1. M. F. Goffman First Lecture Functions: macroscopic electronic properties  Molecular Wires Diodes Switches and storage elements Negative Differential Resistance (NDR) elements Chemical structure Transport mechanisms are determined by Metal-molecule coupling  Weak coupling regime ee Molecule Strong coupling regime Molecule

2. M. F. Goffman Second Lecture Functions: macroscopic electronic properties  Molecular Wires Diodes Switches and storage elements Negative Differential Resistance (NDR) elements Chemical structure Transport mechanisms are determined by Metal-molecule coupling  Weak coupling regime ee Molecule Strong coupling regime Molecule 1 2 Qualitative Picture 3Final Remarks

3. M. F. Goffman Molecular Conduction: Qualitative Picture Energy Diagram showing the molecular levels relative to the electrochemical potential of electrodes Potential Profile across the molecule due to the applied bias. Two Basic Ingredients:

4. M. F. Goffman M0M0 Strong Coupling to Metallic Electrodes (  ) Isolated Molecule E HOMO LUMO Discrete Energy Levels Broadening of the energy levels (  ) M 0  M  n Fractional charge transfer Which is the location µ F with respect to HOMO-LUMO levels?  E Local Density of States Fermi level µ F MnMn  Chemically bonded

5. M. F. Goffman Location of the Fermi Energy UPS Experiments (UV Photo Electron Spectroscopy ) e-e- E Local Density of States  MnMn e-e- e-e- µFµF E µFµF # e per second E µFµF HOMO Vacuum Level e-e- E HOMO UPS spectrum # e per second

6. M. F. Goffman UPS Experiment on Self-assembled Monolayer on Au SeCOCH 3 CH 3 COSe S S S Se 3 e-e- e-e-

7. M. F. Goffman Energy Diagram µ L =µ R -V/2 V/2 L R L R µ L µRµR eVeV At equilibrium (V=0) But how are µ L and µ R disposed with respect to the molecular levels?  Potential profile inside the molecule

8. M. F. Goffman Potential Profile To the lowest approximation Molecular Levels shift "rigidly" by Let us denote this average potential as: Taking the molecular levels as our reference, the electrochemical potential of electrodes are shifted by This voltage division factor has a profound effect on Current-Voltage Characteristics -V/2 V/2 L R Potential Profile -V/2 V/2 r

9. M. F. Goffman Energy Level Diagram (  =0)  =0  Molecular levels remain fixed to µ L V>0  HOMO Conduction V<0  LUMO Conduction I-V Characteristics can look asymetric Positive branch (V>0) and Negative branch (V<0) involve different Molecular levels µ L µRµR eVeV LUMO HOMO µ L µRµR eVeV LUMO HOMO

10. M. F. Goffman Energy Level Diagram (  =1/2)  =1/2  Molecular levels shift with respect to µ L by half the applied bias µ L µRµR eV/2 LUMO HOMO µ L µRµR eV/2 LUMO HOMO Conduction takes place through the nearest molecular level (HOMO in this case) for either bias polarity.

11. M. F. Goffman Toy Model (1) Location of  with respect to µ F (2) Broadening  L,  R due to contacts (  L  R ) Toy Moldel: single level  (HOMO or LUMO) that incorporates relevant ingredients: (3) Potential Profile L R µ L µRµR  

12. M. F. Goffman Discrete One-Level Model -V/2 V/2 L R µ L  LL RR µRµR Current as a "balancing act"

13. M. F. Goffman Discrete One-Level Model -V/2 V/2 L R µ L  LL RR The net flux across left junction will be

14. M. F. Goffman Discrete One-Level Model -V/2 V/2 L R  LL RR The net flux across right junction will be µRµR

15. M. F. Goffman Discrete One-Level Model At the steady state I L +I R =0 (no charge accumulation in the molecule) The current through the metal-molecule-metal structure will be

16. M. F. Goffman µ L µRµR µRµR µRµR One-level Model: Current (I) vs. Voltage (V)  Let us take into account Broadening  of the level

17. M. F. Goffman Broadening  We replace the discrete level by a Lorentzian density of states: µ L µRµR   Expression of the current will be modified We could write in the Landauer-Büttiker form I let for you the demostration that the maximum value of

