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ty atom Xs. Moving to the right, a point defect (here a self-interstitial) is thermally generated and enters the crystal at a large distance from the impurity atom. The energy of the system fluctuates as the selfinterstitial migrates between adjacent stable locations in the crystal. The shaded region of Figure 1 represents the event where the free self-interstitial encounters and reacts with a substitutional dopant atom Xs to form a mobile dopant species Xi (either a dopant-interstitial pair or an interstitial dopant atom). The mobile species may migrate some distance before dissociating. The characteristic migration distance depends exponentially on the energy difference QSiI  QX (see Figure 1), thus leading to the large observed range in dopant diffusivities. Such long-range migration has been directly observed. When a small proportion of B atoms are displaced into mobile form and allowed to diffuse, the result is a B profile with exponential-like tails.2,3 The shape and i

width of the profile provides information on both the kick-out rate g and the migration distance  of the displaced atoms. The temperature dependence of g and  for B (Figure 2) has been measured for various interstitial supersaturations SI  C I/C eq I : during inert-ambient diffusion (SI  1), oxidizing-ambient diffusion (SI  10), and transient-enhanced diffusion (SI  107 ) for nonequilibrium and equilibrium selfinterstitial concentrations (CI and C eq I , respectively).3,4 In all cases, g is proportional to SI , but the dissociation reaction rate is independent of SI. At lower temperatures, g decreases dramatically, being dependent on the energy to form and migrate the self-interstitial. This energy depends on the process involved; under near-equilibrium conditions (N2 ambient), it is close to the self-diffusion activation energy, while during TED, when interstitials evaporate from implant damage, the formation energy requirement is much lower. In contrast,  is the same for all process conditions, characteristic of a purely thermal process that does not depend on a reaction with a point defect. Furthermore, the lower the temperature, the larger  becomes, that is, the farther B atoms migrate before returning to a substitutional site. To summarize the basic mechanisms, dopant impurities in silicon diffuse by an intermittent process where the dopant re-

Point Defects and Dopant Diffusion A generic picture1 of the interaction between a point defect and an impurity atom is shown in Figure 1. The diagram represents the total energy of the system as a function of its configuration. At far left, the system consists of a crystal with a free surface and one substitutional impu-

MRS BULLETIN/JUNE 2000

Figure 1. Configuration diagram showing the energetics of interstitialmediated dopant diffusion. I refers to self-interstitials in silicon; i is the interstitial-like form of an impurity species.

Figure 2. Kick-out frequency (g) and migration length () for B diffusion as a function of processing conditions: solid circles are N2 ambient, solid tri