An extended five-stream model for diffusion of ion-impanted dopants in monocrystalline silicon

Low-energy high-dose ion implantation of different dopants (P, Sb, As, В and others) into monocrystaiiine silicon with subsequent thermal annealing is used for the formation of ultra-shallow p-n junctions in modern VLSI circuit technology. During annealing, dopant activation and diffusion in silicon takes place. The experimentally observed phenomenon of transient enhanced diffusion (TED), which is typically ascribed to the interaction of diffusing species with non-equilibrium point defects accumulated in silicon due to ion damage, and formation of small clasters and extended defects, hinders further downscaling of pn junctions in VLSI circuits. TED is currently a subject of extensive experimental and theoretical investigation in many binary and multicomponent systems. However, the state-of-the-art mathematical models of dopant diffusion, which are based on the socalled "five-stream" approach, and modern TCAD software packages such as SUPREM-4 (by Silvaco Data Systems, Ltd.) that implement these models encounter severe difficulties in describing TED. Solving the intricate problem of TED suppression and development of novel regimes of ion implantation and rapid thermal annealing is impossible without elaboration of new mathematical models and computer simulation of this complex phenomenon. In this work, an extended five-stream model for diffusion in silicon is developed wtiich takes into account all possible charge states of point defects (vacancies and silicon selfinterstitials) and diffusing pairs "dopant atom-vacancy" and "dopant atom-silicon self-interstitial". The model includes the drift terms for differently charged point defects and pairs in the internal electric field and the kinetics of interaction between unlike "species" (generation and annihilation of pairs and annihilation of point defects). Expressions for diffusion coefficients and numerous sink/source terms that appear in the non-linear, non-steady-state reaction-diffusion equations are derived for both donor and acceptor dopants accounting for multiple charge states of the diffusing species