Band structure definition

Because of the inverse relationship between interatomic distances and the directions in which constructive interference between the scattered electrons occurs, the separation between LEED spots is large when interatomic distances are small and vice versa the LEED pattern has the same form as the so-called reciprocal lattice. This concept plays an important role in the interpretation of diffraction experiments as well as in understanding the electronic or vibrational band structure of solids. In two dimensions the construction of the reciprocal lattice is simple. If a surface lattice is characterized by two base vectors a and a2, the reciprocal lattice follows from the definition of the reciprocal lattice vectors a and a2 ... 

The first absorption region of cyclopentanone extends from about 3500 A. to 2300 A. The absorption spectra in the vapor state and in heptane solution appear to be identical and show definite banded structure on both sides of the region of maximum absorption (24). A detailed analysis of the spectrum has been carried out (26a). 

The most direcdy measurable feature of the electronic band structure, the valence band photoelectron spectrum, involves the density-of-valence-states (DOVS), or p(e), which is obtained from the electronic band structure using the standard definition,... 

In order to solve these problems, it is very important and useful to clarify band structures of group-III nitrides and their QW structures and also to obtain their band structure parameters. In this Datareview, definitions of band structure parameters and available data on them for GaN and AIN are given. The data are mainly about theoretical results with first-principles band structure calculations within the local density functional approximation (LDA). They are compared with currently available experimental results. Note that the LDA calculation grossly underestimates a bandgap and that it gives almost zero bandgap for InN. Such a calculation is unlikely to yield reliable parameters for InN, especially effective masses. Therefore, the band structure parameters of InN are not given in this Datareview. 

We emphasize two natural limitations of the finite cluster model. It does not allow to make a statement about the dependence of essential parameters such as adsorption and transition energies on the level of surface coverage, and it does not account adequately for charge delocalization or surface relaxation phenomena. Further, it excludes by definition any information about the modification of the surface band structure as a consequence of the organic molecule adsorption. The following case study of 1-propanol on Si(001) - (2 x 1) is intended to clarify how these elements can be consistently incorporated into the description of the Si surface interaction with organic species. 

Results of photoemission studies of polyethylene have shown definite evidence for wide energy bands among deep valence orbitals ( ), but the nature of the fundamental absorption edge has not been resolved. Band structure calculations predict direct interband excitations to occur above 12.6 eV (.8) whereas the absorption threshold is at 7.2 eV and a strong peak in e occurs at 9.0 eV. The momentum dependence of the absorption threshold indicates that the threshold is of excitonic origin, i.e. the excitation is localized by the strong electron-hole or configuration inter-... 

By definition, a semiconductor does not have a continuum of states (as do metallic conductors) but rather a band structure. The filled levels, called the valence band, are an energetically closely spaced array of orbitals composed of the valence electrons of the material. A gap exists between the top edge of this band and the lower edge of a similar closely spaced array of orbitals that are unoccupied in the ground state, that is, the conduction band. The gap separating these bands is called the band gap. 

Keiderling (7b) has observed that when U Hi ) dissolved in an organic solvent is cooled to 2K, the monomeric Tstructure transforms back into the polymeric structure. Although it is tempting to assign the observed bands based upon the tetrahedral structure, definite conclusions must await comparison with pure Pa(BHif)tf spectra. 

Formally the energy-band structure for an infinite crystal is defined to be the eigenvalues Ej(k) of the one-electron Schrodinger equation (1.4) obtained as functions of the Bloch vector k. Physically, this definition is of course not very illuminating and I shall therefore now give the simplest possible derivation of a condition for the formation of energy bands, which has a very appealing physical interpretation. 

Finite Element Methods Applied to Many-body Perturbation Theory. - Over the past ten years, the finite element method, which is a classical tool in classical science and engineering applications, has been developed into a technique for the accurate solution of the atomic243 and molecular244,245 electronic structure problem. The piece-wise definition of the form functions employed in the finite element method prevents the computational linear dependencies which occur in the finite basis set expansion method and, moreover, leads to sparse, band structured matrices for which efficient solvers are available. 

The values of the TB parameters that reproduce the ab initio band structure are reported in Table 2 for a subset of materials the others show the same behaviour. The variation of Aa and p/Aa as a function of the mixing parameter of the hybrid functional is also depicted in Fig. 6. Trends are again very clear on increasing the fraction of HF exchange, the band gap Aa increases (the change is higher at the HF end of the series) this feature makes the material more ionic. The parameter p/Aa that is the TB definition of covalence in the materials, decreases systematically on moving from the pure DFT to the HF end of the series. 

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