Generalized expression for the tunneling current in scanning tunneling microscopy

Scanning Tunneling Microscopy for Molecules: Effects of Electron Propagation into Vacuum

Using scanning tunneling microscopy (STM), we experimentally and theoretically investigate isolated platinum phthalocyanine (PtPc) molecules adsorbed on an atomically thin NaCl(100) film vapor deposited on Au(111). We obtain good agreement between theory and constant-height STM topography. We theoretically examine why strong distortions of STM images occur as a function of distance between the molecule and the STM tip. The images of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) exhibit for increasing distance, significant radial expansion due to electron propagation in the vacuum. Additionally, the imaged angular dependence is substantially distorted. The LUMO image has substantial intensity along the molecular diagonals where PtPc has no atoms. In the electronic transport gap, the image differs drastically from HOMO and LUMO even at energies very close to these orbitals. As the tunneling becomes increasingly off-resonant, the eight angular lobes of the HOMO or of the degenerate LUMOs diminish and reveal four lobes with maxima along the molecular axes, where both, HOMO and LUMO have little or no weight. These images are strongly influenced by low-lying PtPc orbitals that have simple angular structures.

Atomically resolved STM imaging with a diamond tip: simulation and experiment

The spatial resolution of a scanning tunneling microscope (STM) can be enhanced using light element-terminated probes with spatially localized electron orbitals at the apex atom. Conductive diamond probes can provide carbon atomic orbitals suitable for STM imaging with sub-Ångström lateral resolution and high apex stability crucial for the small tunneling gaps necessary for high-resolution experiments. Here we demonstrate that high spatial resolution can be achieved in STM experiments with single-crystal diamond tips, which are generally only considered for use as probes for atomic force microscopy. The results of STM experiments with a heavily boron-doped, diamond probe on a graphite surface; density functional theory calculations of the tip and surface electronic structure; and first-principles tunneling current calculations demonstrate that the highest spatial resolution can be achieved with diamond tips at tip-sample distances of 3-5 Å when frontier p-orbitals of the tip provide their maximum contribution to the tunneling current. At the same time, atomic resolution is feasible even at extremely small gaps with very high noise in the tunneling current.

Scattering theory of Bardeen's formalism for tunneling: new approach to near-field microscopy

We propose a new theoretical approach to near-field microscopy, which allows one to deal with scanning tunneling microscopy and scanning near-field optical microscopy with a unified formalism. Under the approximation of weak tip-sample coupling, we show that Bardeen's perturbation formula, originally derived for electron tunneling, can be derived from a scattering formalism which extends its validity to electromagnetic vector fields. This result should find broad applications in near-field imaging and spectroscopy.

Theoretical framework for the interpretation of STM images of adsorbates

A theoretical formalism for the interpretation of STM images of adsorbates is developed by approaching the calculation of the observed current as a transport problem in quantum statistical mechanics. The STM configuration is treated as a system of three groups of states--the substrate, the adsorbate and the tip--in contact with a thermal reservoir, with which it exchanges energy. A new definition of current is introduced, and shown to be related to that given in the traditional transfer Hamiltonian approach. The transport instrument used for the description is the stochastic Liouville equation, known to have the advantage of allowing the incorporation of thermal effects as well as arbitrary degree of coherence in the quantum transport. Some preliminary calculations of STM images of simple adsorbate models are presented.