Point defect densities

In the following discussion we will begin with a conceptually easy argument for vacancy formation that does not work in some applications and then consider a less obvious approach that gives a more accurate picture of defect formation. 

The entropy of formation of a vacancy is primarily the configurational entropy with a small contribution from changes in the vibrational entropy. The configurational entropy for a small (n N) number of vacancies, n, in the lattice of N sites is  

The third form of the equation was obtained via Stirling s approximation, as usual. The equilibrium condition is  

Equation 7.6 shows that the concentration of neutral vacancies increases exponentially with increasing temperature. For typical vacancy formation energies the concentration of the defects is very small, even at high temperatures. This is why the diffusivities of atoms in Si and other highly covalent semiconductors are low even at very high fractions of their melting points. 

A more highly-charged defect such as +2 would be determined by the same formula but the ratio would be with respect to the concentration of the less charged (e.g. -1-1) defect rather than the neutral vacancy. The total number of vacancies in the material is then the sum over all charge states. 

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The generation of type-I dislocations by the climb process is enhanced by increasing the point defect density. Therefore, the type-I dislocation should be observed in GaP on Si as the density of point defects is high in GaP grown on Si because of the high growth temperature. But, type-I dislocations are rarely observed in GaP on Si. Therefore, another mechanism should be considered to explain the generation of type-I dislocations. 

Electrical Properties. Generally, deposited thin films have an electrical resistivity that is higher than that of the bulk material. This is often the result of the lower density and high surface-to-volume ratio in the film. In semiconductor films, the electron mobiHty and lifetime can be affected by the point defect concentration, which also affects electromigration. These effects are eliminated by depositing the film at low rates, high temperatures, and under very controUed conditions, such as are found in molecular beam epitaxy and vapor-phase epitaxy. 

The presence of small concentrations of point defects changes the density of a crystal, and four values of the density can be calculated, depending on... 

In a-C H, the tail states are dominated by n electrons, which results, as pointed out by Robertson [99, 100], in an enhanced localization as compared to a-Si H, giving rise to higher band tail density of states and also to higher defect density in the midgap. 

It was realized at an early stage that a comparison of the theoretical and measured density of a solid can be used to determine the notional species of point defect present. The general procedure is ... 

Calculate the theoretical density for alternative point defect populations. 

Compare the theoretical and experimental densities to see which point defect model best fits the data. 

Changes in density, unit cell dimensions, and macroscopic volume have serious effects. In an environment where point defects (or aggregates of point defects) are generated, such as in the components of nuclear reactors, or in vessels used for the storage of nuclear waste, where point defects are produced as a result of irradiation, dimensional changes can cause components to seize or rupture. 

Figure 7.24 Photoelectron emission microscopy images of two Fe304 surfaces that were used as model catalyst in the dehydrogenation of ethylbenzene to styrene at 870 K, showing carbonaceous deposits (bright). These graphitic deposits grow in dots and streaks on a surface of low defect density, but form dendritic structures on surfaces rich in point and step detects (from Weiss et al. f731).

STM and CVs are applied. This is exacerbated by the fact that the extent to which UPD features are suppressed in the CVs depends sensitively on the quality of the SAM. For such a pronounced quenching a good film quality is required, that is, a low defect density is required. To achieve this reproducibly is quite critical as has been pointed out in the literature [40, 183, 204—206]. Therefore, it is no surprise that substantial variations in the blocking properties refiected in the CVs have been observed [39, 183, 203, 207-209]. 

Perfection especially is required on the silicon surface. A 100 surface of silicon contains 6.8 x 1014 atoms/cm2. Surface defect densities must be less than one part in 105—105 defects/cm2 for satisfactory MOSFET operation. In fact, the discovery of the original point contact transistor was only possible because the native oxide on single-crystal germanium has surface defect densities less than one part in 104. Good silicon devices required the discovery (10) that the thermal oxidation of silicon could produce an excellent Si—Si02 interface. 

A variety of interrelated factors affect the chemical reactivity of mineral surfaces with respect to water and aqueous species, including (1) defect density, (2) cooperative effects among adsorbate molecules, (3) differences in intrinsic properties of different mineral surfaces, including different isoelectric points, (4) solution pH,... 

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