18. M. F. Goffman  One-level Model: Current (I) vs. Voltage (V) Next: Potential Profile Conductance Quantum

19. M. F. Goffman Potential Profile The potential profile V MOL (r) will be obtained by solving A solution can be visualized in terms of a capacitance circuit model: -V/2 V/2 L R -V/2 V/2 CLCL CRCR Charging Energy E add The potential U that raises the position of the level is

20. M. F. Goffman Self Consistent Solution Iterative Procedure for calculating N and U self-consistently

21. M. F. Goffman µ L µRµR V>0 One-level Model: Current (I) vs. Voltage (V) IV asymetric Coupling asymetry + charging   µ L µRµR V<0 Positively charges the molecule  shift  down

22. M. F. Goffman  Summary Asymetric IVs  asymetric coupling + charging effect (E add ) even if transport is associated with a single level (symetric molecule) HOMO conduction  I is lower for positive bias on the stronger contact LUMO conduction  I is higher for positive bias on the stronger contact I increases when  is crossed at V~2(µ F -  ) I increases over a voltage width  +k B T I dragged out by charging E add

23. M. F. Goffman Realistic Models Non-Equilibrium Green's Function (NEGF) Formalism Let us rewritte the previous eq. in terms of a Green Function G(E) Then the density of states will be proportional to the so called Spectral function defined as The mean number of excess electrons N and the current can be written as

24. M. F. Goffman NEGF Formalism For a multilevel Molecule (n levels) all quantities are replaced by a corresponding matrix (n x n ) A pedagogical tutorial: S. Datta, Nanotechnology 15, S433 (2004). H : Molecule + surface atoms  : Coupling to bulk contacts U : appropriate functional

25. M. F. Goffman Experiments on Molecular Wires Well coupled to electrodes (at least one of them)

26. M. F. Goffman Molecular Wires A) How conductance depends on the length L of the wire? L~nm Large delocalized  systems Conductance is a property of the Metal-Molecule-Metal structure B) How conductance depends on the binding group of the wire? C) How conductance depends on the structure of the wire?

27. M. F. Goffman How one can measure transport properties of molecular wires? 1) STM: Scanning Tunneling Microscope 2) Break-junctions Electronmigration-induced Mechanically controlled 3) Shadow evaporation on Self-assembled Monolayers (SAMs)

28. M. F. Goffman Adsorption MBE: Molecular "Beaker" Epitaxy Organization Solution Thiol-ended Molecules Au (111) STM Image sssssssss Au (111) Tip

29. M. F. Goffman A) How conductance depends on L?

30. M. F. Goffman Conductive AFM on Self-Assembled Monolayers Sakaguchi et al., APL 2001  =0.41Å -1 for oligothiophene  =1.08 Å -1 for alkanethiol Measured Theory  =0.33Å -1 for oligothiophene  =1.0 Å -1 for alkanethiol

31. M. F. Goffman Langlais et al., PRL 1999 Conductance depends exponentially on L STM on specially designed molecular wire

32. M. F. Goffman Explanation -V/2 V/2 L R µ L µRµR eVeV At low voltages µ F is far from HOMO and/or LUMO  Tunneling Transmission M. P. Samanta et al., PRB 53, R7626 (1996).

33. M. F. Goffman B) How conductance depends on the binding group of the molecular wire?

34. M. F. Goffman  Experiments are needed Conductance of molecular wires: Influence of molecule-electrode binding. S.N. Yaliraki, M. Kemp, and M.A. Ratner, J. Am. Chem. Soc. 121(14), 3428 (1999)  Se > S Theoretical studies Molecular alligator clips for single molecule electronics. Studies of group 16 and isonitriles interfaced with Au contacts. J.M. Seminario, A.G. Zacarias, and J.M. Tour J. Am. Chem. Soc. 121(2), 411 (1999)  S > Se X=S  T3 X=Se  Se3 XCH 3 COX SS S Influence of the binding group of electroactive molecules X = S or Se

35. M. F. Goffman Influence of the binding group: Se vs S Investigation of T3 and Se3 S SCOCH 3 CH 3 COS S S SeCOCH 3 CH 3 COSe S S S T3T3 Se 3 T3 Se3 “Identical” HOMOs quite similar IPs 6.50 eV 6.52 eV

