Silicon crystal structures, lattice parameters

See Herzog, H.J. Crystal structure, lattice parameters and liquidus-solidus curve of the SiGe system, in Properties of Silicon Germanium and SiGe.Carbon. Erich Kasper and Klara Lyutovich, eds., London, INSPEC, 2000, p. 45. 

The nature of the deposit and the rate of nucleation at the very beginning of the deposition are affected, among other factors, by the nature of the substrate. A specific case is that of epitaxy where the structure of the substrate essentially controls the structure of the deposit.Plb lP ] Epitaxy can be defined as the growth of a crystalline film on a crystalline substrate, with the substrate acting as a seed crystal. When both substrate and deposit are of the same material (for instance silicon on silicon) or when their crystalline structures (lattice parameters) are identical or close, the phenomena is known as homoepitaxy. When the lattice parameters are different, it is heteroepitaxy. Epitaxial growth cannot occur if these stmctural differences are too great. 

Silicon is a semiconductor with an intrinsic conductivity of 4.3 x 10" Q" cm and a band gap of I.I2eV at 300K. It has a diamond crystal structure characteristic of the elements with four covalently bonded atoms. As shown in Fig. 2.1, the lattice constant, a, is 5.43 A for the diamond lattice of silicon crystal structure. The distance between the nearest two neighbors is V3a/4, that is, 2.35 A, and the radius of the silicon atom is 1.18 A if a hard sphere model is used. Some physical parameters of silicon are listed in Table 2.1. 

Table 1.1. Abundance of the metal in the earths s crust, optical band gap Es (d direct i indirect) [23,24], crystal structure and lattice parameters a and c [23,24], density, thermal conductivity k, thermal expansion coefficient at room temperature a [25-27], piezoelectric stress ea, e3i, eis and strain d33, dn, dig coefficients [28], electromechanical coupling factors IC33, ksi, fcis [29], static e(0) and optical e(oo) dielectric constants [23,30,31] (see also Sect. 3.3, Table 3.3), melting temperature of the compound Tm and of the metal Tm(metal), temperature Tvp at which the metal has a vapor pressure of 10 3 Pa, heat of formation AH per formula unit [32] of zinc oxide in comparison to other TCOs and to silicon...

The crystal structure of CeRhjSij has been refined by Ballestracci (1976) by means of X-ray powder diffraction data. CeRhjSij adopts the ordered ThCrjSij-type with lattice parameters a = 4.086 and c = 10.17. According to the refinement yielding a reliability value of / = 0.057, the silicon atoms were confirmed to occupy the 4e site of I4/mmm with zg = 0.375. For sample preparation, see YRhjSij. Atomic... 

The role of crystal symmetry properties in determining the shape of the bands has been emphasized, but the few examples reported have also shown that the existence of a gap and the energy range of bands depend on the mutual interactions of all particles, electrons, and nuclei, in the lattice. Therefore, the correctness of a calculation is largely dependent on the kind of approximation used in the evaluation of such interactions. In fact, different approximations of the Hamiltonian can produce a variety of results and, in particular, band structures that are not only quantitatively but also qualitatively different in some cases. In Figure 18, the HF band structure of silicon is compared with that obtained with DFT methods, both in the LDA, in the form of Slater-Vosko-Wilk-Nusair ° functional, and with the Becke 3 (B3) parameter-Lee-Yang-Parr (LYP) approximation, which incorporates a part of the exact exchange... 

---