Diffusion Mechanisms and Intrinsic Point-Defect Properties in Silicon
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Mechanisms and Intrinsic PointDefect Properties in Silicon Hartmut Bracht
terstitially dissolved foreign atoms (Ai), like hydrogen or the 3d transition elements in silicon, proceeds via interstitial lattice sites. No intrinsic point defects are involved in this direct interstitial mechanism. Direct diffusion of atoms on substitutional sites (As) can occur by means of a direct exchange with an adjacent silicon atom or a ring mechanism. No experimental evidence has been found for these direct mechanisms, since the diffusion of As by indirect mechanisms is usually more favorable. Various indirect diffusion mechanisms, which involve intrinsic point defects, are illustrated in Figure 1b. These mechanisms can be expressed by the point-defect reactions As V &? AV,
(1)
As I &? AI ,
(2)
As I &? Ai ,
(3)
and
Introduction High-purity silicon used for the growth of single crystals is a material with a high resistivity. Small traces of foreign atoms, which are mainly substitutionally dissolved on lattice sites, make the material highly conductive and therefore suitable for electronic applications. The controlled incorporation of extrinsic point defects in silicon is the main task for the production of electronic devices. Homogeneous doping is generally achieved by adding a controlled amount of the dopant element to the silicon melt. However, the fabrication of electronic devices like diodes, transistors, and complex integrated circuits requires spatially inhomogeneous dopant distributions. Control of the inhomogeneous doping profiles demanded by the considerations outlined in the article by Packan in this issue requires a detailed knowledge of the atomic mechanisms of dopant diffusion in silicon, the properties of intrinsic point defects like vacancies (V) and self-interstitials (I), and the interactions among different point defects. This article provides a brief overview of the atomic mechanisms of self- and foreign-atom diffusion in silicon and the properties of the intrinsic defects involved. The experimentally observed diffusion coefficient DA of an element A, which includes the silicon self-atom and different foreign atoms, will be interpreted on the basis of the diffusion mechanisms generally considered for that particular element. For more detailed information on diffusion phenomena in silicon, the interested
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reader is referred to the excellent reviews by Fahey et al.1 and Hu.2
Mechanisms of Diffusion in Solids Figure 1 illustrates various mechanisms for the diffusion of an element A in a solid such as silicon. The diffusion of mainly in-
As &? Ai V.
(4)
Reactions 1 and 2 represent the vacancy and interstitialcy mechanisms, respectively. Isolated intrinsic defects approach substitutional impurities and form next-nearest AV and AI defect pairs due to Coulomb attraction and/or minimization of local
Figure 1. Schematic two-dimensional representation of (a) direct and (b) indirect diffusion mechanisms of an element A in a solid. Ai, As, V, and I denote interstitially and substitutionally dissolved
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