36. M. F. Goffman Sample Preparation Adsorption Organization Solution Conducting Molecules Au (111) Solution Thiol-ended Insulating Molecules Insertion

37. M. F. Goffman STM tip 28 nm T3,Vt = +0.78V, It = 10.7pA L. Patrone et al, Chem. Phys.281(2002)325 PRL 91(03) 096802 Molecular structure - transport properties relationship h x S SCOCH 3 CH 3 COS S S SeCOCH 3 CH 3 COSe S S S T3T3 Se 3

38. M. F. Goffman STM tip 28 nm T3,Vt = +0.78V, It = 10.7pA L. Patrone et al, Chem. Phys.281(2002)325 PRL 91(03) 096802 Molecular structure - transport properties relationship h x S SCOCH 3 CH 3 COS S S SeCOCH 3 CH 3 COSe S S S T3T3 Se 3

39. M. F. Goffman STM tip 28 nm T3,Vt = +0.78V, It = 10.7pA L. Patrone et al, Chem. Phys.281(2002)325 PRL 91(03) 096802 Molecular structure - transport properties relationship The apparent height is a (relative) measure of the conductance of the molecular junction h x S SCOCH 3 CH 3 COS S S SeCOCH 3 CH 3 COSe S S S T3T3 Se 3

40. M. F. Goffman S vs Se: Experimental comparison ItIt ItIt STM tip 28 nm T3,Vt = +0.78V, It = 10.7pA L. Patrone et al, Chem. Phys. 281(2002)325 T3 Se3 Topography: 1.0 nm STM on T3 and Se3 Molecules inserted in a dodecanethiol Matrix

41. M. F. Goffman Se give rise to a more efficient transport than S T3 (S) Se3 (Se) Se3 > T3 S vs Se: Experimental comparison

42. M. F. Goffman Current-Voltage characteristic I V eV I 2(E F -E HOMO ) Se3 T3 EFEF HOMOLUMO Position of the HOMO level/ Fermi level (E F -E HOMO ) : T3 > (E F -E HOMO ) : Se3 E F -E HOMO eVeV

43. M. F. Goffman UPS (UV Photoelectron Spectroscopy) 1 monolayer adsorbed onto gold Position of the HOMO / Fermi level T3 : E F -E HOMO > Se3: E F -E HOMO

44. M. F. Goffman C) How conductance depends on the structure of the wire?

45. M. F. Goffman C) Comparaison of backbone conductance Kushmeric, Ratner et al JACS 2003 OPV > OPE OPV vs Othiophene?

46. M. F. Goffman CH 3 COS SCOCH 3 OPV 2 (12.67 Å) CH 3 COSSCOCH 3 SS S T3T3 (15.6 Å) 2.0 Å 4.2 Å OPV2 : HOMO - E F  0.7 eV OPV3: HOMO - E F  0.35-0.7 eV OPV 3 (19.04 Å) CH 3 COS SCOCH 3 7.3 Å C) Influence of the conjugated body: T3 vs OPVn  OPVs are more conducting than Othiophene

47. M. F. Goffman Which is the IV characteristic of a Metal-single molecule-Metal device?

48. M. F. Goffman Single Molecule Measurement Conducting AFM on Alkanedithiol on a alkanethiol matrix X.D. Cui et al., Science 2001. Metallic substrate Tip

49. M. F. Goffman Single Molecule Measurement N. J. Tao, Science 2003. Conductance histograms with STM

50. M. F. Goffman Contacting Single Molecules Mechanically Controlled break-junctions Advantages High stability accuracy  l/  z~10 -5 Freshly exposed metal surfaces Drawbacks No image of contacted molecules No gating ll zz J. M. van Ruitenbeek et al Rev. Sci. Instrum. 67 (1995) 108

51. M. F. Goffman Mechanically Controlled break-junctions (MCBJs) Experimental procedure

52. M. F. Goffman MCBJs Results on Different Molecules (@300K) S S S S S Single Molecule IV characteristics ? M. A. Reed et al, Science 278 (1997) 252 Kergueris et al PRB 59(1999)12505 Reichert et al PRL 88(2002)176804

53. M. F. Goffman Probably Yes! "Lock-in" behavior Similar molecules (length, binding groups) with different spatial symmetry gives corresponding behaviour on IVs modeling consistent with a single molecule NEGF Formalism calculation J. Heurich et al., PRL 88, 256803 (2002).

