A New Kinetic Model for The Nucleation and Growth of Self-Interstitial Clusters in Silicon
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A NEW KINETIC MODEL FOR THE NUCLEATION AND GROWTH OF SELFINTERSTITIAL CLUSTERS IN SILICON Christophe J. Ortiza, and Daniel Mathiotb a DIMES / ECTM Laboratory, TU Delft, Mekelweg 4, 2628 CD Delft, The Netherlands b Laboratoire PHASE-CNRS, 23 rue du Loess, 67037 Strasbourg Cedex 2, France ABSTRACT A model for nucleation and growth of {311} defects is proposed on the basis of thermodynamic and kinetic considerations. Simulated results are discussed and compared to experimental results found in the literature. According to our model it is found that formation energies of self-interstitial clusters depends on the local interstitial supersaturation. Physical parameters extracted from experimental results by inverse modeling are in good agreement with recent values published in the literature. INTRODUCTION Nowadays, Transient Enhanced Diffusion (TED) of dopants is of importance in IC fabrication. As process simulation has become an essential part of new technology development in the silicon IC industry, it is important to have a good understanding of physical mechanisms controlling TED, in order to provide models which are as predictive and efficient as possible. To do so, a considerable effort has been devoted in the last few years to the understanding of the annealing kinetics of Dislocation Loops (DL) [1], {311} defects [2] and even of small selfinterstitial clusters [3], which all maintain an interstitial supersaturation during annealing and thus play an important role in TED of dopants such as boron. In this paper we propose a kinetic model based on thermodynamic considerations for the nucleation and growth of self-interstitial clusters in silicon. As previous models [3,4,5], our model accounts for the attachment and emission of interstitials to and from clusters of different sizes and includes the interstitial recombination at the surface. It will be shown that using only five free physical parameters, our model accounts for main experimental results on TED found in the literature. Physical parameters of main importance for the understanding of dopant diffusion in silicon such as the formation energy of an isolated interstitial, the interstitial diffusion coefficient and the equilibrium interstitial concentration will be fitted separately on published experimental results and will be shown to be in good agreement with recent values found in the literature. FORMULATION OF THE NUCLEATION MODEL In this part we shall give a formulation of our model for the nucleation of self-interstitial clusters. Most emphasis will be placed on the rate constants for absorption and emission of interstitials, especially on the formation and dissociation energies. Thermodynamic considerations as well as the particular geometry of {311} defects will be taken into account for the calculations of these latter. For the remaining, we shall assume the surface to be a perfect sink for interstitials and so that the supersaturation is 1 at the surface, as it has been suggested by previous studies [3,6]. As it is generally assumed in the classical
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