Silicon band structure

Indirect transitions are much weaker thau direct trausitious, because the latter do uot require the participation of photons. However, many indirect-gap materials play an important role in technological applications, as is the case of silicon (band structure diagram iu Figure 4.7(a)) or germanium (baud structure diagram shown later, in Figure 4.11). Hereafter, we will deal with the spectral shape expected for both direct and indirect transitions. 

It has been reported (Huang 1997) that positron irradiation produces a large blueshift ( 126 nm), followed by a two-peak generation in the PL spectrum of PS. Although the exposure time employed was large, the result is important not only because it is a potential tool for the porous silicon band structure engineering but also to prevent modifications in positron annihilation spectroscopic experiments, as it is a characterization technique for porous silicon (Suzuki et al. 1994 Itoh et al. 1993 Dannefaer et al. 1996 Biasini et al. 2000). 

Most of the semiempirical tight-binding methods for nanostructures are based on the parametrization of bulk systems. It consists of an iterative fitting procedure, performed on the tight-binding parameters, to match the bulk silicon band structure calculated using the most advanced techniques [21]. The as-calculated parameters are then applied to the study of the electronic properties of silicon nanostructures. When the nanostructures are well passivated, the surface is expected to play a minor role, and the main electronic and optical properties are determined by the nanocrystal core. 

Figure Al.3.14. Band structure for silicon as calculated from empirical pseudopotentials [25],...

Evidence is presented for continuous tuning of the band-filling between y - 0.00 and 0.50. In comparison, electrochemical oxidation of monoclinic /)-Ni(Pc) under the same conditions is also accompanied by a significant overpotential in forming tetragonal Ni(Pc)-(BF4)0.48- However, electrochemical undoping produces the monoclinic 7-Ni(Pc) phase with far less band structure tunability than in the silicon polymer. Experiments with tosylate as the anion indicate that tetragonal [Si(Pc)0](tosylate)y n can be tuned continuously between y = 0.00 and 0.67. For the anions PFg,... 

LEDs and semiconductor, 22 174-175 in organic semiconductors, 22 201, 202 silicon, 22 485, 488 silicon carbide, 22 530 Band gap transition type, for binary compound semiconductors, 22 145, 146-147t Band structure... 

As the number of silicon atoms in the delocalized backbone cr-electron system increases, the number of HOMO and LUMO states increases, resulting in a band structure for high molecular weight polymers. Electronic absorptions from the HOMO (cr) to LUMO (essentially a ) are responsible for the characteristic UV absorption of polysilanes observed between 300 and 400 nm, the transition moment for which is in the direction of the Si chain.198 Polysilanes are... 

Bulk silicon is a semiconductor with an indirect band structure, as schematically shown in Fig. 7.12 c. The top of the VB is located at the center of the Brillouin zone, while the CB has six minima at the equivalent (100) directions. The only allowed optical transition is a vertical transition of a photon with a subsequent electron-phonon scattering process which is needed to conserve the crystal momentum, as indicated by arrows in Fig. 7.12 c. The relevant phonon modes include transverse optical phonons (TO 56 meV), longitudinal optical phonons (LO 53.5 meV) and transverse acoustic phonons (TA 18.7 meV). At very low temperature a splitting (2.5 meV) of the main free exciton line in TO and LO replicas can be observed [Kol5]. 

The band structure of bulk silicon, with possible optical transitions for (c) absorption and (d) emission of a photon, together with (e) the dispersion curves of phonon branches, is shown on the right. After [Kol5],... 

The minute network structure of microporous silicon is between the two extremes of a single atom and a large crystal. A crystallite of a few hundred silicon atoms is large enough to have a rich electronic band structure but is still small enough to show an increase in the energy of an electron-hole pair (exciton) due to... 

All authors who calculated the increase in bandgap energy A EG found that the approximation of Eq. (7.6), based on an infinite energy barrier, overestimates the size dependence. A linear [Re2, Bui, De2, Hi4, Hi8] dependence between A Eq and 1/tv or a tv-147 law [Pr4] has been found to be more realistic, as shown in Fig. 7.15. In order to simulate the complicated structure of the sponge-like silicon network the band structures for wires along different crystal orientations [Fi2], as well as for wires with constrictions, have been calculated [Hi5], The calculated en-... 

Silicon crystallizes in the diamond structure,16 which consists of two interpenetrating face-centered cubic lattices displaced from each other by one quarter of the body diagonal. In zinc blende semiconductors such as GaAs, the Ga and As atoms lie on separate sublattices, and thus the inversion symmetry of Si is lost in III-V binary compounds. This difference in their crystal structures underlies the disparate electronic properties of Si and GaAs. The energy band structure in... 

As for the fundamental gap of semiconductors, the LDA is known to underestimate its width, typically from half to two thirds of experimental values, while the Hartree-Fock gap is again much worse, for example more than five times larger than the experimental value in the case of silicon. In the case of covalent-bond materials including carbon, the LDA band structure is in general expected to be accurate, while the fundamental gap value should be considered to be larger in semiconductors than the LDA value. 

The presence of an impurity such as an As or a Ga atom in silicon leads to an occupied level in the band gap just below the conduction band or a vacant level just above the valence band, respectively. Such materials are described as extrinsic semiconductors. The n-type semiconductors have extra electrons provided by donor levels, and the p-type semiconductors have extra holes originating from the acceptor levels. Band structures of the different types of semiconductors are shown in Fig. 4.3.4. 

Fig. 2.11 Effect of n- and p-type doping on the band structure of a semiconductor (e.g. silicon).

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