Lattice defects impurity atoms

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 siUcon 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 siUcon, the atom can occupy in interstitial site and then subsequently displace a lattice-site atom. This latter movement is beheved to be the dominant mechanism for diffusion of the common dopant atoms, P, B, As, and Sb (26). 

On the left, in 3.1.1., are the two types of point defects which involve the lattice itself, while the others involve impurity atoms. Indeed, there do not seem to any more than these four, and indubitably, no others have been observed. Note that we are limiting our defect family to point defects in the lattice and are ignoring line and volume defects of the lattice. These four point defects, given above, are illustrated in the following diagram, given as 3.1.2. on the next page. 

All of these point defects are intrinsic to the heterogeneous solid, and cirise due to the presence of both cation and anion sub-lattices. The factors responsible for their formation are entropy effects (stacking faults) and impurity effects. At the present time, the highest-purity materials available stiU contain about 0.1 part per billion of various impurities, yet are 99.9999999 % pure. Such a solid will still contain about IQi impurity atoms per mole. So it is safe to say that all solids contain impurity atoms, and that it is unlikely that we shall ever be able to obtain a solid which is completdy pure and does not contain defects. 

Extrinsic Defects Extrinsic defects occur when an impurity atom or ion is incorporated into the lattice either by substitution onto the normal lattice site or by insertion into interstitial positions. Where the impurity is aliovalent with the host sublattice, a compensating charge must be found within the lattice to pre-serve elec-troneutality. For example, inclusion of Ca in the NaCl crystal lattice results in the creation of an equal number of cation vacancies. These defects therefore alter the composition of the solid. In many systems the concentration of the dopant ion can vary enormously and can be used to tailor specific properties. These systems are termed solid solutions and are discussed in more detail in Section 25.1.2. 

The donor electron level, cd, which may be derived in the same way that the orbital electron level in atoms is derived, is usually located close to the conduction band edge level, ec, in the band gap (ec - Ed = 0.041 eV for P in Si). Similarly, the acceptor level, Ea, is located close to the valence band edge level, ev, in the band gap (ea - Ev = 0.057 eV for B in Si). Figure 2-15 shows the energy diagram for donor and acceptor levels in semiconductors. The localized electron levels dose to the band edge may be called shallow levels, while the localized electron levels away from the band edges, assodated for instance with lattice defects, are called deep levels. Since the donor and acceptor levels are localized at impurity atoms and lattice defects, electrons and holes captured in these levels are not allowed to move in the crystal unless they are freed from these initial levels into the conduction and valence bands. 

The term surface of a metal usually means the top layer of atoms (ions). However, in this book the term surface means the top few (two or three) atomic layers of a metal. Surfaces can be divided into ideal and real. Ideal surfaces exhibit no lattice defects (vacancies, impurities, grain boundaries, dislocations, etc.). Real surfaces have all types of defects. For example, the density of metal surface atoms is about 10 and the density of dislocations is on the order of magnitude 10 cm . ... 

States due to different biographical structural defects existing on any real surface and playing the part of local disturbances in the strictly periodic structure of the surface (Sec. IX,A). These include vacant lattice sites in the surface layer of the lattice, atoms or ions of the lattice ejected onto the surface, and foreign atomic inclusions in the surface of the lattice (surface impurities). 

The second type of point defect is called an impurity. Impurities can occur in two ways as an interstitial impurity, in which an atom occupies an interstitial site (see Figures 1.21, 1.22, and 1.29) or when an impurity atom replaces an atom in the perfect lattice (see Figure 1.29). In the first instance, either the same atom as in the lattice, or an impurity atom, can occupy an interstitial site, causing considerable lattice strain as the atomic planes distort slightly to accommodate the misplaced atom. The amount of strain created depends on how large the atom is relative to lattice atoms. It... 

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. 

It is theoretically possible for cations to occupy anion sites, and vice versa. Kroger-Vink notation, then, dictates that an M atom on an X site be designated as Mx and that an X atom on an M site be designated as Xm- Recall that we can have defect clusters, such as a Frenkel defect. Defect clusters are enclosed in parentheses—for example, (VmVx) or (X Xm)—to indicate that the individual defects are associated with one another. Impurity atoms are also coded as to lattice position. If we introduce a metal impurity atom L into our compound MX, it might occupy a metal cation site, and is thus designated as Lm- Similarly, Sj is an S impurity atom on an interstitial site. 

The discussion of the previous section would also lead us to believe that since most ceramics are poor electrical conductors (with a few notable exceptions) due to a lack of free electrons, electronic conduction would be negligible compared to lattice, or phonon, conduction. This is indeed the case, and we will see that structural effects such as complexity, defects, and impurity atoms have a profound effect on thermal conductivity due to phonon mean free path, even if heat capacity is relatively unchanged. 

In a perfect crystal, all atoms would be on their correct lattice positions in the structure. This situation can only exist at the absolute zero of temperature, 0 K. Above 0 K, defects occur in the structure. These defects may be extended defects such as dislocations. The strength of a material depends very much on the presence (or absence) of extended defects, such as dislocations and grain boundaries, but the discussion of this type of phenomenon lies very much in the realm of materials science and will not be discussed in this book. Defects can also occur at isolated atomic positions these are known as point defects, and can be due to the presence of a foreign atom at a particular site or to a vacancy where normally one would expect an atom. Point defects can have significant effects on the chemical and physical properties of the solid. The beautiful colours of many gemstones are due to impurity atoms in the crystal structure. Ionic solids are able to conduct electricity by a mechanism which is due to the movement of fo/ 5 through vacant ion sites within the lattice. (This is in contrast to the electronic conductivity that we explored in the previous chapter, which depends on the movement of electrons.)... 

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. 

As an example of adatom-lattice defect interactions on a surface, we will describe here a study of the interaction between an adatom and an impurity atom in a surface layer. An impurity atom, like any other lattice defect, in the surface layer can perturb the periodicity of the surface both electronically and elastically. Such a perturbation will change the potential energy of a diffusing adatom on the surface. A study of adatom-... 

If adatom-impurity atom interaction is attractive, then the impurity atom can act as a trapping center. A diffusing adatom may be trapped. In heterogeneous catalysis, the reaction rate may be changed by the trapping effect of impurities as also by lattice defects and lattice steps and so on. 

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. 

The damage and high concentrations of lattice delects, resulting from atomic displacements produced by the incident alums, can change the chemical reactivity and mechanical hardness of a treated surface, Implantation cun enhance the diffusion of impurities already deposited in a substrate, presumably through the motion of the high concentrations of lattice defects produced by the incident ions. 

The presence of lattice defects and/or intentionally placed impurities in the alkali halide crystal will cause the formation of local energy levels in the forbidden gap, called traps or activator centers. Figure 18.19 shows the energy levels of an alkali halide crystal, including the activator centers and traps. (Atomic thallium is a common activator for alkali halide crystals.)... 

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