Electronic level alignment at metal-organic contacts with a GW approach

Transcription

1 Electronic level alignment at metal-organic contacts with a GW approach Jeffrey B. Neaton Molecular Foundry, Lawrence Berkeley National Laboratory Collaborators Mark S. Hybertsen, Center for Functional Nanomaterials, BNL Su Ying Quek, Molecular Foundry, LBNL Latha Venkataraman, Columbia University Hyoung Joon Choi, Yonsei University, Seoul, Korea Steven G. Louie, University of California, Berkeley & LBNL Support DOE, NSF, NCN, NYSTAR, NERSC

2 Conductance of BDA molecular junctions Experiment Theory Au C N Log Counts H 2 N NH 2 G expt = G 0 ± 40% H G theory = G 0 ± 33% Conductance (G 0 ) Conductance distribution agrees well with expts Average DFT-GGA conductance ~7x too large S. Y. Quek, L. Venkataraman, H. J. Choi, S. G. Louie, M. S. Hybertsen & J. B. Neaton, condmat/ (2007)

3 Level alignment at metal-molecule contacts Metal-molecule contacts Energy level diagram Fermi Energy E vacuum LUMO Affinity Level Metal HOMO Ionization Level Ubiquitous in nanoscale devices Single-molecule junctions, organic electronics, passivators for nanoparticle surfaces, etc

4 Level alignment at metal-molecule contacts Metal-molecule contacts Energy level diagram Fermi Energy E vacuum LUMO Affinity Level Metal HOMO Ionization Level z Ubiquitous in nanoscale devices Single-molecule junctions, organic electronics, passivators for nanoparticle surfaces, etc Physical effects Interfacial charge transfer (dipoles) Quantum mechanical (electronic) coupling Surface polarization

5 Level alignment at metal-molecule contacts Metal-organic interfaces Energy level diagram Fermi Energy E vacuum LUMO Affinity Level Metal HOMO Ionization Level z Ubiquitous in nanoscale devices Single-molecule junctions, organic electronics, passivators for nanoparticle surfaces, etc Fundamental issues Kohn-Sham DFT orbitals adequate? Impact of correlation? Quantitative connection to experiment (e.g. STM, photoemission)

6 Naphthalocyanene on graphite STM/STS measurements: HOMO-LUMO gap reduced by graphite surface STM: Bias-contrasted image STS: Level positions and broadening HOMO HOMO LUMO Gap ~ 2.5 ev LUMO HOMO UHV at 50 K, 1.83V, 83pA, 25x25 nm2 UHV at 50 K, 1.83V, 83pA, 25x25 nm2 M. Lackinger et al, J. Phys. Chem. B 108, 2279 (2004) George Flynn Group, Columbia Gas-phase gap ~ 3.6 ev (calc)

7 GW approach Quasiparticle Hamiltonian in the GW approximation (Hedin, 1965; Hybertsen & Louie, 1985) ( H KS " V LDA + #)$ nk = E nk $ nk " = igw #1 W = " RPA (q,$)v Perturbative correction to DFT Kohn-Sham orbitals & energies GW self-energy content (electron addition/removal) "(r, # r ;E) = " X + " SX + " CH Fock exchange Dynamically-screened exchange Dynamical polarization response Physically-motivated, balanced treatment of correlation in different environments No adjustable parameters, reasonable scaling (~N G4 )

8 Model system: Benzene on graphite Benzene on graphite Flat Perpendicular 7.35 Å Gas-phase benzene Solid benzene Extrapolate to polyacenes Benzene monolayer 3.25 Å above graphite 4 layers, 3x3 unit cell, 84 atoms Assessment of correlation in benzene-diamine junctions Fisher & Blöchl (1993)

9 Gas-phase benzene: HOMO-LUMO gap Frontier Levels in the gas phase DFT-LDA GW π LDA underestimates the gap by a factor of two 5.1 ev π 10.5 ev GW HOMO-LUMO gap agrees with experiment π π GW LUMO predicted to be above the vacuum level, in agreement with experiment Experiment: IP EA = ev

10 Benzene orbital energies on graphite Benzene on graphite DFT-LDA Benzene on graphite GW Isolated Benzene GW π* 4 4 P elec E E F (ev) π 5.1 ev E E F (ev) ev 10.5 ev σ Γ π K Γ K P hole π DFT-LDA gap: ~2 ev error Gap narrows by ~3.2 ev Symmetric shifts: P elec ~ P hole ~ 1.5 ev Neaton, Hybertsen, Louie, PRL 97, (2006)

11 HOMO-LUMO gaps: Geometry & Environment Benzene π π* gap Gas phase Flat On Graphite Surface Perp. On Graphite Surface Crystal DFT-LDA (ev) GW (ev) P hole / P elec (ev) 1.45 / / / LDA gaps no geometry or environment dependence GW gaps strong geometry & environment dependence Change in orbital energies symmetric for HOMO & LUMO (P elec P hole ) Why are gaps smaller on graphite? Static polarization

12 Metal Molecule Interface: Weak Coupling Limit Molecule φ j Metal z 0 χ mol χ metal Static polarization energy difference (P j = P elec or P hole ) P j = $$ * drd r "# j ( r) # j ( r ") %V scr r, r " ( )# * j ( r)# j r " Self-energy difference of molecular orbital near surface (weak-coupling) ( ) HOMO LUMO Inkson (1971,1973) " HOMO #$" HOMO % & P hole P hole " LUMO #$" LUMO % P elec = " 1 2 P hole = 1 2 P elec " e2 4z 0 " # e2 4z 0 Image charge limit

