Amorphous free electrons

Fig. 5.3. Schematic dispersion relation of electrons and the corresponding DOS, for the crystalline state (al,a2), and for the amorphous state (bl,b2). The dotted curves indicate the free-electron behaviour. The influence of the pseudo Brillouin zone is drawn by the shadowed area. Kpc indicates the position of a peak in S K) close to 2kr...

To derive the shift in the optical band gap, Tiedje et al (1984) used the conduction and valence densities of states corresponding to the model of free electrons and holes in a one-dimensional periodic potential shown in Fig. 5a. The parameters of the model were chosen as follows bulk amorphous silicon band gap 1.8 eV conduction- and valence-band-edge discontinuities at the a-Si H/a-SiN t H interfaces [4= 1.0 eV and [4 = 0.6 eV, respectively... 

The Ziman-Faber model for liquid metals (Ziman, 1961 Faber and Ziman, 1965) has been widely used to describe the resistivity behaviour of amorphous metals. It is based on the nearly-free-electron approach and the Boltzmann transport equation. When all multiple two-site scattering corrections are neglected, the resistivity for a pure liquid metal can be represented by means of the equation... 

The free electrons in the plasma are reactant or catalyst in chemical reactions. Plasmas shift equilibria or they help thermodynamically allowed reactions that have rates that are too low at the low gas temperature (Table 6.3). Table 8.7 lists selected compounds that have been made with PE-CVD at low temperatures with their precursors and the conditions for their synthesis. The amorphous products of PE-CVD are rarely stoichiometric and almost never pure. 

The rest of this section is devoted to a discussion of amorphous semiconductors, which play a special role within the field of the electronic structures of disordered materials for two reasons. First, as discussed below, the transport properties of amorphous semiconductors are dominated by carriers within kT of the transition energy where the states are uniquely characteristic of disordered materials. Secondly, the amorphous semiconductors are all covalent, and it is the electronic structures of the covalent materials which should be most sensitive to disorder. Simple metals, where the electrons interact weakly with the atoms via small pseudopotentials are free-electron-like near the Fermi surface both as solids and liquids. Insulating materials with large band gaps but narrow bands again have electronic structures relatively insensitive to order. The covalent semiconductors correspond to intermediate cases of maximal sensitivity of electronic structure to atomic structure and composition. 

In two recent papers Allgaier (1969 1970) has emphasised the dangers in extrapolating ideas particular to ordered solids into the liquid and amorphous states. For example, suppose that a liquid exists in which it is permissible to use an energy-momentum description of the electron state. Since the E-k relationship is the same in all directions, the Fermi surface is a sphere enclosing all the valence (free) electrons. Within this framework, the Hall coefficient is given by... 

Y content, if one assumes the relation of 7 h =- INne, which can be derived from the nearly free-electron model, holds. Here, N is the atomic density and n is the number of electrons per atom. The strongly attractive interaction between Al and R atoms suggests that the s- and p-electrons in Al hybridize with s- and d-electrons in R, leading to a decrease of the free electrons which are attributed to electrical conductivity. As a result, the increase of the number of Al-R pairs in Al-R amorphous alloys with increasing... 

The electronic properties of simple metal amorphous alloys are expected to behave according to the free-electron model since the spatial isotropy that should exist in homogeneous amorphous alloys would lead to a spherical Fermi surface. However, substitution of A1 by R and/or M species raises the fundamental question as to how... 

Amorphous materials, transparent conducting oxides Free electrons and free carriers absorption... 

Lund, J., Mehta, R. and Parviz, B. (2005) Label-free electronic detection of biomolecules with amorphous silicon nanostructures. Nanomedicine Nanotechnology, Biology, and Medicine, 2, 230-8. 

Ceramics and glasses are generally multicomponent sohds that are chemically bonded by ionic or covalent bonding such that there are no free electrons. Therefore, the electrical conductivity and the thermal conductivity are low and the material is brittle. If there is crystallinity the material is called a ceramic and if there is no crystallinity (i.e. the material is amorphous) the material is called a glass. Ceramics and glasses are characterized by low ductility and low fracture toughness. Some elemental materials, such as boron, carbon, and silicon, can be formed as amorphous materials, so the definitions must be taken with some exceptions. 

For a free-electron system the band density of states decreases parabolically, as discussed in Chapter 2. The same parabolic decrease is also generally found in amorphous semiconductors. We know that a power-law expansion of any function aroxmd an extremum has quadratic dependence when sufficiently near the maximum or minimum point. Thus, it should not be surprising that the density of states follows a similar behavior in crystalline and amorphous materials. This quadratic behavior is exhibited in region I of Figure 8.11. An absorption edge can be defined based on fitting this portion of the absorption spectrum based on the function... 

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