Theory of the scanning tunnelling microscope

Abstract

The formula for tunaelling between tm objects is fundamental to undw standing the scanning tunnelling microscope. Although an exact expression for the one-electron turmelling m n t is known, its derivation hss previously been complex.Here we present a new derivation which is relatively simple and based on physical arguments. We go on to use OUT methods to show for the first time the connee tion between the e x a d formula and the widely used transfer Hamiltonian method of Bardeen. Finally we emphasize the importance of choosing a form& that minimizes the computational &ort requimd to rastm the STM tip across a d a c e .

Oxidation electronics: bond–band–barrier correlation and its applications

“…The features of an STS spectrum are associated with the on-site DOS of a few atoms at a surface [297,298]. Features below E F (tip negative bias) correspond to the occupied DOS at the surface while features above E F (tip positive) represent the allowed, yet unoccupied, DOS of the sample surface [16].…”

STS and PES: Valence DOS

“…The features of an STS spectrum are associated with the on-site DOS of a few atoms at a surface [1,2]. Features below E F (tip negative bias) correspond to the occupied DOS at the surface, while features above E F (tip positive) represent the allowed, yet unoccupied, DOS of the sample surface [3].…”

Carrier wave effect in nonresonant inelastic scanning tunneling spectroscopy of molecules with delocalized frontier orbitals

“…II B, we discuss the relation between Green's function in tight-binding basis and the Todorov-Pendry ͑TP͒ tunneling equation. 12,13 TP approach can be rephrased in terms of spectral terms including matrix elements of retarded and advanced Green's function and the imaginary part of the total self-energy, which formally is similar to the nonequilibrium LandauerBüttiker approach as formulated by Meir and Wingreen. 17 Although we consider the equilibrium Green's-function limit, this representation is able to expose the matrix elements of the density matrix explicitly for further tunneling channel analysis.…”

“…To compute the tunneling spectra we apply the TodorovPendry expression 12,13 for the differential conductance between orbitals of the tip ͑t , tЈ͒ and the sample ͑s , sЈ͒, which in our case yields…”

“…9,10 In order to improve recognition of different modes, symmetry selection rules have been incorporated into this theory by Lorente et al 11 The transparency of theoretical calculations can be taken a step further by utilizing Green'sfunction methods in an atomic-or molecular-orbital basis. Especially the formalism independently derived by Todorov 12 and Pendry 13 has proven very useful in decomposing the tunneling signal into tunneling channels, 14 and there is no restriction against applying channel analysis to inelastic tunneling. Inelastic effects have been incorporated into STS calculations at least in connection with high-temperature superconductivity.…”