Silicon crystal vacancies

Theoretical studies of diffusion aim to predict the distribution profile of an exposed substrate given the known process parameters of concentration, temperature, crystal orientation, dopant properties, etc. On an atomic level, diffusion of a dopant in a silicon crystal is caused by the movement of the introduced element that is allowed by the available vacancies or defects in the crystal. Both host atoms and impurity atoms can enter vacancies. Movement of a host atom from one lattice site to a vacancy is called self-diffusion. The same movement by a dopant is called impurity diffusion. If an atom does not form a covalent bond with silicon, the atom can occupy in interstitial site and then subsequently displace a lattice-site atom. This latter movement is believed to be the dominant mechanism for diffusion of the common dopant atoms, P, B, As, and Sb (26). 

Surface roughness of silicon crystals has clear crystallographic characteristics as illustrated in Fig. 34 [78]. On a microscopic scale, roughness is associated with lattice steps, vacancies, and so on, which are determined by the lattice structure of the surface. At a macroscopic level, crystallographic character may be revealed in the topographic features, for example, the hillocks formed on (100) surface. 

Oxygen. - IR spectroscopy was used to characterise 02 molecules trapped in vacancies in silicon crystals.607 The high-pressure Raman spectrum of 02 (to 134 GPa) shows significant Raman intensity in the metallic phase, showing that this still retains molecular character.608 High-resolution IR spectra were reported for a number of isotopomers of 03 for a variety of fundamental and overtone/combination bands.609 611... 

The opposite effect occurs if boron is added to silicon. A boron atom has three valence electrons (ls 2s 2p ). Thus, for every boron atom in the silicon crystal there is a single vacancy in a bonding orbital. It is possible to excite a valence electron from a nearby Si into this vacant orbital. A vacancy created at that Si atom can then be fdled by an electron from a neighboring Si atom, and so on. In this manner, electrons can move through the crystal in one direction while the vacancies, or positive holes, move in the opposite direction, and the solid becomes an electrical conductor. Impurities that are electron deficient are called acceptor impurities. Semiconductors that contain acceptor impurities are called p-type semiconductors, where p stands for positive. 

It is also possible to dope semiconductors with atoms that have fewer valence electrons than the host material. Consider what happens when a few aluminum atoms replace silicon atoms in a silicon crystal. Aluminum has only three valence electrons compared to silicon s four. Thus, there are electron vacancies, known as holes, in the valence band when silicon is doped with aluminum [Figure 12.32(c)]. Since the negatively charged electron is not there, the hole can be thought of as having a positive charge. Any adjacent electron that jumps into the hole leaves behind a new hole. Thus, the positive hole moves about in the lattice like a particle. A material like this is called a p-type semiconductor, p signifying that the number of positive holes in the material has increased. 

Using the SED technique, Colhns and coworkers determined that SWNTs prepared by chemical vapor deposition (CVD) had one defect per 4 pm of nanotube. Compared to high-quahty silicon crystals, which are employed in modem semiconductor technologies and have oxygen impurities of one per 10 atoms and silicon vacancies or interstitials of one per 10 atoms, SWNTs had a defect density of one... 

Kulkami, M.S. (2008a). Lateral incorporation of vacancies in Czochralski silicon crystals. Journal Crystal Growth, Vol. 310, No. 13, pp. 3183-3191, ISSN 0022-0248. 

Fig. 3.2 Dependence of vacancy- and interstitial-related defect distributions in silicon crystals on the R/C ratio with R - growth rate, C - temperature gradient, (R/C)cr - critical ratio of total vacancy and...

Figure 1 Oxygen impurity in a silicon crystal lattice. The lowest energy position of an oxygen atom in a silicon lattice is shown on the left hand side. Calculations show that a Frenkel pair, i.e., a combined silicon vacancy and silicon interstitial is a possible metastable state due to the presence of an oxygen impurity (right hand side). Silicon atoms are represented by dark spheres, the oxgyen atom is drawn in light gray. After Dal Pino et al. ...

Neutral vacancies formed during the growth are rarely observed in CVD crystals. Instead, vacancies appear as silicon (or silicon pair)-vacancy complexes. This defect is frequently observed in diamond crystals grown on Si. Growth sector (111) can be doped with Si to levels above 1 at%. This doping level introduces displacement disorder of atoms in the diamond lattice to such an extent that the 1332 cm Raman peak almost disappears. This means that the vibration mode related to the optical phonon becomes weak in such a distorted lattice. 

No material is completely pure, and some foreign atoms will invariably be present. If these are undesirable or accidental, they are termed impurities, but if they have been added deliberately, to change the properties of the material on purpose, they are called dopant atoms. Impurities can form point defects when present in low concentrations, the simplest of which are analogs of vacancies and interstitials. For example, an impurity atom A in a crystal of a metal M can occupy atom sites normally occupied by the parent atoms, to form substitutional point defects, written AM, or can occupy interstitial sites, to form interstitial point defects, written Aj (Fig. 1.4). The doping of aluminum into silicon creates substitutional point defects as the aluminum atoms occupy sites normally filled by silicon atoms. In compounds, the impurities can affect one or all sublattices. For instance, natural sodium chloride often contains... 

For example, the formation of an intrinsic interstitial defect requires the simultaneous creation of a vacancy. These may not remain close together in the crystal, and it is legitimate to consider that the two defects occur in equal numbers. Thus, in silicon it is possible to write the formation equation for silicon self-interstitials, Sii as... 

On the supposition that the total number of unit cells keeps invariable and no aluminum atoms are lost during the boronation, the composition of unit cell and the population of vacancies can be estimated as listed in composition of unit cell (I) in Table 2. It can be seen that the vacancies occupy about 30-50% of total T sites after the boronation. However, it should be noted that the population of vacancies thus obtained by chemical analysis is only a bulk average result. The composition on the surface of crystallites is actually different from that in the bulk because the dissolution of silicon starts first from the outer surface, so that the vacancies on the surface are much more than those in the interior of crystallites. Such a large number of vacancies on the surface will result in corrosion and dissolution of the surface parts of crystal particles. Therefore, the number of unit cells in the sample after the boronation is actually less than that before the boronation, whereas boron atoms in each unit cell should be more than those shown in composition of unit cell (1) in Table 2. On the other hand, if all the 64 T sites are occupied by silicon and trivalent atoms, we can give another set of compositions as shown in composition of unit cell (II) in Table 2. The real composition of a unit cell should be between these two sets of compositions, that is, the 64 T sites are neither occupied completely nor vacated so severely that the collapse of the framework occurs. It can also be seen that the introduction of boron atoms is so limited that there are no more than 1.5 atoms per unit cell even though the repeated boronation is performed. 

When a silicon ciystal is doped with atoms of elements having a valence of less than four, e.g., boron or gallium (valence =3), only three of the four covalent bonds of the adjacent silicon atoms are occupied. The vacancy at an unoccupied covalent bond constitutes a hole. Dopants that contribute holes, which in turn act like positive charge earners, are acceptor dopants and the resulting crystal is p-type (positive) silicon. See Fig. 1(d). 

---