1 / 47

Topics on Molecular Electronics M. F. Goffman L aboratoire d’ É l ectronique M oléculaire

Topics on Molecular Electronics M. F. Goffman L aboratoire d’ É l ectronique M oléculaire CEA Saclay. Introduction. Feynman’s Talk in 1959: “There is Plenty of Room at the Bottom” http://www.zyvex.com/nanotech/feynman.html

atalo
Télécharger la présentation

Topics on Molecular Electronics M. F. Goffman L aboratoire d’ É l ectronique M oléculaire

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Topics on Molecular Electronics M. F. Goffman Laboratoire d’ÉlectroniqueMoléculaire CEA Saclay

  2. Introduction • Feynman’s Talk in 1959: “There is Plenty of Room at the Bottom” http://www.zyvex.com/nanotech/feynman.html "I don't know how to do this on a small scale in practical way, but I do know that computing machines are very large; they fill rooms. Why can't we make them very small, make them of litle wires, little elements- and by little, I mean little. For instance, the wires should be 10 or 100 atoms in diameter, and the circuits should be a few thousand of angstroms across…there is plenty of room at the bottom to make them smaller. There is nothing that I can see in the physical laws that says the computer elements cannot be made enormously smaller than they are now. In fact, there may be certain advantages." Can we control the position of individual Molecules to make them do useful tasks? Can we use electronic properties of Molecules to build up devices?  MOLECULAR ELECTRONICS

  3. S O O S S S S Molecular Electronics: possible building blocks Synthetic Molecules Nanoparticules • electronic properties Ûchemical structure • easy to fabricate IDENTICAL in huge quantities (1023) • Self-assembly quantification of energy levels ADN/ARN Nanotubes de carbone Nano-leads • Self-assembly Þtemplates for other nano-objects • Metallic or semiconducting • Link between µm and nm scale

  4. Molecular Wires Why Synthetic Molecules? • Electronic functions can be adjusted by design of the chemical structure Diodes Storage Switches In principle a whole set of functions can be embedded in a circuit by appropriate choice of the molecule Electronic Function is a property of the Metal-Molecule-Metal structure

  5. Basic device: Metal-Molecule-Metal junction Electronic Function is a property of the Metal-Molecule-Metal structure Current-Voltage (IV) Characteristic (Electronic Function) I V Source Drain Metal-Molecule Coupling (G) plays a key role

  6. piezo scanning unit I=cte Metallic Tip z V Electrically conducting surface Scanning Tunneling Microscope as a two electrode probe Topographic measurement (I fixed) C. Joachim et al Phys. Rev. Lett. 74 (1995)2102 S. Datta et al Phys. Rev. Lett. 79(1997) 2530 L. A. Bumm et al Science 271 (1996) 1705 A. Dhirani et al J. Chem. Phys. 106 (1997) 5249 V. Langlais et al, Phys. Rev. Lett. 83 (1999) 2809 L. Patrone et al Chem Phys. 281 (2002) 325 Drawbacks Advantages Asymmetric contacts Reduced in plane position stability no gating I(V) spectroscopy only in rare cases Imaging and electrical measurements Tip Manipulation

  7. Topographic measurement (I fixed) z V GT V Insulating layer GS I=cte I STM experiments on C60 (I) IV measurement (z fixed) D. Porath et al. J. Appl. Phys.81, 2241 (1997) Phys. Rev. B 56, 9829 (1997) C60 molecule C60 Monolayer • Current "blocked" up to Vth • IV highly non-linear

  8. V I STM experiments on C60 (II) C. Joachim et al. Phys. Rev. Lett.74, 2102 (1995) Europhys. Lett.30, 409 (1995) C60 molecules on Au 110 • Linear IV characteristic at low V

  9. Metal- Molecule Coupling G plays a key role V V I I Weak coupling regime Strong coupling regime single electron effects  Coulomb addition energy Eadd Strong hybridization  Coherent transport (Landauer-Buttiker formalism)

  10. Outline I Molecular conduction in the weak limit regime • Energy diagram of the metal-molecule-metal structure • Description of metallic electrodes • Characteristic energies of the molecule: Eadd and Molecular Levels (ML) • Coupling to metallic electrodes G • Weak Coupling limit GEaddSingle electron effects Analogy with Quantum Dots Revisiting Quantum Dot physics Addition spectrum from conductance measurements Stability Diagram in the (V,Vg) plane • Experiments on single molecules in the weak coupling limit

