ABSTRACT
So far, in this book, we have paid great attention to the distribution of carriers in the energy axis, and to the equilibration of a carrier distribution across a contact between different materials. For the production of useful action in energy devices, it is necessary to consider the displacement of carriers in a material and their flux across the interfaces. These features are generally termed kinetics and they lie at the heart of the observed electric current and the rate of production of a given compound by electrochemical reaction. There are many important aspects to the electric current in practical devices, but here we focus on the physical origin of the current and its suitable description based on phenomenological models for electron transference mechanisms between molecules, inside a transport medium, or at interfaces between different materials. Electron transfer in a particular circumstance could be determined from first principle calculations by solving Schrödinger’s equation for the electron’s wave function, provided that sufficient information is available about the interactions in the electron environment. However, often we cannot afford a useful device description based on first principle alone. In addition, following Franck-Condon principle the transition of a carrier is so fast that the environmental degrees of freedom can be considered as frozen. We will focus here on jumping or hopping models in which the transition is viewed as an instantaneous event between states that obey a thermal distribution. As a fundamental basis to the analysis of physical characteristics of electron transfer between different media, or between different states in a single material, a very general detailed balance principle will be explained. This principle facilitates to establish specific forms of carrier transfer rates. The properties of trapping and detrapping of electrons in semiconductors are discussed specifically, and we derive the rate of recombination of electrons and holes mediated by a trap in the center of the bandgap. Then we provide an overview of the Marcus model that starts from the important fact that transference of charge provokes a large change of equilibrium state of a molecule, both for the internal state corresponding to the change in bond-length, as well as for the surrounding polarization of the molecule if it lies in a polar medium. The polarization of the medium also has a great influence in the displacement of a carrier in the phenomenon of polaron hopping. In the final section of the chapter, we present models of macroscopic current flow at interfaces in various instances. We first determine the rate of electron transfer at the metal/solution interface that allows us to derive the central expression for current-voltage characteristics of electrodes in electrochemical cells. Then, we analyze the different types of electron transfer at the metal-semiconductor contact that is ubiquitous in electronic devices. Finally, we describe the specific characteristics of electron transfer at the semiconductorelectrolyte contact that explain primary characteristics of photoelectrochemical cells.
