STM as a Tool to Understand the Electronic

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

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

P. Grutter

History P. Grutter

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

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

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

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

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

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

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

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

[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) Operation of an STM 1, 2 P. Grutter

Current theoretical models Theoretical methods: Landauer formula or Keldysh non-equilibrium Green’s functions 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) P. Grutter 1 -4

[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) Landauer formula for the STM 1, 2 The tunnel current for non-interacting electrons 3: P. Grutter

[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 Transfer Hamiltonian method 1, 2 M…overlap of wavefunctions (--> resolution!) …. DOS ( --> spectroscopy !) P. Grutter

[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) Bardeen approach 1, 2 P. Grutter

Tunneling Current Q…. Workfunction, typically 3 -5 e. V z…. . Tip-sample separation, typically 4 -10 A D z = 1 A --> D I one order of magnitude ! P. Grutter

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

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

[1] G. Kresse and J. Hafner, Phys. Rev. B 47, R 558 (1993) [2] Ph. Kurz et al. J. Appl. Phys. 87, 6101 (2000) [3] J. P. Perdew et al. Phys. Rev. B 46, 6671 (1992) 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: PW 91[3] Brillouin-zone sampling: 10 k-points Convergence parameter: < 0. 01 e/au 3 P. Grutter

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

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

[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) 2. The influence of forces in STM scans 1 Force measurement on Au(111)2 P. Grutter Simulation of forces: Simulation: VASP GGA: PW 91 4 x 4 x 1 k-points

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 5 A P. Grutter

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

[1] V. M. Hallmark et al. , Phys. Rev. Lett. 59, 2879 (1987) Corrugation enhancement STM simulation: b. SCAN Bias voltage: - 100 m. V Energy interval: +/- 100 me. V Current contour: 5. 1 n. A Due to relaxation effects in the low distance regime the corrugation of the Au(111) surface is enhanced by about 10 -15 pm 1 P. Grutter

[1] W. A. Hofer, J. Redinger, A. Biedermann, and P. Varga, Surf. Sci. Lett. 466, L 795 (2000) [2] V. L. Moruzzi et al. Phys. Rev. B 15, 6671 (1977) 3. Change of electronic surface properties 1 System: Fe(100) bcc lattice DFT calculation: FLEUR Lattice constant: 2. 78 A P. Grutter LDA: Moruzzi et al [2] No of k-points: 36

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 P. Grutter

5. Importance of different effects P. Grutter

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

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

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

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

Geometric and Electronic Properties of Molecules II C 60 on Au(111) P. Grutter J. Mativietsky, S. Burke, Y. Sun, S. Fostner, R. Hoffmann, P. Grutter

Single-Molecule Vibrational Spectroscopy and Microscopy 25 averages, 2 minutes per spectrum Ds/s= 4. 2% (1 -2) Ds/s= 3. 3% (3, different molecule) B. C. Stipe, M. A. Rezaei, W. Ho Science 280, 1733 (1998) P. Grutter

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

Geometric and Electronic Properties of Nanowires I 0. 3 ML Cs on Ga. As and In. Sb (fig. C) P. Grutter Whitman et al, PRL 66, 1338 (1991)

Geometric and Electronic Properties of Nanowires II 0. 36 ML Ho on Si, 400 nm image Anisotropic lattice mismatch --> wires. Are they conductive? P. Grutter Ohbuchi and Nogami, PRB 66, 165323 (2003)

Geometric and Electronic Properties of Nanowires III 0. 04 ML In on Si(001), 14 nm image However: In wires are NOT conductive ! Nogami, Surf. Rev. & Letters, 6, 1067 (1999) Evans and Nogami, PRB 59, 7644 (1999) P. Grutter

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

Other spectroscopies of molecules: may the force be with you Experimental variation o f the conductance of C 60 modulated by Vin (t). The time variation o f the voltage Vz piezo applied to the piezoelectric actuator is shown as a dashed line and the experimental C 60(t) conductance response as a solid line. Ch. Joachim and J. Gimzewski, Chem. Phys. Lett 265, 353 (1997) P. Grutter

Interpretation of C 60 amplifier Calculated variations of surface resistance of C 60 on Au(110) as a function of applied force Ch. Joachim and J. Gimzewski, Proc. IEEE 86, 184 (1998) P. Grutter

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

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

Calculation of electrical transport P. Grutter

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

DFT plus non-equilibrium Green’s Functions J. Taylor, H. Guo , J. Wang, PRB 63, R 121104 (2001) 1. Calculate long, perfect lead. Apply external potential V by shifting energy levels -> create electrode data base and get potential right lead 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 P. Grutter

STM/STS and conductivity • STM measures DOS(EFermi) • DOS related to conductivity • BUT: how does the tunneling current couple to molecular conductivity? – Very indirect: • function of – – P. Grutter 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)

So is SPM useful in molecular electronics? P. Grutter

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

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

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

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

Low-T UHV STM/AFM/FIM 140 K, 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 P. Grutter

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

P. Grutter

FIM of W(111) tip A. Schirmeisen, G. Cross, A. Stalder, U. Durig Imaging at 5. 0 k. V P. Grutter

FIM of W(111) tip Imaging at 5. 0 k. V Manipulating at 6. 0 k. V P. Grutter

FIM of W(111) tip Imaging at 5. 0 k. V Manipulating at 6. 0 k. V P. Grutter

FIM of W(111) tip Imaging at 5. 0 k. V Manipulating at 6. 0 k. V P. Grutter

Single Au atom on W(111) tip Imaged at 2. 1 KV P. Grutter

Anne-Sophie Lucier P. Grutter

W(111) tip on Au(111) Cross et al. PRL 80, 4685 (1998) Schirmeisen et al, NJP 2, 29. 1 (2000) P. Grutter

W(111) trimer tip on Au(111) Ead = 21 e. V l = 0. 2 nm P. Grutter

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

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

Making contact ~0. 1 G 0, 50 m. Vbias C 1 C 2 tic s la e ~± 0. 2Å P. Grutter

Work Function vs. Apparent Barrier Height Vbias=0. 05 V dln. I/dz=-(2 m)1/2/ħ 1/2 ~9. 4 e. V 2 =0. 95(dln. I/dz) Vbias=0. 1 V ~ 0. 4 e. V ~ 4. 5 e. V Ze I[n. A] and Z[Å] Å W tip-Au surface Hofer, Fisher, Wolkow, Grutter, Phys. Rev. Lett. , 87, 2001, 236104 P. Grutter

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

Major Conclusions: • Forces cannot be neglected! – Different decay lengths -> non-local, nonuniform! – Substantial (n. N) – 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. P. Grutter

Beware of Power. Point Engineering or Cartoon Physics!!! 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 4 K STM) D. Eigler, IBM Almaden P. Grutter

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