Silicon vacancy concentration

Polytype Hexagonality D Chemical shift (eV) Effective charge q Ratio of silicon and carbon concentrations CJC, Lattice parameters X-ray and practical density Carbon and silicon vacancy concentration Debye- temperature 0D Formation enthalpy A77°298 (kJ/mol) Entropy °298 (J/mol K)... 

Your supervisor suggests that the total copper concentration will be reduced if Si is doped with phosphorus. Write defect equilibria equations for the incorporation of each of these species to examine the effect of phosphorus doping on each type of Cu impurity. At what concentration of P will you get the minimum total Cu concentration. By how much will the amount of Cu be reduced over intrinsic Si Assume that the silicon vacancy concentration does not change with impurity concentration. 

Point Defect Generation During Phosphorus Diffusion. At Concentrations above the Solid Solubility Limit. The mechanism for the diffusion of phosphorus in silicon is still a subject of interest. Hu et al. (46) reviewed the models of phosphorus diffusion in silicon and proposed a dual va-cancy-interstitialcy mechanism. This mechanism was previously applied by Hu (38) to explain oxidation-enhanced diffusion. Harris and Antoniadis (47) studied silicon self-interstitial supersaturation during phosphorus diffusion and observed an enhanced diffusion of the arsenic buried layer under the phosphorus diffusion layer and a retarded diffusion of the antimony buried layer. From these results they concluded that during the diffusion of predeposited phosphorus, the concentration of silicon self-interstitials was enhanced and the vacancy concentration was reduced. They ruled out the possibility that the increase in the concentration of silicon self-interstitials was due to the oxidation of silicon, which was concurrent with the phosphorus predeposition process. 

It is clear Ifom Fig. 7 that the silicon self-diffusion coefficient in undoped crystals is lower than in doped crystals. An opposite dependence was observed for the carbon self-diffusion coefficient. According to the law of acting masses, the silicon vacancy (acceptor) concentration increases with increasing donor dopant concentration (nitrogen). AU this leads to an increase in the diffusion coefficient in the presence of a vacancy mechanism of self-diffusion. Carbon vacancies are donors, and their concentration decreases when the donor concentration is increased. This leads to a decrease in the carbon self-diffusion coefficient. 

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... 

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). 

Point Defect Models of Diffusion in Silicon. Under conditions of thermal equilibrium, a Si crystal contains a certain equilibrium concentration of vacancies, C v°, and a certain equilibrium concentration of Si self-interstitials, Cz°. For diffusion models based on the vacancy, Cv° Cf and the coefficients of dopant diffusion and self-diffusion can be described by equation 27 (15)... 

Vacancies and self-interstitials can exist in equilibrium with each other in the silicon lattice. The concentration of each species can be described by equilibrium equations of the following type. 

To our knowledge there have been no reported measurements of equilibrium defect concentrations in soft-sphere models. Similarly, relatively few measurements have been reported of defect free energies in models for real systems. Those that exist rely on integration methods to connect the defective solid to the perfect solid. In ab initio studies the computational cost of this procedure can be high, although results have recently started to appear, most notably for vacancies and interstitial defects in silicon. For a review see Ref. 109. 

The most popular semiconductor material is silicon (hence Silicon Valley). Fig. 12.9a is a schematic representation of a pure Si crystal. Each Si atom has rout-valence electrons and bonds to four other atoms to form Lewis octets. The crysttil can become a conductor if some of the valence electrons are shaken loose. This produces both negative and positive charge carriers—electrons and l-uilcs. Much more important are extrinsic semiconductors in which the Si crystal is doped with impurity atoms, usually at concentrations of several parts per million (ppm). For example, Si can be doped with P (or As or Sb) atoms, which has five valence electrons. As shown in Fig. 12.9b, a P atom can replace a Si atom in the lattice. The fifth electron on the P is not needed for bonding and becomes available as a current carrier. Thus, Si doped with P is a n-type semiconductor. The Si can instead be doped with B (or Ga or Al). which has only three valence eleetrons. As shown in Fig. 12.9c, a B atom replacing a Si atom leaves an electron vacancy in one of its four bonds. Such positive holes can likewise become current carriers, making Si doped with B a p-type semi con duetor. 

The explicit correlation between changes in the minority carrier life time for p -n diodes upon irradiations at different temperatures and changes in the concentration of vacancy and vacancy-oxygen complexes is established. The information obtained in the present work on the electronic parameters of the V 0 complexes and their introduction rates can be used for careful controlling the carrier lifetime and, therefore, the switching characteristics of silicon power devices. 

The third aspect in the etching mechanism concerns the nature and concentration of the active surface silicon atoms. Because the surface atom stability depends on the number of back bonds, it can be proposed that the probability of atom removal from a perfect (111) surface lattice is very small and etching on the (111) surface proceeds only at lattice inhomogeneities such as steps, kinks, and vacancies. Thus, a perfect (111) surface will have an extremely low etch rate and the etch rate of real (111) surfaces is determined by the etch rate at the steps (including other surface lattice defects) and the density of steps. 

Intrinsic vacancies are much more numerous in metals. For example, in a 1-cm crystal of aluminum at room temperature there are about 9 billion vacancies. In a crystal of silicon in equilibrium at room temperature there are only about 1 x 10 intrinsic vacancies per cubic centimeter. This is considerably less than typical concentrations of extrinsic point defects (dopants) in silicon—about 0.0001% another fortunate fact. 

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