  11. e e e e 1. To Build Up the Energy Level Diagram Weak Coupling G Transfer of e- by sequential tunneling In the transport process the molecule will be oxydized orreduced Metal Reservoir Metal Reservoir Molecule M0 M+ M0 M0M- M0 • Description of metallic electrodes  Energy cost for extracting a conduction electron • Description of the molecule  Energies involved in reactions : M0 M+ • M0 M-

  12. Vacuum Level Metallic Electrodes In the independent electron approximation Ground state of N (~1023 ) electrons system  energy levels of a single electron W empty states Fermi level µ occupied states For Au(111) W ~ 5.3 eV Good aproximation: continuous distribution of states W: Energy required to remove an electron (Work function)

  13. Energy Level Diagram Molecule Metal Reservoir Metal Reservoir Characteristic Energies of a Molecule

  14. Isolated Molecule (M0) : Strong correlated N-electron system with M- M+ M0 Isolated Molecule The density functional theory (DFT) can provide the ground state energy of the molecule M0 and its ions Mk. E(N) : Total energy of the N-electron Molecule (M 0) Energy Levels and Total Energy E(N) E(N) LUMO HOMO ?? ?? # of electrons N -1 N+1 N

  15. M- M+ M0 Characteristic energies of a molecule E(N) : Total energy of the N-electron Molecule (M 0) E(N) N -1 N+1 # of electrons N Ionization Potential Electron affinity How this characteristic energies determine the Coulomb addition energy Eadd ?

  16. Coulomb Addition Energy Eadd of an Isolated Molecule The Coulomb Addition Energy is defined as The capacitance of a charged system can be defined as Amount of work per unit charge, DV, required to bring a fixed charged, DQ, from the vacuum level to the system From an atomistic viewpoint Since Electron affinity Ionization Potential

  17. Vacuum Level Energy Diagram of an isolated molecule Eadd Example Isolated C60 in vacuum I0=7.58 eV and A0=2.65 eV  Eadd = 4.93 eV Can we estimate Eadd using the geometry of the molecule ?

  18. Why is underestimated ? Anwser:C60 has a completely filled HOMO M0 Geometrical Calculation of Eadd The geometrical capacitance D D=7.1~10.2 Å Does this estimation generally work?

  19. I - A (eV) e2/CG Experiments vs Geometrical Estimation For Molecules DFT reveals If HOMO level is fully populated The Larger N Better the agreement Important remark: Ionization and Affinity of the molecule depends on the environment where the molecule is embedded.

  20. Modification by Metallic Electrodes (Image Potential Effect) Ex. adsorbed molecule M-1 M+1 e- e+ + - x d The image force acting on the outgoing electron at position x is The resulting force is repulsive for x > d and I0 is decreased by an amount

  21. Modification by Metallic Electrodes (Image Potential Effect) Similarly, when an additional electron approaches and thus For C60 weakly coupled to a metal electrode For d = 6.2 Å (van der Waals) D  7.1 Å d Addition energy of the embedded molecule Eaddis modified by metallic electrodes as

  22. M0 Isolated Molecule Coupling to Metallic Electrodes (G) G can be related to the time t it takes for un electron to escape into the metallic contact G M0 Metal Reservoir can be interpreted as the rate at which electrons are injected into the molecule from the contact

  23. Characteristic Energies of the Metal-Molecule-Metal structure determined by the extent of the electronic wave function in the presence of metal electrodes. determined by the overlap of the electronic wave function and the delocalized wave function of metal electrodes. Weak Coupling  Transfer of e- by sequential tunneling

  24. W µL µR=µL=µ Eadd Vacuum Level Energy Diagram of Metal-Molecule-Metal structure In equilibrium, V=0  Statistical Mechanics The probability of having N electrons in the Molecule is  if (I-W) and (W-A) are greater than kBT  The molecule will remain neutral (N0)  Current will be blocked (Coulomb blockade)

  25. Vacuum Level Energy Diagram of Metal-Molecule-Metal structure µL µR=µL=µ Eadd When current will flow? More generally electrons can flow when

  26. Vacuum Level Vacuum Level eV eV -I Analogy with quantum dot For a Molecule For a Quantum Dot (JanMartinek’s lectures) µL µL µR µR Transport experiment in weak coupling limit : spectroscopy of a molecule embedded in a circuit Does the Constant Interaction Model used for QD apply to Single molecules?

