M. F. Goffman

Topics on Molecular Electronics M. F. Goffman Laboratoire d’Électronique Moléculaire CEA Saclay

M. F. Goffman Introduction Feynman’s Talk in 1959: “There is Plenty of Room at the Bottom” "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

M. F. Goffman Molecular Electronics: possible building blocks Nanoparticules Nanotubes de carbone Nano-leads Synthetic Molecules S S S SS O O ADN/ARN electronic properties Û chemical structure easy to fabricate IDENTICAL in huge quantities (10 23 ) Self-assembly Self-assembly Þ templates for other nano-objects Metallic or semiconducting Link between µm and nm scale quantification of energy levels

M. F. Goffman Why Synthetic Molecules? Electronic functions can be adjusted by design of the chemical structure Molecular Wires Diodes Switches Storage 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

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

M. F. Goffman Scanning Tunneling Microscope as a two electrode probe Topographic measurement (I fixed) V I=cte z piezo scanning unit Metallic Tip Electrically conducting surface Advantages Imaging and electrical measurements Tip Manipulation Drawbacks Asymmetric contacts Reduced in plane position stability no gating I(V) spectroscopy only in rare cases 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

M. F. Goffman STM experiments on C 60 (I) D. Porath et al. J. Appl. Phys. 81, 2241 (1997) Phys. Rev. B 56, 9829 (1997) Current "blocked" up to V th IV highly non-linear SS TT V I IV measurement (z fixed) Insulating layer Topographic measurement (I fixed) V I=cte z C60 molecule C60 Monolayer

M. F. Goffman STM experiments on C 60 (II) C. Joachim et al. Phys. Rev. Lett. 74, 2102 (1995) Europhys. Lett. 30, 409 (1995) Linear IV characteristic at low V V I C60 molecules on Au 110

M. F. Goffman V I Metal- Molecule Coupling  plays a key role V I Weak coupling regime Strong coupling regime single electron effects  Coulomb addition energy E add Strong hybridization  Coherent transport (Landauer-Buttiker formalism)

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

M. F. Goffman 1. To Build Up the Energy Level Diagram Metal Reservoir Metal Reservoir Molecule e M 0  M + e M0M0 e e In the transport process the molecule will be oxydized or reduced Weak Coupling   Transfer of e - by sequential tunneling M0M M0M  M0M0 Description of metallic electrodes  Energy cost for extracting a conduction electron Description of the molecule  Energies involved in reactions : M 0  M + M 0  M 

M. F. Goffman Metallic Electrodes occupied states empty states In the independent electron approximation Ground state of N (~10 23 ) electrons system  energy levels of a single electron Fermi level µ Vacuum Level W W: Energy required to remove an electron (Work function) Good aproximation: continuous distribution of states For Au(111) W ~ 5.3 eV

M. F. Goffman Energy Level Diagram Metal Reservoir Metal Reservoir Molecule Characteristic Energies of a Molecule

M. F. Goffman MM M0M0 Isolated Molecule Energy Levels and Total Energy E(N) The density functional theory (DFT) can provide the ground state energy of the molecule M 0 and its ions M  k. Isolated Molecule (M 0 ) : Strong correlated N-electron system with M+M+ E(N) : Total energy of the N-electron Molecule (M 0 ) E(N) LUMO HOMO N N+1N -1 # of electrons ??

M. F. Goffman Characteristic energies of a molecule Electron affinity How this characteristic energies determine the Coulomb addition energy E add ? E(N) : Total energy of the N-electron Molecule (M 0 ) MM M0M0 M+M+ E(N) N N+1N -1 # of electrons Ionization Potential

M. F. Goffman Coulomb Addition Energy E add of an Isolated Molecule The Coulomb Addition Energy is defined as The capacitance of a charged system can be defined as From an atomistic viewpoint Amount of work per unit charge,  V, required to bring a fixed charged,  Q, from the vacuum level to the system Since Electron affinity Ionization Potential

M. F. Goffman Energy Diagram of an isolated molecule Vacuum Level E add Example Isolated C60 in vacuum I 0 =7.58 eV and A 0 =2.65 eV  E add = 4.93 eV Can we estimate E add using the geometry of the molecule ?

M. F. Goffman Geometrical Calculation of E add D The geometrical capacitance D=7.1~10.2 Å Why is underestimated ? M0M0 Anwser:C60 has a completely filled HOMO Does this estimation generally work?

