1. P. Grutter STM as a Tool to Understand the Electronic Properties of Molecules Peter Grutter Physics Department McGill University Part of SPM lecture series in 534A ‘Nanoscience and Nanotechnology’

2. P. Grutter Outline Motivation and Intro History of tunneling STM and STS theory Wires Molecules Chemically and atomically defined contacts

3. P. Grutter

4. History

5. Binnig and Rohrer obtained the Nobel prize in 1986 for the discovery of the STM First STM

6. But: 1972! Topografiner System very similar to today’s STM, but atomic resolution was not achieved 30 A vertical, 4000 A lateral resolution

7. How does it work? Tunneling current between tip and sample I ~ (V/s) exp (- A√φ*s)

8. Tunneling current Exponential dependence on distance I ~ (V/s) exp (- Aφ1/2s) “Proof of concept” March 18 th, 1981 Binnig et al, APL 1982 Very sensitive to gap size!

9. First STM image Binnig et al. 1982, PRL First atomic resolution image of the Si (111) 7x7 reconstruction

10. Tip preparation Tip must be as sharp and narrow as possible Chemically etched or mechanically cut.

11. Tip effects The shape of the tip may affect the image -More than one tip -“flat” or irregular shape -Structure change during scan

12. Scan resolution STM Large Range Comparable (or better) to most techniques

13. P. Grutter Operation of an STM 1,2 [1] C. Julian Chen, Introduction to Scanning Tunnelling Microscopy, Oxford (1993) [2] G.A.D. Briggs and A. J. Fisher, Surf. Sci. Rep. 33, 1 (1999)

14. P. Grutter Current theoretical models Theoretical methods: Landauer formula or Keldysh non-equilibrium Green’s functions 1-4 Transfer Hamiltonian methods 5 Methods based on the properties of the sample surface alone 6 [1] R. Landauer, Philos. Mag. 21, 863 (1970) M. Buettiker et. al. Phys. Rev. B 31, 6207 (1985) [2] L. V. Keldysh, Zh. Eksp. Theor. Fiz. 47, 1515 (1964) [3] C. Caroli et al. J. Phys. C 4, 916 (1971) [4] T. E. Feuchtwang, Phys. Rev. B 10, 4121 (1974) [5] J. Bardeen, Phys. Rev. Lett. 6, 57 (1961) [6] J. Tersoff and D. R. Hamann, Phys. Rev. B 31, 805 (1985)

15. P. Grutter Landauer formula for the STM 1,2 [1] Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992) [2] A.A. Abrikosov, L.P. Gorkov and I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Dover, NY (1975) [3] M. Buettiker et al. Phys. Rev. B 31, 6207 (1985) The tunnel current for non-interacting electrons 3 :

16. P. Grutter Transfer Hamiltonian method 1,2 [1] J. Pendry et al. J. Phys. Condens Matter 3, 4313 (1991) [2] J. Julian Chen, Introduction to Scanning Tunneling Microscopy Oxford (1993) pp. 65 - 69 M…overlap of wavefunctions (--> resolution!)  …. DOS ( --> spectroscopy !)

17. P. Grutter Bardeen approach 1,2 [1] C.J. Chen, Introduction to Scanning Tunneling Microscopy, Oxford Univ. Press (1993) [2] W.A. Hofer and J. Redinger, Surf. Sci. 447, 51 (2000)

18. P. Grutter Tunneling Current  …. Workfunction, typically 3-5 eV z….. Tip-sample separation, typically 4-10 A one  z = 1 A -->  I one order of magnitude !

