Defect self interstitial

Native defects have sometimes been invoked not just as sources of compensation, but as sources of doping. The nitrogen vacancy in GaN is a prime example for a long time the nitrogen vacancy was thought to be the source of n-type conductivity in GaN. As early as 1983 it was pointed out that unintentional incorporation of oxygen was a more likely explanation [1], Still, it is only recently that unintentional impurities have become widely accepted as the source of n-type conductivity, thanks in part to contributions from first-principles theory (see Datareview A8.1). In this Datareview we will describe some of those theoretical results, for vacancies as well as other native defects (self-interstitials and antisites). Experimental information about native defects in the nitrides is very scarce at this time we will include references where available. 

Intrinsic defects (or native or simply defects ) are imperfections in tire crystal itself, such as a vacancy (a missing host atom), a self-interstitial (an extra host atom in an otherwise perfect crystalline environment), an anti-site defect (in an AB compound, tliis means an atom of type A at a B site or vice versa) or any combination of such defects. Extrinsic defects (or impurities) are atoms different from host atoms, trapped in tire crystal. Some impurities are intentionally introduced because tliey provide charge carriers, reduce tlieir lifetime, prevent tire propagation of dislocations or are otlierwise needed or useful, but most impurities and defects are not desired and must be eliminated or at least controlled. 

The presence of defects and impurities is unavoidable. They are created during tire growtli or penetrate into tlie material during tlie processing. For example, in a crystal grown from tire melt, impurities come from tire cmcible and tire ambient, and are present in tire source material. Depending on factors such as tire pressure, tire pull rate and temperature gradients, tire crystal may be rich in vacancies or self-interstitials (and tlieir precipitates). 

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. 

Additionally, we have Illustrated another type of defect that can arise within the homogeneous lattice of 3.1.2. (in addition to the vacancy and substitutional impurities that are bound to arise). This is called the "selfinterstitial". Note that it has a decisive effect on the structure at the defect. Since the atoms are all the same size, the self-interstitial introduces a line-defect in the overall structure. It should be evident that the line-defect introduces a difference in packing order since the close packing at the arrows has changed to cubic and then reverts to hexagonal in both lower and upper rows of atoms. 

On the right are the t5rpes of point defects that could occur for the same sized atoms in the lattice. That is, given an array of atoms in a three dimensional lattice, only these two types of lattice point defects could occur where the size of the atoms are the same. The term vacancy is self-explanatory but self-interstitial means that one atom has slipped into a space between the rows of atoms (ions). In a lattice where the atoms are all of the same size, such behavior is energetically very difficult unless a severe disruption of the lattice occurs (usually a "line-defect" results. This behavior is quite common in certain types of homogeneous solids. In a like manner, if the metal-atom were to have become misplaced in the lattice cuid were to have occupied one of the interstitial... 

Figure 1.2 Point defects in a pure monatomic crystal of an element M, a vacancy, VM, and a self-interstitial, Mj.

Figure 1.3 Point defects in a crystal of a pure compound, MX, VM, a metal vacancy Vx a nonmetal vacancy Mj, a metal (self-)interstitial and Xs a nonmetal (self-)interstitial.

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... 

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. 

Because the configurational entropy of interstitial defects has the same form as that of vacancies, a population of self-interstitial atoms is also thermodynamically stable. The creation of these defects can then also be treated as a pseudochemical equilibrium, and an equation for the relationship between the number of self-interstitials and the appropriate equilibrium constant for interstitial generation, Kv is readily... 

Internal boundaries are important in influencing the properties of single crystals in a number of ways. Impurities and other point defects, such as self-interstitials or vacancies, often congregate near to such interfaces. Moreover, because the regularity of the crystal structure is disrupted at the interface, unusual atom coordination can occur, allowing impurity atoms to be more readily accommodated. This in turn leads to differing, often enhanced, chemical reactivity, dissolution, and other physicochemical properties. 

Figure 5.11 Diffusion mechanisms (a) exchange (e) and ring (r) diffusion (b) kick-out diffusion, leading to (c) a substitutional defect and a self-interstitial.

Figure 9.2 Schematic representation of magnetic defects in a magnetic matrix (a) vacancy or nonmagnetic impurity, (b) self-interstitial, (c) magnetic Frenkel defect , (d) magnetic foreign substituent, and (e) magnetic foreign interstitial. The magnetic matrix can have ordered (as drawn) or disordered spins.

Defect Reaction Equilibrium Constants. Recall that a Frenkel disorder is a self interstitial-vacancy pair. In terms of defect concentrations, there should be equal concentrations of vacancies and interstitials. Frenkel defects can occur with metal... 

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. 

Figure 8.5 Geometric configurations for a self-interstitial defect atom in an f.c.c. crystal (a) octahedral site, (b) tetrahedral site, (c) (110) crowdion, (d) (100) split, dumbbell, (e) (111) split., (f) (110) split crowdion [2].

As discussed in Section 8.3.1, the (100) split-dumbbell self-interstitial in the f.c.c. structure can exist with its axis along [100], [010], or [001], Under stress, certain of these orientation states are preferentially populated due to the tetragonality of the defect as a center of dilation. When the stress is suddenly released, the defects repopulate the available states until the populations in the three states become equal. Show that the relaxation time for this repopulation is... 

Multiple-Charge-State Vacancy Model. On the basis of the previous discussion, diffusion depends upon the concentration of point defects, such as vacancies or self-interstitials, in the crystal. Therefore, diffusion coefficients can be manipulated by raising or lowering the concentration of point defects. 

Point Defects. Point defects are defined as atomic defects. Atomic defects such as metal ions can diffuse through the lattice without involving themselves with lattice atoms or vacancies (Figure 9), in contrast to atomic defects such as self-interstitials. The silicon self-interstitial is a silicon atom that is bonded in a tetrahedral interstitial site. Examples of point defects are shown in Figure 9. 

One of the major controversies in solid-state science is the nature of the dominant native point defect in silicon. Is the dominant native point defect in silicon the monovacancy or the silicon self-interstitial Well-developed arguments have been proposed for each type, but the current consensus is that both types are present and important. 

The Silicon Self-Interstitial Atom. A similar consistent statistical thermodynamic analysis of the existence of self-interstitials shows that silicon self-interstitials are stable point defects. The following arguments further support the silicon self-interstitial. 

The current majority opinion is that both types of point defects are important. Thermal equilibrium concentrations of point defects at the melting point are orders of magnitude lower in Si than in metals. Therefore, a direct determination of their nature by Simmons-Balluffi-type experiments (26) has not been possible. The accuracy of calculated enthalpies of formation and migration is within 1 eV, and the calculations do not help in distinguishing between the dominance of vacancies or interstitials in diffusion. The interpretation of low-temperature experiments on the migration of irradiation-induced point defects is complicated by the occurrence of radiation-induced migration of self-interstitials (27, 28). 

In addition, the structure and properties of point defects at low temperatures and at high temperatures may be different (29). The observation of extrinsic-type dislocation loops in dislocation-free, float-zone Si indicate that self-interstitials must have been present in appreciable concentrations at high temperature during or after crystal growth (30, 31). However, it is unclear whether these self-interstitials were present at thermal equilibrium or were introduced during crystal growth by nonequilibrium processes. 

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