54. M. F. Goffman Conclusions for Molecular Wires B) The role of the binding group has been decoupled from that of the rest of the molecule: Se yields a better molecule-metal coupling efficiency than S since the Fermi level is nearer to the HOMO level. At low Voltage Bias A) Exponential dependence on L is confirmed. C) IVs Phenylene-Vinylene (OPV) is more efficient than thiophene as backbone. Single Molecule IV characteristics can be measured. Qualitative agreement between experiments and theory

55. M. F. Goffman 2. Diodes Aviram & Ratner Theoretical Proposal (1974) V>0 V<0 Rectifying behavior: expected from asymmetry of the D-A structure -V/2 L V/2 R

56. M. F. Goffman The Langmuir-Blodgett technique Solution eau molécules a b Single Molecular Film formation Hydrophobic part Transfer to a solid substrate Special design of the molecule

57. M. F. Goffman 2. Diodes Metzger et al.,JACS 119, 10455 (1997). Al Experimental Realization Spacer:  -conjugated Some differences Aviram & Ratner Metzeger et al Spacer:  -saturated aliphatic chain (donor side) Is Rectification due to the Aviram & Ratner mechanism ? Answer: No!

58. M. F. Goffman Which is the Rectification Mechanism Aviram & Ratner Spacer:  -saturated Spacer:  -conjugated Metzeger et al Donor and Acceptor molecular orbitals remain localized  LUMO HOMO DFT calcultion: HOMO and LUMO delocalized

59. M. F. Goffman Rectification Mechanism: Asymmetric Coupling Metzger et al.,JACS 119, 10455 (1997). aliphatic chain (donor side)  As a first approximation Al DD AA Potential Profile -V/2 V/2 r -V/2 V/2 Asymetric Coupling can be used for fabricating Diodes.

60. M. F. Goffman Using asymmetric coupling for Diode function N. Lenfant et al., Nanoletters 3, 741 (2003). Two step fabrication: Self-assembly of alkyl chains  -conjugated groups Control measurement on Alkyl chains n-doped Silicon Al n-doped Silicon

61. M. F. Goffman 2. Diodes and NDR N. P. Guisinger et al, Nanoletters 4, 55 (2004) NDR behavior: due to resonance conditions The NDR bias varies by as much as 1 V from experiment to experiment

62. M. F. Goffman 3. Switches At least two different stable states  different conductance (high /low) D A D+D+ A-A- Reduction-Oxidation (Redox) process  R R' R Conformation Change   light-triggered Open form Closed form UV R R R R Recent review: Masahiro Irie, Chem. Rev.100, 1685 (2000). Collier at al., Science 285, 391 (1999) Collier at al., Science 289, 11721 (2000) D. R. Stewart at al., NanoLett. 4, 133 (2004)

63. M. F. Goffman Light-triggered Switches Switches in Toluene Absorption (nm) Closed Open Typically Courtesy of D. Dulić and S.J. van der Molen Does it work in a solid state device ?

64. M. F. Goffman Breakjunction experiment =546 nm =313 nm One way Photochromism No switching back !? Why closing is quenched? OPEN QUESTION D. Dulić et al, PRL 91,207402 (2003).

65. M. F. Goffman Final Remarks Conductance properties of single molecules can be probed. However reproducibility and stability remains a challenge. More experiments are needed in order to refine theory and more theoretical calculation are needed to design interesting experiments (feedback!). Molecular Diodes can be obtained using asymetric coupling. Molecular Electronics on silicon can be a way of fabricating hybrid devices taking profit of the powerful infrastructure of the silicon-based IC industry  Resonant tunneling devices. Light Triggered switches are promising molecules. Tuning of the coupling between the active part and the electrodes are needed to get reversible operation.

66. M. F. Goffman MCBJs Results on Different Molecules (@4K) High stability (>10 hs) at 4K d 2 I/dV 2 spectrum  Fingerprint of the molecule ? A. Isambert, D. Dulić, JP Bourgoin, M. F. Goffman, unpublished Improved Stability CH 3 COS SCOCH 3