19. P. Grutter Small V approximation! Simmon’s equation (Simmon, 1963) Fowler-Nordheim regime (V>>  Measure log I vs log V -> resonances! Resolution due to exp dependence! (not so on metals -> later)

20. P. Grutter Unknown/Challenges: 1. Chemical nature of STM tip (problem for spectroscopy, corrugation) 2. Relaxation of tip/surface atoms (tip sample separation not equal to piezo scale) 3. Effect of tip potential on electronic surface structure (quenching of surface states) 4. Influence of magnetic properties on tunnelling current/surface corrugation (is spin-STM possible?) 5. Relative importance of the effects

21. P. Grutter 1. Chemical nature of the tip 1 [1] P. Varga and M. Schmid, Appl. Surf. Sci. 141, 287 (1999)

22. P. Grutter Model of the STM tip 1,2,3 Number of layers: 7 Free standing film Numerical method: DFT Relaxations: VASP [1] Electronic structure: FLEUR [2] Lattice constant: 6.016 au (GGA) Exchange/correlation: PW91[3] Brillouin-zone sampling: 10 k-points Convergence parameter: < 0.01 e/au 3 [1] G. Kresse and J. Hafner, Phys. Rev. B 47, R558 (1993) [2] Ph. Kurz et al. J. Appl. Phys. 87, 6101 (2000) [3] J. P. Perdew et al. Phys. Rev. B 46, 6671 (1992)

23. P. Grutter Electronic properties of the tip: non-magnetic tip models

24. P. Grutter Chemical contrast on PtRh(100) 1,2 [1] P.T. Wouda et al. Surf. Sci. 359, 17 (1996) [2] P. Varga and M. Schmid Appl. Surf. Sci. 141, 287 (1999) Experiments: 22 pm contrast Simulations: interval E F +/- 80 meV

25. P. Grutter 2. The influence of forces in STM scans 1 [1] W.A. Hofer, A.J. Fisher, R.A. Wolkow, and P. Grutter, Phys. Rev. Lett 87, 236104 (2001) [2] G. Cross, A. Schirmeisen, P. Grutter, U. Durig, Phys. Rev. Lett. 80, 4685 (1998) Force measurement on Au(111) 2 Simulation of forces: Simulation: VASP GGA: PW91 4x4x1 k-points

26. P. Grutter Tip relaxation effects W tip on Au(111) surface The force on the apex atom is one order of magnitude higher than forces in the second layer Substantial Relaxations occur only in a distance range below 5A

27. P. Grutter Tip relaxation effects Hofer, Fisher, Wolkow and Grutter Phys. Rev. Lett. 87, 236104 (2001) W tip on Au(111) surface The real distance is at variance with the piezoscale by as much as 2A The surplus current due to relaxations is about 100% per A

28. P. Grutter Corrugation enhancement STM simulation: bSCAN Bias voltage: - 100mV Energy interval: +/- 100meV Current contour: 5.1 nA Due to relaxation effects in the low distance regime the corrugation of the Au(111) surface is enhanced by about 10-15 pm 1 [1] V. M. Hallmark et al., Phys. Rev. Lett. 59, 2879 (1987)

29. P. Grutter 3. Change of electronic surface properties 1 [1] W.A. Hofer, J. Redinger, A. Biedermann, and P. Varga, Surf. Sci. Lett. 466, L795 (2000) [2] V. L. Moruzzi et al. Phys. Rev. B 15, 6671 (1977) System: Fe(100) bcc lattice DFT calculation: FLEUR Lattice constant: 2.78 A LDA: Moruzzi et al [2] No of k-points: 36

30. P. Grutter Quenching of surface states Simulation of quenching: distance dependent reduction of the occupation number of single Kohn-Sham states of the surface, 2 nd order polynomial

31. P. Grutter 5. Importance of different effects

32. P. Grutter Tunneling Spectroscopy (cartoon version) Elastic: linear I-V Inelastic: non-linear I-V

33. P. Grutter Tunneling Spectroscopies I(V) at constant z or variable z dI/dV at constant z or constant average I d (log I)/dz (barrier height measurement)

34. P. Grutter Tunneling Spectroscopy: an example Hyrogen on SiC surface: goes from insulator -> conductor Derycke et al., Nature Mater. 2, 253 (2003) UPS