M. F. Goffman Experiments vs Geometrical Estimation I - A (eV) e2/CGe2/CG The Larger N Better the agreement Important remark: Ionization and Affinity of the molecule depends on the environment where the molecule is embedded. For Molecules DFT reveals If HOMO level is fully populated

M. F. Goffman Modification by Metallic Electrodes (Image Potential Effect) The image force acting on the outgoing electron at position x is Ex. adsorbed molecule M +1 e-e- e+e+ x d The resulting force is repulsive for x > d and I 0 is decreased by an amount  M -1 +

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

M. F. Goffman Coupling to Metallic Electrodes (  )  can be related to the time  it takes for un electron to escape into the metallic contact can be interpreted as the rate at which electrons are injected into the molecule from the contact Isolated Molecule M0M0 Metal Reservoir  M0M0

M. F. Goffman Characteristic Energies of the Metal-Molecule-Metal structure Weak Coupling  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. Transfer of e - by sequential tunneling

M. F. Goffman Energy Diagram of Metal-Molecule-Metal structure In equilibrium, V=0  Statistical Mechanics if (I-W) and (W-A) are greater than k B T  The molecule will remain neutral (N 0 )  Current will be blocked (Coulomb blockade) The probability of having N electrons in the Molecule is  Vacuum Level µLµL µ R = µ L =µ E add W

M. F. Goffman Energy Diagram of Metal-Molecule-Metal structure Vacuum Level µLµL E add When current will flow? µ R = µ L =µ More generally electrons can flow when

M. F. Goffman Analogy with quantum dot Vacuum Level -I eV For a Molecule For a Quantum Dot (JanMartinek’s lectures) Vacuum Level eV µLµL µLµL µRµR µRµR 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?

M. F. Goffman 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 QD V/2 VgVg L R CLCL CRCR CgCg I -V/2 Where Chemical potential of the dot is Chemical Potential of the Electrodes are

M. F. Goffman Measuring the Addition Spectrum LR At V  0 Electrons can flow when N0N0 µLµL µRµR

M. F. Goffman Measurering the Addition Spectrum LR At V  0 Electrons can flow when N0N0 µLµL µRµR µLµL µRµR µLµL µRµR

M. F. Goffman µLµL µRµR µLµL µRµR µLµL µRµR Measurering the Addition Spectrum LR At V  0 Electrons can flow when N0N0 N 0 +1N 0 +2

M. F. Goffman Measuring the Addition Spectrum LR At V  0 Electrons can flow when N0N0 N 0 +1N 0 +2N 0 -1 µLµL µRµR

M. F. Goffman 4 µLµL µRµR µRµR µLµL µRµR µLµL 3 µLµL µRµR µLµL µRµR µLµL µRµR µRµR µLµL µLµL µRµR 2 V 1 N 0 -1 N0N0 N

M. F. Goffman Stability Diagram N0N0 N 0 +1 N 0 -1 V V C (N 0 ) is obtained by equating 1 3 Then Stability diagram  Experimental determination of the addition spectrum E add (N)

M. F. Goffman 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

M. F. Goffman Fabrication of Single-Molecule Transistors I Shadow evaporation 4.2K 1. Electrode separation controlled by  in situ conductance measurements (2nm ~ G  Al 2 O 3 Al Gate Oxidized Si wafer PMMA  -V/2 V/2 I VgVg 2. Deposition of OPV5 molecules by quench low temperatures K for activating thermal motion of molecules 4. Monitoring of I for trapping detection S. Kubatkin,et al, Nature 425, 698 (2003).

M. F. Goffman Experimental Results on OPV5 S. Kubatkin,et al, Nature 425, 698 (2003). Addition Energy Spectrum M0M0 HOMO LUMO M-M- HOMO LUMO M -2 HOMO LUMO M+M+ HOMO LUMO Interpretation within the CI model 10 times lower than isolated OPV5 ! M ++ HOMO LUMO

M. F. Goffman Experimental Results on OPV5 Image charge effect  localization of charges near electrodes Hubbard Model p z 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 t U, E add strongly depends on the embedding environement of the molecule

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

M. F. Goffman C 60 based Single Electron Transistor V I without C60 with C60 V is swept up to ~2.5 V to ensure I though the junction in the tunneling regime. Al 2 O 3 V I VgVg

M. F. Goffman C 60 based Single Electron Transistor IV different gate bias V g strongly suppressed conductance near zero bias step-like current jumps at higher voltages The voltage width of the zero-conductance region modulated by V g

M. F. Goffman Experiments: C 60 based Single Electron Transistor Two-dimensional Differential Conductance (G=  I/  V) plot (4 different samples) G (nS) 0 30 N N+1 N N N What are the meaning of the lines (white arrows) parallel to the boundary of the Coulomb diamonds? Information on the quantized excitations spectrum of (white arrows) 

M. F. Goffman Excitation Spectrum µRµR µLµL µRµR µLµL N N-1 Excited States (ES) of N-charged Molecule Excited States (ES) of (N-1)-charged Molecule Tunneling into GS or ES of N-charged Molecule VgVg Tunneling out from GS or ES of (N-1)-charged Molecule

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

M. F. Goffman Experiments on OPV5 Van der Zant group (DELFT) Molecular vibration assisted tunneling

M. F. Goffman Conclusions In the weak coupling limit Transport experiment : spectroscopy of a molecule embedded in a circuit Addition Spectrum E add (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

M. F. Goffman McEuen & Ralph groups Nature 2002 Park group Nature 2002 Single molecule transistor Charge state of Co ion well defined Co 2+  Co 3+ 3d 7 3d 6

M. F. Goffman Kondo Resonance