electron microscopy? – N-fold symmetrical correction elements • Atomic force microscopy (AFM)? • … • But – Is there a convolution???

7. Scanning probe microscopy - classification • Scanning tunneling microscopy - STM • Atomic force microscopy - AFM • Electric force microscopy - EFM • Magnetic force microscopy - MFM • Scanning near-field optical microscopy - SNOM • ...

8. Scanning tunneling microscopy • Mironov: Fundamentals of scanning probe microscopy, 2004

9. Scanning tunneling microscopy • 1981 – Swiss scientists Gerd Binnig • and Heinrich Rohrer • Atomic resolution, simple • 1986 – Nobel prize Chen: Introduction to scanning tunneling microscopy, 1993

10. Scanning tunneling microscopy • The first demonstration of the atomic-resolution capability of STM – Si(111)-7x7, Binnig, Rohrer, Gerber, Weibel, 1983 Chen: Introduction to scanning tunneling microscopy, 1993

11. Scanning tunneling microscopy Chen: Introduction to scanning tunneling microscopy, 1993

12. Atomicforce microscopy • Mironov: Fundamentals of scanning probe microscopy, 2004 • 1986, Binnig, Quate, Gerber • 1989 – the first commercially available AFM

13. Magneticforce microscopy • Mironov: Fundamentals of scanning probe microscopy, 2004 • Local magnetic properties • AFM + tip covered by a layer of ferromagnetic material with specific magnetization

14. Atomicforce microscopy in detail • Forces can be explained by e.g. van der Waals forces – approximated by Lennard-Jones potential • Mironov: Fundamentals of scanning probe microscopy, 2004

15. Tip – sample force • Energy of interaction • Force – normal + lateral component • Corresponds to deflections of an elastic cantilever • Mironov: Fundamentals of scanning probe microscopy, 2004

16. STM vs. AFM • STM • Tunneling current drops off exponentially  spatially confined to the frontmost atom of the tip and surface • Distance dependence is monotonic  simple feedback scheme • Modest experimental means, excellent SNR • AFM • Force – short range + long range – less tractable as a feedback signal • Not monotonic with distance • Giessibl, Quate: Physics Today, 2006

17. Beam-bounce technique • Mironov: Fundamentals of scanning probe microscopy, 2004

18. Feedback system • Mironov: Fundamentals of scanning probe microscopy, 2004

19. Examples of cantilevers • Si3N4, Si • Different spring constants and resonant frequencies • Images: Mironov, Fundamentals of scanning probe microscopy, 2004

20. Methods used to acquire images • Contact vs. non-contact modes • Contact modes • attractive or repulsive • Balance between atomic and elastic forces • Small stiffness – high sensitivity, gentle to the sample • Tip breakage, surface damages • Not suitable for soft samples (biological) • Constant force • Constant average distance • Mironov: Fundamentals of scanning probe microscopy, 2004

21. AFM image acquisition at constant force • Mironov: Fundamentals of scanning probe microscopy, 2004

22. AFM image acquisition at average distance • Mironov: Fundamentals of scanning probe microscopy, 2004

23. Force-distance curves – elastic interaction • Mironov: Fundamentals of scanning probe microscopy, 2004

24. Force-distance curves – plastic interaction • Mironov: Fundamentals of scanning probe microscopy, 2004

25. Forced oscillations of a cantilever • Better for soft samples • Reduce mechanical influence of the tip on the surface • Possible to investigate more surface properties • Piezo-vibrator • Motion equation • Mironov: Fundamentals of scanning probe microscopy, 2004

26. Forced oscillations of a cantilever • Mironov: Fundamentals of scanning probe microscopy, 2004

27. Contactless mode of AFM cantilever oscillations • Small forced oscillations amplitude – 1nm • Close to surface – additional force • Small oscillation around z0 • Presence of a gradient in the tip-surface interaction force  Additional shift of the amplitude and phase response curves • Additional phase shift  phase contrast AFM image • Mironov: Fundamentals of scanning probe microscopy, 2004

