Metal surfaces electronic three-dimensional case

In the past the theoretical model of the metal was constructed according to the above-mentioned rules, taking into account mainly the experimental results of the study of bulk properties (in the very beginning only electrical and heat conductivity were considered as typical properties of the metallic state). This model (one-, two-, or three-dimensional), represented by the electron gas in a constant or periodic potential, where additionally the influence of exchange and correlation has been taken into account, is still used even in the surface studies. This model was particularly successful in explaining the bulk properties of metals. However, the question still persists whether this model is applicable also for the case where the chemical reactivity of the transition metal surface has to be considered. 

The electronic properties of organic conductors are discussed by physicists in terms of band structure and Fermi surface. The shape of the band structure is defined by the dispersion energy and characterizes the electronic properties of the material (semiconductor, semimetals, metals, etc.) the Fermi surface is the limit between empty and occupied electronic states, and its shape (open, closed, nested, etc.) characterizes the dimensionality of the electron gas. From band dispersion and filling one can easily deduce whether the studied material is a metal, a semiconductor, or an insulator (occurrence of a gap at the Fermi energy). The intra- and interchain band-widths can be estimated, for example, from normal-incidence polarized reflectance, and the densities of state at the Fermi level can be used in the modeling of physical observations. The Fermi surface topology is of importance to predict or explain the existence of instabilities of the electronic gas (nesting vector concept see Chapter 2 of this book). Fermi surfaces calculated from structural data can be compared to those observed by means of the Shubnikov-de Hass method in the case of two- or three-dimensional metals [152]. 

The simplest photoelectrochemical cells consist of a semiconductor working electrode and a metal counter electrode, both of which are in contact with a redox electrolyte. In the dark, the potential difference between the two electrodes is zero. The open circuit potential difference between the two electrodes that arises from illumination of the semiconductor electrode is referred to as the photovoltage. When the semiconductor and counter electrode are short circuited, a light induced photocurrent can be measured in the external circuit. These phenomena originate from the effective separation of photogenerated electron-hole pairs in the semiconductor. In conventional photoelectrochemical studies, the interface between the flat surface of a bulk single crystalline semiconductor and the electrolyte is two dimensional, and the electrode is illuminated from the electrolyte side. However, in the last decade, research into the properties of nanoporous semiconductor electrodes interpenetrated by an electrolyte solution has expanded substantially. If a nanocrystalline electrode is prepared as a film on a transparent conducting substrate, it can be illuminated from either side. The obvious differences between a flat (two dimensional) semiconductor/ electrolyte junction and the (three dimensional) interface in a nanoporous electrode justify a separate treatment of the two cases. 

Electron transport properties of metal oxides nanoparticles are very important for electrical and electronic applications as well as for understanding the unique one-dimensional carrier transport mechanism. It has been noticed that the diameter of metal oxides nanoparticles, surface conditions, crystal structure and its quality i.e., chemical composition, crystallographic orientation along the film axis etc are important parameters that influence the electron transport mechanism. It is found that conductance of a nano-structure strongly depends on their crystalline structure. For example, in the case of perfect crystalline Si nanowires having four atoms per unit cell, generally three conductance channels are found [51], One-or two-atom defect, either by addition or removal of one or two atoms may disrupt the number of such conductance channel and may cause variation in the conductance. It has been observed that change in the surface conditions of the nanowires can cause remarkable... 

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