35. P. Grutter Geometric and Electronic Properties of Molecules I P. Weiss et al., Science 271, 1705 (1996) Y. Sun, H. Mortensen, F. Mathieu, P. Grutter (McGill) Porphrin on Au(111) Alkane thiols

36. P. Grutter Geometric and Electronic Properties of Molecules II J. Mativietsky, S. Burke, Y.Sun, S. Fostner, R. Hoffmann, P. Grutter C60 on Au(111)

37. P. Grutter Single-Molecule Vibrational Spectroscopy and Microscopy B.C. Stipe, M.A. Rezaei, W. Ho Science 280, 1733 (1998) 25 averages, 2 minutes per spectrum  = 4.2% (1-2)  = 3.3% (3, different molecule)

38. P. Grutter Single-Molecule Vibrational Spectroscopy and Microscopy B.C. Stipe, M.A. Rezaei, W. Ho Science 280, 1733 (1998) C 2 H 2 and C 2 D 2 comparison

39. P. Grutter Geometric and Electronic Properties of Nanowires I Whitman et al, PRL 66, 1338 (1991) 0.3 ML Cs on GaAs and InSb (fig. C)

40. P. Grutter Geometric and Electronic Properties of Nanowires II Ohbuchi and Nogami, PRB 66, 165323 (2003) 0.36 ML Ho on Si, 400 nm image Anisotropic lattice mismatch --> wires. Are they conductive?

41. P. Grutter Geometric and Electronic Properties of Nanowires III Evans and Nogami, PRB 59, 7644 (1999) 0.04 ML In on Si(001), 14 nm image However: In wires are NOT conductive ! Nogami, Surf. Rev. & Letters, 6, 1067 (1999)

42. P. Grutter Defined, reproducible, understandable I-V of molecules Chemically reliable contact Cui et al. Nanotechnology 13, 5 (2002), Science 294, 571 (2001)

43. P. Grutter Other spectroscopies of molecules: may the force be with you Ch. Joachim and J. Gimzewski, Chem. Phys. Lett 265, 353 (1997) Experimental variation o f the conductance of C60 modulated by V in (t). The time variation o f the voltage V z piezo applied to the piezoelectric actuator is shown as a dashed line and the experimental C60(t) conductance response as a solid line.

44. P. Grutter Interpretation of C60 amplifier Ch. Joachim and J. Gimzewski, Proc. IEEE 86, 184 (1998) Calculated variations of surface resistance of C60 on Au(110) as a function of applied force

45. P. Grutter STM/STS and conductivity So if STM/STS is so powerful - can we use it to determine the conductivity of molecules???

46. P. Grutter ‘Traditional’: infinite, structureless leads -> periodic boundary conditions. but: - result depends on lead size! - bias not possible due to periodic boundary condition! Calculating Conductance Jellium lead molecule

47. P. Grutter Calculation of electrical transport

48. P. Grutter ab-initio modelling of electronic transport lead Hong Guo’s research group, McGill Physics

49. P. Grutter DFT plus non-equilibrium Green’s Functions J. Taylor, H. Guo, J. Wang, PRB 63, R121104 (2001) 1. Calculate long, perfect lead. Apply external potential V by shifting energy levels -> create electrode data base and get potential  right lead

50. P. Grutter 2. Solve Poisson equation for middle part (device plus a bit of leads); match wavefunctions  and potential as a function of V to leads (use data base) in real space. 3.  calculated with non-equilibrium Green’s functions (necessary as this is an open system). This automatically takes care of bound states

51. P. Grutter STM/STS and conductivity STM measures DOS(E Fermi ) DOS related to conductivity BUT: how does the tunneling current couple to molecular conductivity? –Very indirect: function of –DOS, E (where does potential drop off?) –symmetry/coupling (electrode vs. complex molecule) –k vector (lateral vs. perpendicular conductivity) –internal transport mechanism (tunneling, hopping, ballistic)

