^{1}and Tamar Seideman

^{1,a)}

### Abstract

We develop a theoretical framework for the study of inelastic resonant transport and current-driven dynamics in molecular nanodevices. Our approach combines a Born-Oppenheimer solution of the coordinate-, energy-, and voltage-dependent self-energy with a time-dependent scattering solution of the vibrational dynamics. The formalism is applied to two classic problems in current-triggered dynamics. As a simple example of bound-bound events in the nuclear subspace we study the problem of current-induced oscillations in heterojunctions. As a well-studied example of bound-free events in the nuclear subspace we revisit the problem of scanning-tunneling-microscopy-triggered H-atom desorption from a Si(100) surface. Our numerical results are supported by a simple analytically soluble model.

We are grateful to Dr. C.-C. Kaun for many interesting discussions and to the NSF for generous support within Grant No. CHEM/MRD-0313638.

I. INTRODUCTION

II. THEORY

A. An analytically soluble model

III. RESULTS AND DISCUSSION

A. Bound-bound dynamics: Current-driven vibration in junctions

B. Bound-free dynamics: STM-driven desorption of H atoms from Si(100)

IV. CONCLUSIONS

### Key Topics

- Electrodes
- 25.0
- Gold
- 21.0
- Surface dynamics
- 21.0
- Vibration resonance
- 20.0
- Molecular dynamics
- 19.0

## Figures

Potential energy curves for the neutral (solid curve) and charged (dashed curve) states of the junction for an equilibrium displacement of . The van der Waals interaction is modeled as a Lennard-Jones function with the set of parameters computed in Ref. 76. The inset illustrates schematically our model junction (see Ref. 17 for details), indicating the interelectrode distance and the distance of the center of mass from the nearest electrode.

Potential energy curves for the neutral (solid curve) and charged (dashed curve) states of the junction for an equilibrium displacement of . The van der Waals interaction is modeled as a Lennard-Jones function with the set of parameters computed in Ref. 76. The inset illustrates schematically our model junction (see Ref. 17 for details), indicating the interelectrode distance and the distance of the center of mass from the nearest electrode.

The bound-bound probability amplitudes of Eq. (14) for [(a)–(c)] harmonic potential energy curves with the force constant for the molecular junction and (d) the full (anharmonic) junction potential. The numerical results (solid curves) are shown along with their fits to Lorentzian functions (dashed curves). The resonance lifetime varies from the sudden to the adiabatic limit: (a) , (b) , and (c) . The equilibrium displacement in all panels is .

The bound-bound probability amplitudes of Eq. (14) for [(a)–(c)] harmonic potential energy curves with the force constant for the molecular junction and (d) the full (anharmonic) junction potential. The numerical results (solid curves) are shown along with their fits to Lorentzian functions (dashed curves). The resonance lifetime varies from the sudden to the adiabatic limit: (a) , (b) , and (c) . The equilibrium displacement in all panels is .

The bound-bound probability amplitudes of Eq. (14) for the anharmonic junction potential with different values of (a) the equilibrium displacement and (b) the resonance lifetime. In panel (a) (solid), (dashed), (dot-dashed), and (dotted). In panel (b) (solid), (dashed), (dot-dashed), and (dotted).

The bound-bound probability amplitudes of Eq. (14) for the anharmonic junction potential with different values of (a) the equilibrium displacement and (b) the resonance lifetime. In panel (a) (solid), (dashed), (dot-dashed), and (dotted). In panel (b) (solid), (dashed), (dot-dashed), and (dotted).

The variation of the resonance width and position (relative to the Fermi energy level) with the center-of-mass coordinate and the bias voltage for a junction with (see Fig. 1).

The variation of the resonance width and position (relative to the Fermi energy level) with the center-of-mass coordinate and the bias voltage for a junction with (see Fig. 1).

The bound-bound probability amplitudes for the junction potential with coordinate-dependent (solid) and coordinate-independent (dotted) self-energies for several values of . The result for has been scaled down by a factor of 2 to allow plotting on the same scale. The self-energy data were extracted from the resonance peak of Ref. 17. Inset: Expectation value of the center-of-mass coordinate vs time for coordinate-dependent (solid) and coordinate-independent (dashed) lifetimes.

The bound-bound probability amplitudes for the junction potential with coordinate-dependent (solid) and coordinate-independent (dotted) self-energies for several values of . The result for has been scaled down by a factor of 2 to allow plotting on the same scale. The self-energy data were extracted from the resonance peak of Ref. 17. Inset: Expectation value of the center-of-mass coordinate vs time for coordinate-dependent (solid) and coordinate-independent (dashed) lifetimes.

The rate of molecular excitation to the vibrational level for the anharmonic junction potential with coordinate-dependent (solid) and coordinate-independent (dashed) self-energies. The result for has been scaled down by a factor of 2 to allow plotting on the same scale. The self-energy data were extracted from the resonance peak of Ref. 17.

The rate of molecular excitation to the vibrational level for the anharmonic junction potential with coordinate-dependent (solid) and coordinate-independent (dashed) self-energies. The result for has been scaled down by a factor of 2 to allow plotting on the same scale. The self-energy data were extracted from the resonance peak of Ref. 17.

The bound-free probabilities of Eq. (22) vs the energy transfer with (a) , (b) , (c) , and (d) . The initial electron energy is (solid), (dashed), and (dot-dashed).

The bound-free probabilities of Eq. (22) vs the energy transfer with (a) , (b) , (c) , and (d) . The initial electron energy is (solid), (dashed), and (dot-dashed).

The bound-free probabilities of Eq. (22) vs the incident electron energy for (a) , (b) , (c) , and (d) . The energy transferred is (solid), (dashed), (dot-dashed), and (dotted).

The bound-free probabilities of Eq. (22) vs the incident electron energy for (a) , (b) , (c) , and (d) . The energy transferred is (solid), (dashed), (dot-dashed), and (dotted).

## Tables

Computational parameters.

Computational parameters.

Converged fitting parameters from wave packet calculations and expected results according to Eq. (27).

Converged fitting parameters from wave packet calculations and expected results according to Eq. (27).

Article metrics loading...

Full text loading...

Commenting has been disabled for this content