13 Benzene on graphite: GW vs Image model V(r,r) (ev) V image ΔV scr V image ΔV scr

14 Image model for P elec /P hole Gas-phase gap Benzene: E mol = EA - IP = 10.5 ev Molecular wavefunctions z DFT/quantum chemistry Image plane position, relative to outer graphitic plane z im =1.0 Å Lang & Kohn (1973); Lam & Needs (1993)

15 How accurate is the image model? Benzene-graphite interface Flat Perpendicular Full GW Model Full GW Model LUMO P elec (ev) E F Metal P hole (ev) HOMO HOMO-LUMO gap E g = E mol - 2P (ev) Simple model for molecular gaps in the weak-coupling limit Stronger coupling? Larger molecules?

16 Impact of Polarization Energy: Acene Series Benzene Calculated gaps Pentacene Image model Neaton, Hybertsen, Louie, PRL 97, (2006)

17 Comparison with recent experiments Benzene Calculated gaps Pentacene Low Temp STM Study NaCl Image model 3 ML 2 ML 1 ML Cu Repp, Meyer, Stojkovic, Gourdon and Joachim, PRL, 2005 Conclusion Static polarization effects renormalize molecular gaps at metal contacts

18 Implications for BDA molecular junctions? Experiment Theory Au C N Log Counts H 2 N NH 2 G expt = 6.4x10-3 G 0 ± 40% H G theory = 0.04 G 0 ± 33% Conductance (G 0 ) Distribution agrees well with expts DFT-GGA conductance ~7x too large S. Y. Quek, L. Venkataraman, H. J. Choi, S. G. Louie, M. S. Hybertsen & J. B. Neaton, condmat/ (2007)

19 Level diagram of gas-phase benzene diamine -0.6 ev Vacuum level LUMO DFT-GGA µ = -2.2 ev -3.8 ev HOMO

20 Level diagram of gas-phase benzene diamine LUMO -0.6 ev Vacuum level DFT-GGA µ = -2.2 ev HOMO -3.8 ev Expt IP ev

21 Level diagram of gas-phase benzene diamine LUMO -0.6 ev Vacuum level DFT-GGA µ = -2.2 ev HOMO -3.8 ev Expt IP Σ ~ -3 ev Self-energy correction ev

22 Level diagram of benzene diamine & Au contact E DFT-GGA LUMO 2.2 ev E F = 0 1 ev DFT-GGA HOMO -1.0 ev Au

23 Level diagram of benzene diamine & Au contact E DFT-GGA LUMO 2.2 ev E F = 0 1 ev DFT-GGA HOMO -1.0 ev Au Σ ~ -3 ev Difference between DFT and expt l IP

24 Level diagram of benzene diamine & Au contact E DFT-GGA LUMO 2.2 ev E F = 0 1 ev DFT-GGA HOMO -1.0 ev Au ΔΣ ~ +1 ev Static polarization

25 Level diagram of benzene diamine & Au contact E DFT-GGA LUMO 2.2 ev E F = 0 Au 1 ev DFT-GGA HOMO -1.0 ev Net downshift ~ -2 ev Corrected HOMO -3.0 ev

26 Estimating corrections to resonance position DFT resonance position: ~ -1 ev below E F (II, II) junction Transmission E E F (ev)

27 Estimating corrections to resonance position Self-energy correction in gas phase ~ -3 ev (II, II) junction Static polarization response ~ 1 ev Transmission Conductance 0.046G 0 (GGA) Corrected 0.007G G 0 (expt) E E F (ev)

28 Conclusions Molecular resonance energies at metal contacts: Not well represented by DFT in the weak-coupling limit Strongly renormalized relative to their gas-phase values Molecular levels are, in general, too close to the metal Fermi energy in DFT. Self-energy corrections will suppress off-resonance tunneling & reduce conductance. Self-interaction corrections are not enough: Nonlocal, static polarization effects, not captured by DFT, can be significant (~ 1 ev for benzene levels). Simple estimate accounting for static polarization effects can explain discrepancy between DFT and experiment for benzenediamine-au molecular junctions Outlook: GW + transport: more accurate, but much more expensive!

29 Acknowledgements Students Khoonghong Khoo, UC-Berkeley (Louie) Lingzhu Kong, UT-Austin (Chelikowsky) Bhupesh Chandra, Columbia (Hone) Postdocs Su Ying Quek, Molecular Foundry Joydeep Bhattacharjee, Molecular Foundry Zhigang Wu, UCB (Grossman) Support DOE, NSF, NERSC, NCN Collaborators Mark S. Hybertsen, BNL Latha Venkataraman, Columbia Hyoung Joon Choi, Yonsei U, Korea Steven G. Louie, UC-Berkeley Young Woo Son, Konkuk U, Korea Jeff Grossman, UC-Berkeley Jim Hone, Columbia Tim Kaxiras, Harvard Jim Chelikowsky, UT-Austin Wenchang Lu, NCSU Jerry Bernholc, NCSU

30 Estimating corrections to resonance position Self-energy correction to HOMO level in gas phase ~ -3 ev (II, II) junction Self-interaction errors, dynamical polarization response Transmission E E F (ev)