Tight-binding approach

The second theoretical approach uses an ab initio or tight-binding approach to the description of electronic structure. Determination of the interlayer magnetic coupling can be achieved by calculating the total energy difference, A = — ap,... 

P. E. A. Turchi, A. Gonis and L. Colombo, eds., Tight-Binding Approach to Computational Materials Science (Materials Research Society, Warrendale, 1998). 

Figure 28 Calculated electronic band structure of (n,4) carbon nanotubes using the simple tight binding approach outlined in the text. Each of the sub-bands are characterized by its angular momentum quantum number, and the number of sub-bands is equal to the number of atoms in the unit cell. Note that the (4,4) and (1,4) tubes are metallic, where two sub-bands intercept the Fermi level, and that the others have gaps.

Concomitant with the experimental work described above, several attempts have been made to calculate the surface electronic structure of 110 GaAs, and we can now consider how the theoretical models compare with and explain the experimental results. The first point to make is that where calculations consider only an unrelaxed, i.e. ideal, surface, one or two bands of intergap states are predicted, from either a tight binding approach [167, 188, 189] or a self-consistent pseudo-potential treatment [190]. There is an occupied As dangling bond band and an unoccupied band corresponding to Ga dangling bonds. 

Self-consistent pseudo-potential calculations, based on a relaxed surface demonstrating this movement, were carried out by Chalikowsky et al. [191], while Mele and Joannopoulos [188], Calandra et al. [192] and Pandey et al. [167] used a tight-binding approach and obtained similar results, but in general there were still intrinsic gap states, contrary to experimental data. 

Three different approaches have been followed to solve this clue, and they form the backbones of all existing band-structure methods in terms of their nuclear potentials. Somewhat simplified, one may either ignore the core functions (empirical tight-binding approaches), one may modify the potential, thereby also ignoring the core functions (pseudopotential approach), or one may modify the basis sets and split the functions into core and beyond-core functions (cellular approaches and successors) [210]. 

A number of recent studies have attempted to improve on the standard tight binding approach. Rather than use a simple pair sum for A, for example, Xu et al. used the many-body expression... 

Taken separately, the approximations used in the tight binding approach... 

Figure 11.4 illustrates the cohesive energy for different crystalline structures of silicon. It is evident that data of a tight-binding approach fit the results obtained from the first-principles calculations well. 

The binding energy Eb within the tight binding approach equals... 

This chapter summarizes the main theoretical approaches to model the porous silicon electronic band structure, comparing effective mass theory, semiempirical, and first-principles methods. In order to model its complex porous morphology, supercell, nanowire, and nanocrystal approaches are widely used. In particular, calculations of strain, doping, and surface chemistry effects on the band structure are discussed. Finally, the combined use of ab initio and tight-binding approaches to predict the band structure and properties of electronic devices based on porous silicon is put forward. 

COMPUTATIONAL SPECTROSCOPY TO SILICON NANOCRYSTALS TIGHT-BINDING APPROACH... 

The semiempirical tight-binding approach is a computationally light, well-established tool to study semiconductor nanocrystals [19]. The starting point of the method is the expansion of the nanocrystal wavefunctions into a localized basis set of atomic orbitals. 

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