28. Contactless mode of AFM cantilever oscillations • Mironov: Fundamentals of scanning probe microscopy, 2004

29. Semi-contact mode of AFM cantilever oscillations • Before – high sensitivity and stability feedback required • In practice often semi-contact mode • Excited near resonance frequency, amplitude 10-100nm • Working point: • Mironov: Fundamentals of scanning probe microscopy, 2004

30. Semi-contact mode of AFM cantilever oscillations • Mironov: Fundamentals of scanning probe microscopy, 2004

31. Frequency modulation AFM • Si(111) Reactive surface → • Dynamic mode • Ultrahigh vacuum • FM-AFM – frequency modulation – introduced in 1991 • First with commercial cantilevers with a limited range of spring constants • Strong bonding energy Si-Si  large amplitude of vibrations 34nm  no atomic resolution •  small amplitudes  stiff cantilevers  dramatic improvement in spatial resolution Giessibl, Quate: Physics Today, 2006

32. From static to dynamic mode • Static approach still in use • Materials in liquids • Tip subject to wear • Large lateral forces • Absolute force measurements are noisy • Amplitude modulation AFM • Driven near fundamental resonance frequency • Less noise • Sensing variations in amplitude • Lateral forces minimized – broken contacts Giessibl, Quate: Physics Today, 2006

33. From static to dynamic mode • Frequency modulation AFM • Even less noisy • Fixed amplitude • Frequency as a feedback signal • Lateral forces minimized – broken contacts • Average tip-sample force gradient • Frequency shift • Further improvement – exploiting signal proportional to higher-order derivative – better spatial resolution • And next – reconstruction using the frequency shift and higher-harmonic components of the cantilever vibrations • Higher harm. can be viewed as a convolution of the nth-order derivative of the force with some weight function Giessibl, Quate: Physics Today, 2006

34. Revealing angular symmetry of chemical bonds • Combined STM and FM AFM • Angular dependence of chemical bonding forces between CO on copper surface Cu(111) and the terminal atom of metallic tip • Forces depend also on angles between atoms • Other opinions: feedback artifact or multiple-atom tips • 3D force spectroscopy used Welker, Giessibl, Science, 2012

35. Revealing angular symmetry … Welker, Giessibl, Science, 2012

36. Silicon (111)-(7x7) surface Giessibl, Hembacher, Bielefeldt, Mannhart, Science, 2000

37. Non-expert ideas in the field of AFM • Two ways of imaging • Tip imaging • Surface imaging • Surface symmetry • Tip symmetry • Do we need to register (align) two blurred images, or one sharp and one blurred? • Images with different class of blur – generates new mathematical task for us

38. Registration of images blurred by kernels with different symmetry • Example: • Tip imaging by surface with 4-fold (C4) symmetry … • Followed by tip imaging (the same one) by surface with 3-fold symmetry • Both kill different frequencies – together we might reconstruct them more easily and precisely • Another example: • Scanning the same surface with 4-fold symmetrical and 3-fold symmetrical tip (due to crystallic structure)

39. Is there any convolution? • We are not sensing surface height (z-coordinate) - we are sensing force / potential energy • Can potential energy be calculated as a 3D convolution? • What we measure is a 2D surface in the 3D potential map • Probe influences atom distribution • We are sensing force through approx. linear dependence F(z) • What if we do not measure pure force but rather frequency shift or higher order force derivatives?

40. Mathematical morphology based reconstruction • Intuitively degradation corresponds to the dilation operation in mathematical morphology • Why not if the region where the forces are significant is << tip size Villarrubia, J. Res. Natl. Inst. Stand. Technol., 1997

41. Critical dimension AFM • Higher throughput during quality control • Not so ambitious resolution Dahlen et al., Veeco

42. AFM imaging artifacts West, Starostina, Pacific Nanotechnology, Inc.

43. AFM imaging artifacts West, Starostina, Pacific Nanotechnology, Inc.

44. AFM imaging artifacts West, Starostina, Pacific Nanotechnology, Inc.

45. AFM imaging artifacts West, Starostina, Pacific Nanotechnology, Inc.

46. AFM imaging artifacts Mates, Summer school of SPM microscopy, 2007

47. Recommended reading: Giessibl, Quate: Physics Today, Exploring the nanoworld with atomic force microscopy, 2006 Thank you!