Substitutional point defect

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... 

A number of other -alumina related phases have been prepared. In some of these the spinel blocks have an increased thickness, the so-called P, P" and P " phases, while in others, the Na or A1 components have been replaced with similar species. Related structures, such as BaMgAlnOiy doped with Eu +, are widely used as phosphors. Crystal-structure studies on such materials show that the defects present depend sensitively upon both temperature and the constituents of the phase. Large replacement ions, lanthanide or alkali metals, tend to occupy the interlayer regions as interstitial defects, but surprisingly, some also enter the spinel blocks as substitutional defects, in association with oxide ion vacancies. Smaller ions occupy the spinel blocks as substitutional point defects. The delicate balance between oxygen interlayer interstitials and spinel block cation vacancies varies with composition. These defect interactions can often be successfully explored by using simulation techniques. Ordering occurs at lower temperatures see Ionic Conductors). 

The concept of paracrystallinity introduced by Hosemann et al. in 1966 was used earlier to describe the phenomenon of ammonia iron. They developed the theory of paracrystallinity from XRD data which seemed to explain the special properties of the activated iron catalyst. A three-dimensional, endotactic incorporation of hercynite (FeAl204) motives into the a-iron lattice was thought to create substitutional point defects in the crystal lattice leading to a modified bulk and surface structure of the activated catalyst material. The interplanar spacings change... 

Shallow level defects can be understood, at least approximately, based on the hydrogenic model. This approximates the defect as a H atom in the dielectric medium of the semiconductor. An impurity that is chemically similar to the matrix atom it replaces but has one more or one fewer electron and proton (a monovalent substitution) often results in this type of state. Examples of such impurities are P (considered in detail below) or A1 in Si. The hydrogenic model can be applied to any monovalent substitutional point defect in either an elemental or a compound semiconductor and to both n and p type dopants. 

If tlie level(s) associated witli tlie defect are deep, tliey become electron-hole recombination centres. The result is a (sometimes dramatic) reduction in carrier lifetimes. Such an effect is often associated witli tlie presence of transition metal impurities or certain extended defects in tlie material. For example, substitutional Au is used to make fast switches in Si. Many point defects have deep levels in tlie gap, such as vacancies or transition metals. In addition, complexes, precipitates and extended defects are often associated witli recombination centres. The presence of grain boundaries, dislocation tangles and metallic precipitates in poly-Si photovoltaic devices are major factors which reduce tlieir efficiency. 

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

Changes in the atomic correlations are enabled by atomic jumps between neighbouring lattice sites. In metals and their substitutional solutions point defects are responsible for these diffusion processes. Ordering kinetics can therefore yield information about properties of the point defects which are involved in the ordering process. 

Equivalent formulae can be produced in terms of the other point defect concentrations by substituting from (8). 

One type of point defect that cannot be entirely eliminated from a solid compound is the substituted ion or impurity defect. For example, suppose a large crystal contains 1 mole of NaCl that is 99.99 mole percent pure and that the 0.01% impurity is KBr. As a fraction, there is 0.0001 mole of both K+ and Br ions, which is 6.02 X 1019 ions of each type present in the 1 mole of NaCl Although the level of purity of the NaCl is high, there is an enormous number of impurity ions that occupy sites in the lattice. Even if the NaCl were 99.9999 mole percent pure, there would still be 6.02 X 1017 impurity cations and anions in a mole of crystal. In other words, there is a defect, known as a substituted ion or impurity defect, at each point in the crystal where some ion other than Na+ or Cl- resides. Because K+ is larger than Na+ and Br is larger than Cl-, the lattice will experience some strain and distortion at the sites where the larger cations and anions reside. These strain points are frequently reactive sites in a crystal. 

The topic of defects in semiconductors encompasses point, line, planar and volume defects. Point defects include those defects occupying, or sharing, a single lattice site these would include substitutional impurities... 

Figure 1.4 Impurity or dopant (A) point defects in a crystal of material M, substitutional, Ainterstitial, A,.

A point defect is a localized defect that consists of a mistake at a single atom site in a solid. The simplest point defects that can occur in pure crystals are missing atoms, called vacancies, or atoms displaced from the correct site into positions not normally occupied in the crystal, called self-interstitials. Additionally atoms of an impurity can occupy a normal atom site to form substitutional defects or can occupy a normally vacant position in the crystal structure to form an interstitial. Other point defects can be characterized in pure compounds that contain more than one atom. The best known of these are Frenkel defects, Schottky defects, and antisite defects. 

It is important that the copper is in the monovalent state and incorporated into the silver hahde crystals as an impurity. Because the Cu+ has the same valence as the Ag+, some Cu+ will replace Ag+ in the AgX crystal, to form a dilute solid solution Cu Agi- X (Fig. 2.6d). The defects in this material are substitutional CuAg point defects and cation Frenkel defects. These crystallites are precipitated in the complete absence of light, after which a finished glass blank will look clear because the silver hahde grains are so small that they do not scatter light. 

Photochromic behavior depends critically upon the interaction of two point defect types with light Frenkel defects in the silver halide together with substitutional Cu+ impurity point defects in the silver halide matrix. It is these two defects together that constitute the photochromic phase. 

The point defects present are Al3+ cations substituted on Mg2+ sites, Al g and Mg2+ vacancies, V g. 

The simplest way to account for composition variation is to include point defect populations into the crystal. This can involve substitution, the incorporation of unbalanced populations of vacancies or by the addition of extra interstitial atoms. This approach has a great advantage in that it allows a crystallographic model to be easily constructed and the formalism of defect reaction equations employed to analyze the situation (Section 1.11). The following sections give examples of this behavior. 

At low concentrations, defect clusters can be arranged at random, mimicking point defects but on a larger scale. This seems to be the case in zinc oxide, ZnO, doped with phosphorus, P. The favored defects appear to be phosphorus substituted for Zn, P n, and vacancies on zinc sites, Vzn. These defects are not isolated but preferentially form clusters consisting of (Pzn + 2V n). 

The second type of impurity, substitution of a lattice atom with an impurity atom, allows us to enter the world of alloys and intermetallics. Let us diverge slightly for a moment to discuss how control of substitutional impurities can lead to some useful materials, and then we will conclude our description of point defects. An alloy, by definition, is a metallic solid or liquid formed from an intimate combination of two or more elements. By intimate combination, we mean either a liquid or solid solution. In the instance where the solid is crystalline, some of the impurity atoms, usually defined as the minority constituent, occupy sites in the lattice that would normally be occupied by the majority constituent. Alloys need not be crystalline, however. If a liquid alloy is quenched rapidly enough, an amorphous metal can result. The solid material is still an alloy, since the elements are in intimate combination, but there is no crystalline order and hence no substitutional impurities. To aid in our description of substitutional impurities, we will limit the current description to crystalline alloys, but keep in mind that amorphous alloys exist as well. 

The lattice defects are classified as (i) point defects, such as vacancies, interstitial atoms, substitutional impurity atoms, and interstitial impurity atoms, (ii) line defects, such as edge, screw, and mixed dislocations, and (iii) planar defects, such as stacking faults, twin planes, and grain boundaries. 

The simplest lattice defects as far as FIM observations are concerned are point defects, such as vacancies, self-interstitials and substitutional as well as interstitial impurity atoms. Vacancies invariably show up as dark spots in the field ion images. Other point defects may appear as either bright image spots or vacancies in the image. Thus these defects can be identified from field ion images of high index planes where all the atoms in a plane are fully resolved. 

---