Impurity Diffusion in Silicon
The general discussion of diffusion in Section 1.3 did not take into account the particular structure of silicon. The intention of this chapter is to discuss the atomistic processes associated with the diffusion of impurities and their interaction with in
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Impurity Diffusion in Silicon The general discussion of diffusion in Section 1.3 did not take into account the particular structure of silicon. The intention of this chapter is to discuss the atomistic processes associated with the diffusion of impurities and their interaction with intrinsic point defects in more detail. In Section 3.1, the various mechanisms for diffusion of impurities in silicon are introduced and discussed. Most important for impurities residing predominantly on substitutional sites are mechanisms in which they form mobile pairs with intrinsic point defects. The energetics of such pairs is discussed in detail in Section 3.2. Diffusion of mobile complexes can be described within the method of diffusion-reaction equations. The derivation of the basic equations and of special cases will be explained in Section 3.3. The most important special cases, pair diffusion, diffusion via the Frank-Turnbull mechanism, and diffusion via the kick-out mechanism are discussed in detail in the Sections 3.4 to 3.6.
3.1
Basic Mechanisms
Impurities may reside on various sites in the crystal lattice and even more diverse are their diffusion paths. Some impurities dissolve predominantly on interstitial sites. Their diffusion , as outlined in Section 3.1.1, does then not involve intrinsic point defects and can be described simply by Fick's laws. Most other impurities prefer substitutional sites. The most direct way for their diffusion, discussed briefly in Section 3.1.2, would be to directly exchange sites with neighboring atoms. Such processes are usually not considered energetically favorable and the vast bulk of the diffusion theories are based on an interaction of the impurities with intrinsic point defects . Historically, interactions with vacancies were considered first. The respective concepts are summarized in Section 3.1.3. The alternative, diffusion via interactions with selfinterstitials, will be touched on in Section 3.1.4. Mechanisms involving interactions with vacancies and self-interstitial s will be discussed in detail in the remaining sections of this chapter.
3.1.1 Interstitial Diffusion Because of the very open nature of the silicon crystal many atoms dissolve on interstitial sites, i. e. on tetrahedral , hexagonal, or bond-centered positions between the lattice atoms, and diffuse likewise. These include most alkali and heavy metals like copper, iron, and nickel, but also hydrogen and oxygen. Because of the low concentration of atoms on such interstitial sites, all interstitial sites neighboring to an occupied interstitial site will, in general, be free. Interstitial diffusion does not involve direct interaction with intrinsic point defects. As a consequence, such atoms perform 229 P. Pichler, Intrinsic Point Defects, Impurities, and Their Diffusion in Silicon © Springer-Verlag Wien 2004
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CHAPTER 3. IMPURITY DIFFUSION IN SILICON
a random walk as outlined in Section 1.3.2, characterized by a diffusion coefficient which is a function of temperature only. These diffusion coefficients are usual
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