52. P. Grutter So is SPM useful in molecular electronics?

53. P. Grutter Molecular electronics: the issues Contacts Structure-function relationship between transport process and molecular structure Dissipation Crosstalk (interconnects) Architecture I-O with a trillion processors Fault tolerance Manufacturing costs

54. P. Grutter Does atomic structure of the contact matter? YES !

55. P. Grutter Does atomic structure of the contact matter? Mehrez, Wlasenko, et al, Phys. Rev. B 65, 195419 (2002)

56. P. Grutter Electronic Properties of Molecules: Requirements R. Reifenberger

57. P. Grutter Low-T UHV STM/AFM/FIM 140K, 10 -11 mbar quick change between FIM - AFM/STM mode Stalder, Ph.D. Thesis 1995 Cross et al. PRL 80, 4685 (1998) Schirmeisen et al. NJP 2, 29.1 (2000) Sun, Lucier, Mortensen, Schaer

58. P. Grutter Field Ion Microscopy (FIM) E. Muller, 1950’s

59. P. Grutter

60. FIM of W(111) tip Imaging at 5.0 kV A. Schirmeisen, G. Cross, A. Stalder, U. Durig

61. P. Grutter FIM of W(111) tip Imaging at 5.0 kV Manipulating at 6.0 kV

62. P. Grutter FIM of W(111) tip Imaging at 5.0 kV Manipulating at 6.0 kV

63. P. Grutter FIM of W(111) tip Imaging at 5.0 kV Manipulating at 6.0 kV

64. P. Grutter Single Au atom on W(111) tip Imaged at 2.1 KV

65. P. Grutter Anne-Sophie Lucier

66. P. Grutter W(111) tip on Au(111) Cross et al. PRL 80, 4685 (1998) Schirmeisen et al, NJP 2, 29.1 (2000 )

67. P. Grutter W(111) trimer tip on Au(111) E ad = 21 eV  = 0.2 nm

68. P. Grutter Molecular Dynamics Simulations U. Landman et al, Science 248, 454 (1990)

69. P. Grutter Force and Current vs. Distance Sun et al, subm. PRL

70. P. Grutter Making contact elastic C2 ~±0.2Å C1 ~0.1G 0, 50mV bias

71. P. Grutter Work Function vs. Apparent Barrier Height Hofer, Fisher, Wolkow, Grutter, Phys.Rev. Lett., 87, 2001, 236104 ZeZe  ~ 0.4eV  ~ 4.5eV  ~9.4eV Å W tip-Au surface dlnI/dz=-(2m) 1/2 /ħ  1/2  =0.95(dlnI/dz) 2 I[nA] and Z[Å] V bias =0.05V V bias =0.1V

72. P. Grutter Atomic Structure Matters W.A. Hofer, U. of Liverpool, unpublished

73. P. Grutter Major Conclusions: Forces cannot be neglected! –Different decay lengths -> non-local, non- uniform! –Substantial (nN) –Major relaxation effects Point of contact determined both electronically and mechanically: they are identical to within measurement error. W an atomically very robust electrode material. In tunneling regime: modeling in quantitative agreement with experiment.

74. P. Grutter Beware of PowerPoint Engineering or Cartoon Physics!!!

75. P. Grutter Storing information atom by atom Ultra high density (library of congress on a pin head) Ultra slow (needs life time of universe to write) Huge footprint (UHV 4K STM) D. Eigler, IBM Almaden

76. P. Grutter Conductance via dissipation imaging? Stowe et al., APL 75, 2785 (1999) Denk and Pohl, JAP 59, 2171 (1991)

77. P. Grutter Summary Tools, both experimental and theoretical, drive our capabilities to understand the nanoworld! STM spectroscopy very powerful, but big challenge to extract conductivity. STM and AFM have only started to make an impact in the field of nanoelectronics.