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Deriving Insights from Computation: Molecular Electronics to Self-trapped Excitons

Deriving Insights from Computation: Molecular Electronics to Self-trapped Excitons. Steven G. Louie Physics Department, UC Berkeley and MSD, LBNL. Electron Transport: Self-trapped Excitons: Supported by: NSF and DOE. J.-H. Choi Y.-W. Son J. Neaton J. Ihm (Korea)

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Deriving Insights from Computation: Molecular Electronics to Self-trapped Excitons

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  1. Deriving Insights from Computation: Molecular Electronics to Self-trapped Excitons Steven G. Louie Physics Department, UC Berkeley and MSD, LBNL • Electron Transport: • Self-trapped Excitons: • Supported by: NSF and DOE J.-H. Choi Y.-W. Son J. Neaton J. Ihm (Korea) K. Khoo M. Cohen S. Ismail-Beigi (Yale) Si2 O1 Si1

  2. Molecular Electronics (Electron transport through single molecules, atomic wires, …) Present approach: Ab initio scattering-state method Other ab initio approaches: NEGF methods -- (e.g., TRANSIESTA, Guo, et al., …) Lippman-Schwinger -- (e.g., di Ventra & Lang, …) Master equation -- (e.g., Gebauer & Car, …)

  3. Example of a Molecular Electronic Device (For a review, see Reed & Chen, 2000) Chen, et al (1999); Rawlett, et al (2002)

  4. Some fundamental issues µL µR • Open system: infinitely large and aperiodic • Out of equilibrium: Chemical potential ill-defined across molecule • Nanometer length scales:atomic details of contact and self-consistent electronic structure are important Current mL Vscf = Vpp + VHa + Vxc mR Self-consistent potential

  5. L lead Conductor R lead i t r Theoretical framework • Formalism for an open, infinite system out of equilibrium • capturing the atomic-scale details of the molecular junction • Two-terminal geometry with semi-infinite leads • Compute bias-dependent transmission coefficients t • Current from transmission of states T(E,V)

  6. Choi, Cohen & Louie (2004) First-principles Scattering-State Approach to Molecular Electronic Devices

  7. L lead Conductor R lead i t r Closer look at a scattering state Example state propagating from left to right with energy E Transmitted R lead state & evanescent waves Conductor C state Incident L lead state Reflected L lead state & evanescent waves Transmission matrix where, e.g.,

  8. Conductance of Pt-H2 junction Pt • Conductance of single H2 molecule has been interpreted • by break-junction measurements to be close to 1 G0 = 2e2/h • Single channel Number of Counts Conductance (2e2/h) [1] R.H.M. Smit et al., Nature 419, 906 (2002)

  9. Pd Pd-H2 junction: Reduced conductance Increasing H2 conc. x Counts PdHx PdHx 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 Conductance (2e2/h) Conductance (2e2/h) Conductance (2e2/h) Similar experiments with Pd nanojunctions yields about 0.3-0.5 G0, a factor of two or three less than Pt.

  10. Tip—H? H—H? [111] Modeling the junction Break junction

  11. Transmission spectra EF Pt Plateau Resonances G=1.01G0 Pd Resonances G=0.35G0 Khoo, Neaton & Louie (2005)

  12. Physical picture Metal Junction E • Junction states are band-like • Scattering is minimal over a range of energies EF Pt case Pt E • Junction states are resonant • Scattering is large and energy dependent EF Pd case Pd

  13. H2 Pt H2 Pd Tip atom Tip atom Local density of states Bulk atom Bulk atom Local electronic structure Pt Pd Transmission (2e2/h) Khoo, Neaton and Louie (2005)

  14. Local electronic structure Pt Pd Transmission (2e2/h) H2 Pt H2 Pd Localized Tip atom Tip atom Band-like Local density of states Bulk atom Bulk atom Khoo, Neaton and Louie (2005)

  15. Conductance of H2 nanojunctions • H2 nanojunction conductance • Strongly lead-dependent: Tip atoms play a key role • Closed-shell molecule is a good conductor! • Transport properties of small molecules are strongly affected by lead • Our calculations characterize conduction in the junction and explain experiment Khoo, Neaton & Louie (2005)

