Theory of Electron Transport in Scanning Tunneling Microscopy and Applications to the Simulation of Images of Metal Surfaces and Adsorbed Molecules.

Scanning Tunneling Microscopy (STM) has revealed the possibility of imaging bare metal surfaces and molecules adsorbed on a metal substrate with atomic resolution. Yet, the mechanism of contrast responsible for the observed features is not completely understood in the context of former theories of STM. Clarification of this issue is of central importance to the experimentalist both to interpret data and to determine the optimal imaging conditions of specific samples. We have developed a theoretical framework suitable to describe the STM current between the probe and either a bare or an adsorbate-covered metal surface. We model the Scanning Tunneling Microscope as a problem of quantum mechanical electron transport in a system made of the tip, the substrate and the molecule, that exchanges electrons with two reservoirs. We derive the tunneling current and other STM observables in terms of electron probability propagators that depend upon the microscopic interactions between the states of the system, as well as on bath interactions. This approach overcomes the limitations of perturbative theories and allows the inclusion of temperature and dissipative effects in the calculation of the current. The widely adopted Transfer Hamiltonian theory can be recovered as a particular case. Within this framework, we use simple Hamiltonian models and simple transport theories (Master Equation, Stochastic Liouville Equation) to rationalize the factors that determine the contrast in STM images, and we find interesting and sometimes counter-intuitive results. In particular, we show how the STM current can increase due to the presence of adsorbed molecules on a metal surface. Also the possibility of building simple electric circuits at atomic level is investigated. Finally we present a computational method to simulate STM images with Extended Huckel Hamiltonian and Stochastic Liouville Equation within our framework. We apply it to cluster models of the STM system to reproduce experimental STM images of metal surfaces and adsorbed molecules on metals.