A theoretical model of scanning tunneling microscopy: Application to the graphite (0001) and Au(111) surfaces

An expression for the scanning tunneling microscopy (STM) current between the tip and sample is presented using first-order perturbation theory for a two-Hamiltonian formalism ("reactants" and "products"). The calculated STM current depends on the square of the sample-tip matrix elements, averaged over a selection of random points in wave vector space. In the limit of low voltage and temperature, this averaging is over the Fermi surface of the sample. The model is applied to the graphite (0001) and Au(111) surfaces using a simple model (chain) of a tungsten tip and the tight-binding approximation. Comparisons with experiments and with the result for graphite obtained by Tersoff and Lang using a molybdenum tip are given. The theory is applied elsewhere to STM of adsorbates

Surface properties of solids using a semi-infinite approach and the tight-binding approximation

A semi-infinite approach (rather than a slab method or finite number of layers) is used to treat surface properties such as wave functions, energy levels, and Fermi surfaces of semi-infinite solids within the tight-binding (TB) approximation. Previous single-band results for the face-centered cubic lattice with a (111) surface and for the simple cubic lattice with a (001) surface are extended to semi-infinite layers, while the extension to calculations of other surfaces is straightforward. Treatment of more complicated systems is illustrated in the calculation of the graphite (0001) surface. Four interacting bands are considered in the determination of the wave functions, energies, and Fermi surface of the graphite (0001) surface. For the TB model used, the matrix elements in the secular determinants for the semi-infinite solid and for the infinite bulk solid obey the same expressions, and the wave functions are closely related. Accordingly, the results for the bulk system can then be directly applied to the semi-infinite one. The main purpose of the present paper is to provide wave functions and other properties used elsewhere to treat phenomena such as scanning tunneling microscopy and electron transfer rates at electrodes

Scanning tunneling microscopy theory for an adsorbate: Application to adenine adsorbed on a graphite surface

An expression is obtained for the current in scanning tunneling microscopy (STM) for a single adsorbate molecule. For this purpose the ``Newns–Anderson'' treatment (a ``discrete state in a continuum'' treatment) is used to obtain wave functions and other properties of the adsorbate/substrate system. The current is expressed in terms of the adsorbate–tip matrix elements, and an effective local density of states of the adsorbate/substrate system, at the adsorbate. As an example, the treatment is applied to the STM image of adenine adsorbed on a graphite surface, and the results are compared with experiment. The dependence of the image on the position of adenine with respect to the underlying graphite is considered. A discussion is given of the type of experimental STM data needed for suitable comparison of theory and experiment. In an analysis of the calculations, the role of each atom, its neighbors, next nearest neighbors, etc., in an adsorbed molecule is considered. The need for using in the present calculation more orbitals than only the HOMO and the LUMO of the adsorbate is also noted