MaximumA posterioriestimation of transient enhanced diffusion energetics

Abstract

( ) Transient enhanced diffusion TED of boron limits the formation of ultrashallow junctions needed in next-generation microelectronic de®ices. A comprehensi®e TED model needs many parameters go®erning the physical and chemical processes. Prior estimates of the most likely ®alues for the parameters as well as their accuracies are determined from maximum likelihood estimation applied to estimates from focused indi®idual experiments and density functional theory calculations. Here a systematic approach to model-parameter identification using maximum a posteriori estimation is employed combining the maximum likelihood parameter estimates and their uncertainties in conjunction with after-anneal boron SIMS profiles to obtain accurate TED energetics. Guidance on future experimental and ab initio efforts are gi®en based on the agree-( ) ment and disagreement between the prior and posterior distributions. IntroductionTechnological advances in packing an ever-increasing number of transistors into a single chip drive the evolution in the microelectronics industry. Because future Si-based CMOS requires formation of junction depths between 13 and 25 nm in the source and drain extension regions by the year 2005 according to the 2001 International Technology Roadmap for Semiconductors, problems accompanying ultrashallow junction processing have become increasingly important. The current technology for forming ultrashallow junctions relies on using ion implantation to introduce dopant into the wafer. However, ion implantation causes lattice damage, producing junctions with high sheet resistance, which motivates postimplant annealing to remove the implant damage. Transient en-Ž . hanced diffusion TED occurs during annealing of ion-implanted Si in which dopant, especially boron, diffuses exceptionally fast, resulting in an undesirable increase of junction depth. TED is often attributed rather generically to the supersaturation of Si interstitials produced during ion implantation of dopant and during thermal annealing. However, obtaining a detailed kinetic understanding of how the Si interstitials mediate dopant diffusion is more challenging. Furthermore, as thermal annealing advances toward rapid ther-Ž . mal annealing RTA , it becomes crucial to implement more precise kinetic expressions to capture the transient behavior.Correspondence concerning this article should be addressed to R. D. Braatz.For this reason, modeling of TED has generated a great deal Ž Ž . . of interest see, for example, Agarwal et al. 2000 .Here, a comprehensive TED model is developed combin-Ž ing elementary physicochemical processes such as diffusion . of interstitials and boron activation reaction and Poisson's equation. The model includes continuity equations describing Fickian diffusion and electric drift motion, and formation and Ž annihilation rates due to chemical reactions such as dopant . activation, dopant-defect clustering . Poisson's equation describes the electric field due to spatial imbalance of the charge density. The TED model consists of 2...

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