Bardeen’s tunnelling theory as applied to scanning tunnelling microscopy: a technical guide to the traditional interpretation

Gottlieb, Alex D.; Wesoloski, Lisa M.

doi:10.1088/0957-4484/17/8/r01

Cited by 50 publications

(39 citation statements)

References 48 publications

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“…Following Bardeen theory in the single particle form, (see Eq. 23 in, Gottlieb et al 32 ), the matrix element entering the Fermi Golden…”

Section: Appendix A: Multipole Momentsmentioning

confidence: 99%

“…is the energy of the electrode basis state, and the matrix element appearing in the above equation represents the hybridization between the QD and the electrode states, which we evaluate using the Bardeen tunneling theory 15,32 . We let H(r) be the single particle Hamiltonian of the complete system, such that H(r) = H L (r) for r inside the electrode and H(r) = H D (r) outside, where H D is defined by (1).…”

Section: B Tunneling Ratesmentioning

confidence: 99%

“…The form (15), which is more convenient for our calculations, actually appears as an intermediate step in Bardeen's derivation 15 (see also Gottlieb et al 32 ). To proceed from here to Bardeen's surface integral formula, one subtracts zero in the forḿ…”

Section: B Tunneling Ratesmentioning

confidence: 99%

“…33 . Using the fact that initial and final energies are equal in (14), the surface integral formula follows after using integration by parts and the divergence theorem 32 . We do not use the surface integral formula in this work for the following reason.…”

Section: B Tunneling Ratesmentioning

confidence: 99%

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Effects of the interfacial polarization on tunneling in surface coupled quantum dots

2012

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Polarization effects are included exactly in a model for a quantum dot in close proximity to a planar interface. Efficient incorporation of this potential into the Schrödinger equation is utilized to map out the influence of the image potential effects on carrier tunneling in such heterostructures. In particular, the interplay between carrier mass and the dielectric constants of a quantum dot, its surrounding matrix, and the electrode is studied. We find that the polarizability of the planar electrode structure can significantly increase the tunneling rates for heavier carriers, potentially resulting in a qualitative change in the dependence of tunneling rate on mass. Our method for treating polarization can be generalized to the screening of two particle interactions, and can thus be applied to calculations such as exciton dissociation and the Coulomb blockade. In contrast to tunneling via intermediate surface localized states of the quantum dot, our work identifies the parameter space over which volume states undergo significant modification in their tunneling characteristics.2

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“…Following Bardeen theory in the single particle form, (see Eq. 23 in, Gottlieb et al 32 ), the matrix element entering the Fermi Golden…”

Section: Appendix A: Multipole Momentsmentioning

confidence: 99%

Section: B Tunneling Ratesmentioning

confidence: 99%

Section: B Tunneling Ratesmentioning

confidence: 99%

Section: B Tunneling Ratesmentioning

confidence: 99%

See 2 more Smart Citations

Effects of the interfacial polarization on tunneling in surface coupled quantum dots

2012

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“…13,14 The transition rate given by Eq. ͑6͒ can be separated into the partial decay rates into the right and left electrodes designated by ⌫ j L͑R͒ .…”

Section: ͑5͒mentioning

confidence: 99%

Model of resonant quantum tunneling through isolated molecules

Flory

2006

Phys. Rev. B

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A model is described for the resonant-tunneling current between two metal electrodes with an isolated molecule situated between them. The most significant parameters governing this process are the couplings between the electrode and molecular electronic states. The calculation of these couplings using the full atomicscale treatment of the molecular system, and extended to include the proximal surface atoms of the metal electrode, becomes computationally prohibitive for most systems. However, for a weakly coupled system, the eigenstates of the molecule and electrodes can be considered separable, and the isolated molecule can be analyzed independently from the tunneling dynamics. Following the formalism originally developed by Oppenheimer to analyze field ionization of atoms and extended by Bardeen to general tunneling phenomena, an integral expression is written down for the explicit determination of the electrode-molecule coupling, using as an input the independently computed molecular wave functions. These couplings can then be used as inputs to a rate-equation treatment of the electronic transport between the electrodes and through the intermediate molecule. This treatment is then applied to a simple idealized system consisting of an isolated hydrogen atom situated between two metal electrodes. The current, differential conductivity, and level occupation probabilities are computed, plotted, and discussed. An interesting bias dependence of the tunneling current is observed and discussed.

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Ab Initio Molecular Dynamics Studies of Conjugated Dienes on Semiconductor Surfaces

Tuckerman

2012

Functionalization of Semiconductor Surfaces

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Bardeen’s tunnelling theory as applied to scanning tunnelling microscopy: a technical guide to the traditional interpretation

Cited by 50 publications

References 48 publications

Effects of the interfacial polarization on tunneling in surface coupled quantum dots

Effects of the interfacial polarization on tunneling in surface coupled quantum dots

Model of resonant quantum tunneling through isolated molecules

Ab Initio Molecular Dynamics Studies of Conjugated Dienes on Semiconductor Surfaces

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