Encounter, vacancy with atom

This important result modifies the description of encounters between tagged atoms and vacancies. If the fraction 7Vv is sufficiently low, then the encounters of a specified atom with different vacancies are independent of each other. In this case, the correlation factor depends only on the properties of a single encounter... 

The diffusion of dopants in semiconductors has been briefly discussed in Sect. 2.1.3. At an atomic scale, the diffusion of a FA in a crystal lattice can take place by different mechanisms, the most common being the vacancy and interstitial mechanisms in silicon and germanium (see for instance [25]). The interstitial/substitutional or kick-out mechanism, which is an interstitial mechanism combined with the ejection of a lattice atom (self-interstitial) and its replacement by the dopant atom is also encountered for some atoms like Pt in silicon. 

We have shown that by stacking atoms or propagation units together, a solid with specific symmetry results. If we have done this properly, a perfect solid should result with no holes or defects in it. Yet, the 2nd law of thermod5mamics demands that a certain number of point defects (vacancies) appear in the lattice. It is impossible to obtain a solid without some sort of defects. A perfect solid would violate this law. The 2nd law states that zero entropy is only possible at absolute zero temperature. Since most solids exist at temperatures far from absolute zero, those that we encounter are defect-solids. It is natural to ask what the nature of these defects might be. 

We have a Vm (a eation vacancy) associated with an Mx, an M atom on an anion site.The total number of atoms remains eonstant, but there is an excess of cations, notably Mx Fortunately, we do not have to deal with these equations very much but include them for the sake of completeness. Note that we have used a h3rpothetical compound to represent aU of the possible compounds that we might encounter. 

This fraction is determined by the step-dance between a specified vacancy and the (tagged) atom during their encounter, which does not end before the atom-vacancy pair has definitely separated. Normally, a new and independently moving vacancy comes along much later and begins the next encounter with the tagged atom. 

In Section 3 we derive that for the vacancy-mediated diffusion mechanism, one expects the shape of the jump length distribution to be that of a modified Bessel function of order zero. Both distributions can be fit very well with the modified Bessel function, again confirming the vacancy-mediated diffusion mechanism for both cases. The only free parameter used in the fits is the probability prec for vacancies to recombine at steps, between subsequent encounters with the same embedded atom [33]. This probability is directly related to the average terrace width and variations in this number can be ascribed to the proximity of steps. The effect of steps will be discussed in more detail in Section 4. 

A general advantage of numerical modeling is that we have access to quantities which are difficult or impossible to measure experimentally. One example in our calculation is the probability that a tracer atom had an encounter with a vacancy, but its net displacement was zero. Although this value is non-zero, its temperature dependence is weak, which means that it can be incorporated in the constant jump-rate prefactor. This justifies the simplifying approach in the analysis of the experimental measurements to associate In-vacancy encounters with detectable (non-zero) jumps of the indium atom. 

If we assume that the steps are indeed the sources and sinks for surface vacancies and we confine ourselves to the simplest case where there is no interaction between the vacancy and the tracer atom, the recombination probability of a vacancy, prec, introduced in the previous section, will decrease with increasing distance from a step. This is schematically illustrated in Fig. 10. This decrease in prec with distance from a step allows us to experimentally verify whether the steps are indeed the sole sources and sinks for vacancies. The experimental verification consists of the following. Assume that we are tracking the motion of an embedded atom somewhere in a terrace, a given distance away from a step. Once a vacancy has formed at the step, has diffused to the embedded atom, and has had an initial exchange with the atom (i.e. in our measurements we observe the embedded atom to make a jump), the probability for it to have further encounters with the same vacancy is determined by the value 1 — prec. Since prec decreases with increasing distance to the step, the vacancy will on average have more encounters with the tracer atom the further it is away from the step. This will cause the atom... 

Figure 10 A schematic illustration of the effect of the presence of a step on the diffusion of a surface vacancy, (a) Schematic topography, with a step in the middle, (b) The recombination probability depends logarithmically on the distance, (c) Random walks that bring the vacancy far from the step will result on average in a much larger number of encounters with a tracer atom on the terrace than shorter random walks.

Figure 2.9 The photoelectric interaction, (a) Before photoelectric interaction a photon of energy E encounters the atom, (b) In the photoelectric interaction the photon is absorbed by a K-shell electron, and the electron is ejected with an energy equal to the photon energy less the K-shell electron-binding energy, (c) the K-shell vacancy is filled by an L-shell electron, and the difference in binding energies is given off as either (c) a characteristic x-ray photon or (d) an Auger electron. (Reprinted by courtesy of EG G ORTEC.)...

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