Galperin Michael. Electron tunneling through molecular layers

Thesis submitted for the degree of Doctor of Philosophy. — Submitted to the Senate of Tel-Aviv University. — June 2002. — P. 1-54.
This work was carried out under the supervision of Professor Abraham Nitzan.Abstract. This thesis deals with processes involving electron transport through molecules and thin molecular layers. It is divided into three parts that discuss (a) the transmission probability, (b) dynamics and time-scale considerations, and (c) many-body aspects of such processes.
My investigation of transmission probabilities have focused on three issues. First, I studied the validity of computations based on the super-exchange mechanism in the electron transfer modelling. The super-exchange mechanism is essentially a reduced basis description of the electron transmission problem, in which a molecular bridge is represented by a sequence of coupled levels. Using a simple 1-dimensional barrier model for which an “exact” numerical solution can be obtained, the validity of reduced basis representations can be critically evaluated. This work also establishes the connection between the scattering approach to tunneling that is common in transmission studies and a perturbation theory approach based on localized initial and final states, as is used in electron transfer theories. Secondly, I study electron transmission through water layers confined between Pt(100) planar surfaces. The calculation is based on the absorbing boundary conditions Green’s function (ABCGF) method. This work, which continues earlierefforts in our group, focuses on the role of resonance tunneling in the process. We find that water configurations that contain holes in the water structure support such resonances. The lifetime of resonance supporting structures and their probability to occur were also studied, establishing the plausibility of the role of resonance tunneling events in the enhancement of current through water layers. The absolute current expected in STM operation in clear water was calculated and found to be in the order of magnitude observed experimentally.
Finally, numerical methods were developed and implemented for these studies. This includes writing an efficient code for computing the electrostatic potential in STM configuration on one hand and the development of a method that replaces absorbing boundary condition originally used in these studies by an exact evaluation of the corresponding self-energy. As a test of these numerical developments I have studied the feasibility of observing in STM experiments the structure of electronic wavefunctions localized in the barrier.Contents
Introduction
The transmission probability
Perturbation theory approach to tunneling
Elastic transition through water layers
Tunneling currents in water
Numerical issues
Dynamic issues and inelastic tunneling
Traversal time for tunneling
Inelastic tunneling through water layers
Present work
Future directions
References
Papers