  27. Revisiting Quantum Dot Theory (few electron QD) Constant Interaction Model • Electron-electron interactions are parameterized by a constant capacitance C • Single electron energy spectrum calculated for non-interacting e- is unaffected by interactions The total ground state energy of an N electron dot can be approximated by CL CR I QD L R Cg -V/2 V/2 Where Vg Chemical potential of the dot is Chemical Potential of the Electrodes are

  28. µL µR Measuring the Addition Spectrum L R Electrons can flow when At V0 N0

  29. µL µL µL µR µR µR Measurering the Addition Spectrum L R Electrons can flow when At V0 N0

  30. µL µR µL µR µL µR Measurering the Addition Spectrum L R Electrons can flow when At V0 N0 N0+1 N0+2

  31. Measuring the Addition Spectrum L R Electrons can flow when µL µR At V0 N0-1 N0 N0+1 N0+2

  32. µL µL µL µL µR µR µR µR V 3 1 µL µL µR 3 4 2 µR 4 µR µR µL µL 1 N0+1 N0-1 N0 2

  33. Stability Diagram 3 1 V N0+1 N0-1 N0 VC(N0)is obtained by equating Then Stability diagram  Experimental determination of the addition spectrum Eadd(N)

  34. Experiments on Single Molecules To address single molecules individually 1. Fabricate two metallic electrodes separated by the size of the molecule  Small molecules 1-3nm  Long Molecules (like CNT or DNA) ~100 nm 2. Connect the molecule to the electrodes

  35. I a V/2 Vg PMMA -V/2 Al2O3 Al Gate Oxidized Si wafer Fabrication of Single-Molecule Transistors I S. Kubatkin,et al, Nature 425, 698 (2003). Shadow evaporation technique @ 4.2K 3. Annealing @ 70 K for activating thermal motion of molecules 4. Monitoring of I for trapping detection 1. Electrode separation controlled by a in situ conductance measurements (2nm ~ GW ) 2. Deposition of OPV5 molecules by quench condensation @ low temperatures

  36. Interpretation within the CI model M-2 M- M++ LUMO M+ HOMO LUMO LUMO M0 HOMO HOMO LUMO HOMO LUMO HOMO 10 times lower than isolated OPV5 ! Experimental Results on OPV5 Addition Energy Spectrum S. Kubatkin,et al, Nature 425, 698 (2003).

  37. U, t Experimental Results on OPV5 Image charge effect  localization of charges near electrodes Hubbard Model pz orbitals t adjusted to give the optical H-L gap (2.5 eV) where d = 4.7 Å in reasonable agreement with van der Waals distances Eaddstrongly depends on the embedding environement of the molecule

  38. V Fabrication of Single-Molecule Transistors II Electromigration-induced break-junctions H. Park et al., APL 1999 M. Lambert et al Nanotech. 2003. Adsorption of molecules Breakdown & Trapping

  39. V V C60 based Single Electron Transistor Al2O3 without C60 I with C60 V is swept up to ~2.5 V to ensure I though the junction in the tunneling regime. I Vg

  40. C60 based Single Electron Transistor IV characteristics @ different gate bias Vg • strongly suppressed conductance near zero bias • step-like current jumps at higher voltages • The voltage width of the zero-conductance region modulated by Vg

  41. Information on the quantized excitations spectrum of (white arrows) Experiments: C60 based Single Electron Transistor Two-dimensional Differential Conductance (G=I/V) plot (4 different samples) G (nS) 0 N N+1 N N+1 30 N N N+1 N+1 What are the meaning of the lines (white arrows) parallel to the boundary of the Coulomb diamonds?

  42. µL µL µR µR Excitation Spectrum Excited States (ES) of N-charged Molecule Vg N-1 N Excited States (ES) of (N-1)-charged Molecule Tunneling into GS or ES of N-charged Molecule Tunneling out from GS or ES of (N-1)-charged Molecule

  43. Internal vibrations of C60 33meV (lowest energy mode) Eexp = 35 meV M k k =70 Nm-1 e- C60 transistor: Excitation Spectrum Park et al Nature 407 57-60(2000) Experimental Facts 5meV excitation energy independent of the number N of electrons in the C60 molecule Excited electronic states? No Vibrational excitation ? Possible Coupling between vibronic modes and electrons are important

  44. Experiments on OPV5 Van der Zant group (DELFT) Molecular vibration assisted tunneling

  45. Conclusions In the weak coupling limit Transport experiment : spectroscopy of a molecule embedded in a circuit Addition Spectrum Eadd(N) Excited states Experiments show that spectra are not well-described by simple models of non-interacting electrons (Constant Interaction Model) Why study the spectra of discrete states ? Good way to learn about the consequences of electron interactions at a very fundamental level

  46. Single molecule transistor McEuen & Ralph groups Nature 2002 Park group Nature 2002 Charge state of Co ion well defined Co2+Co3+ 3d7 3d6

  47. Kondo Resonance

More Related