Band structure strain effects

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. 

Syy, E = exx-Eyy 2i8xy, and e+z = 8xz iEyz. In order to help the derivation of the deformation potentials for WZ structure, we investigate the strain effect on the eigenstates at the F point. At the T point, assuming that e = ew and Exy = Eyz = En = 0, we can analytically solve the 6x6 strain Hamiltonian for valence bands and obtain the three doubly degenerate eigenstates ... 

Analogous effects have also been discussed for the reactivity of different bulk metal surfaces, where the center of gravity of the d-band determines the bonding [350]. In this case, the effects on the reactivity are considerably smaller than in the case of clusters in the nonscalable size regime and are size independent. Additional factors that change the d-band structure for a particular element are strain effects and the crystallographic orientation of the respective surface plane (see Chap. 3). 

We have employed the recently developed Valence Effective Hamiltonian technique (16) and MNDO calculations (22) to study the influence of strain in TKe sidegroups on the geometry of the backbone and the resulting polymer band structure, bandgap, and ionization potential. The molecule used in our simulation of strain... 

The electric conductivity of carbon nanotubes is largely influenced by the presence of defects. Even effects as modest as axial strain with bond expansion change the band structure. Stone-Wales defects and other imperfections diminish the electric conductivity as well. This effect is especially pronounced for defects with two adjacent vacancies. The resistance of a 400 nm long SWNT, for example, increases by a factor of 1000 if the tube bears as little as 0.03% of these double vacancies. Single vacancies, on the other hand, do not cause such dramatic changes. In any case, however, the free path of the electrons is reduced considerably by the defects (in parts down to a few nanometers). Still, due to the multitude of existing conduction channels, this has no large influence on the overall conductivity. 

Piezoresistive sensors. To measure the pressure, the resistance change to stress (the piezoresistance effect) may be employed. When silicon is stressed, the resulting strain breaks the cubic symmetry of the underlying crystal structure. The band structure of silicon is very sensitive to its crystal structure and, as a result, the consequent modification causes changes in the resistivity of the material (holes in the case of p " material). This change is... 

Photoluminescence (PL) of individual microtubes containing GaAs quantum wells has been examined by means of microfluorescence spectroscopy. PL spectrum of a microtube was found to exhibit a pronounced red shift by about 70 meV with respect to the reference planar film. The shift is attributed to an interplay of strain effects on semiconductor band structure. 

The band structure of the SLS is determined not only by the composition of the layers and their thicknesses but also by the strain in the layers and quantum size effects ( 5). The strain affects the energy of the band minima, and splits certain degenerate levels in both the conduction and valence band. The splitting which results from the strain can also alter the effective mass of the holes in the SLSs (20). 

He R, Yang P (2006) Giant piezoresistance effect in silicon nanowires. Nat Nanotechnol 1 42-46 Hong K-H, Kim J, Lee S-H, Shin JK (2008) Strain-driven electronic band structure modulation of Si nanowires. Nano Lett 8(5) 1335-1340... 

The effect of strains on the band structure of crystals has been intensively investigated by Bir and Pikus, using both the theory of perturbation and a group-theoretical method, namely the theory of invariants. The approach can be applied to deduce the strain derivatives of the wavefunctions appearing in Eq. (5). Following the procedure of the authors of Ref. 8, the Kohn-Sham operator for a valence electron in a strained crystal can be written in the form... 

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