Electrons, crystalline solid materials

For many years, during and after the development of the modem band theory of electronic conduction in crystalline solids, it was not considered that amorphous materials could behave as semiconductors. The occurrence of bands of allowed electronic energy states, separated by forbidden ranges of energy, to become firmly identified with the interaction of an electronic waveform with a periodic lattice. Thus, it proved difficult for physicists to contemplate the existence of similar features in materials lacking such long-range order. 

The pursuit of further miniaturization of dectronic circuits has made submicrometer resolution lithography a crucial dement in future computer engineering. LB films have long been considered potential candidates for resist applications, because conventional spin-coated photoresist materials have large pinhole densities and variations of thickness. In contrast, LB films are two-dimensional, layered, crystalline solids that provide high control of film thickness and are impermeable to plasma down to a thickness of 40 nm (46). The electron beam polymerization of (Q-tricosenoic acid monolayers has been mentioned. Another monomeric amphiphile used in an attempt to develop dectron-beam-resist materials is a-octadecylacryhc acid (8). 

Metal-insulator transitions in both crystalline and non-crystalline materials are often associated with the existence of magnetic moments. Moments on atoms in a solid are of course an effect of correlation, that is of interaction between electrons, and their full discussion is deferred until Chapter 3. But even within the approximation of non-interacting electrons in crystalline solids, metal-insulator transitions can occur. These will now be discussed. 

In the case of metal clusters, for example, valence electrons show the shell structure which is characteristic of the system consisting of a finite number of fermions confined in a spherical potential well [2]. This electronic shell structure, in turn, motivated some theorists to study clusters as atomlike building blocks of materials [3]. The electronic structure of the metallofullerenes La C60 [4] and K C60 [5] was investigated from this viewpoint. This theorists dream of using clusters as atomlike building blocks was first realized by the macroscopic production of C60 and simultaneous discovery of crystalline solid C60, where C60 fullerenes form a close-packed crystalline lattice [6]. 

We have given this primitive modelling of the density to stress the importance of finding localized descriptions of the electron density in a molecule (or solid, especially amorphous materials, e.g. Si, where the periodicity that is so helpful in a crystalline solid no longer is present). 

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