  16. Negative Differential Resistance and Lead Geometry Effects

  17. Calculated I-V Curve of a Tour Molecular Junction Son, Choi, Ihm, Cohen and Louie (2004)

  18. occupied unoccupied

  19. mL mU Dominant transmitting state

  20. mL mU

  21. Potential Drop across Molecular Junction Potential at 0.6 A above molecular plane

  22. Forces in the Photo-Excited State: Self-trapped Exciton

  23. Forces in Excited State • For many systems, photo-induced structural changes are important • – differences between absorption and luminescence • – self-trapped excitons • – molecular/defect conformation changes • – photo-induced desorption • Need excited-state forces • – structural relaxation • – luminescence study • – molecular dynamics, etc. • GW+BSE approach gives accurate forces in photo- excited state Ismail-Beigi & Louie, Phys. Rev. Lett. 90, 076401 (2003)

  24. Excited-state Forces ES = E0 + ΩS ∂RES= ∂RE0+ ∂RΩS E0& ∂RE0: DFT ΩS: GW+BSE Ismail-Beigi & Louie, Phys. Rev. Lett. 90, 076401 (2003).

  25. Verification on molecules • Excited-state force methodology • Proof of principle: tests on molecules • - CO and NH3 • GW-BSE force method works well • Forces allow us to efficiently find excited-state energy minima Ismail-Beigi & Louie, Phys. Rev. Lett.90, 076401 (2003).

  26. [1] • Silicon • Oxygen SiO2 (-quartz): optical properties Emission at ~ 3 eV! [1] Ismail-Beigi & Louie (2004) [2] Philipp, Sol. State. Comm. 4 (1966)

  27. Self-trapped exciton (STE) in SiO2 (a-quartz) Triplet STE has t≈1 ms and ~ 6 eV Stokes shift [1] 1. Start with 18 atom bulk cell • 2. Randomly • displace atoms • by ±0.02 Å • 3. Relax triplet • exciton state 4. Repeat steps 2&3: same final config. [1] e.g. Itoh, Tanimura, & Itoh, J. Phys. C21 (1988). Ismail-Beigi & Louie (2005)

  28. Silicon • Oxygen Structural Distortion from Self-Trapped Exciton in SiO2 Final configuration: Broken Si-O bond Hole on oxygen Electron on silicon Si in planar sp2 configuration Ismail-Beigi & Louie (2005)

  29. Si2 O1 Si1 Self-Trap Exciton Geometry

  30. Atomic rearrangement for STE No activation barrier!

  31. Electron-Hole Wavefunction of Self-Trapped Exciton in SiO2 Hole probability distribution with electron any where in the crystal Electron probability distribution given the hole is in the colored box

  32. Silicon • Oxygen Electron & Hole Distributions of Self-Trapped Exciton in SiO2 Final configuration: Broken Si-O bond Hole on oxygen (brown) Electron on silicon (green) Si in planar sp2 configuration Ismail-Beigi & Louie, PRL (2005)

  33. Constrained DFT Calculations • Constrained LSDA: DFT with excited occupations • Problems: • Relaxes back to ideal bulk from random initial displacements: excited-state energy surface incorrectly has a barrier. • Large initial distortion needed for STE [1,2] • Predicted Stokes shift and STE luminescence energy are very poor to correlate with experiments • [1] Song et al., Nucl. Instr. Meth. Phys. Res. B166-167, 451 (2000). • [2] Van Ginhoven and Jonsson, J. Chem. Phys.118, 6582 (2003).

  34. (*) STE in SiO2: Comparison to Experiment Tanimura et al., Phys. Rev. Lett.51, 423 (1983). Tanimura et al., Phys. Rev. B34, 2933 (1986). Itoh et al., J. Phys. C21, 4693 (1988). Itoh et al., Phys. Rev. B39, 11183 (1989). Joosen et al., Appl. Phys. Lett.61, 2260 (1992). Kalceff & Phillips, Phys. Rev. B52, 3122 (1996).

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