Responsible: Jens Lang, Peter Deuflhard

Cooperation: W. Merz, K.-H. Hoffmann, TU Munich
E. Wilczok, Siemens AG

Literature: J. Lang,  W. Merz, Two-dimensional Adaptive Simulation of Dopant Diffusion in Silicon, Report ZR-00-03 (2000), Konrad-Zuse-Zentrum.

An elementary process step in the fabrication of silicon-based integrated circuits is the diffusion mechanism of dopant impurities into silicon. The study of diffusion processes is of great technological importance since their quality strongly influences the quality of electronical materials. Impurity atoms of higher or lower chemical valence, such as arsenic, phosphorus, and boron, are introduced under high temperatures (900  -  1100 oC) into a silicon crystal to change its electrical properties. This is the central process of modern silicon technology. Various pair-diffusion models have been developed to allow accurate modelling of device processing (see next Fig.).
Scheme of Pair Diffusion Model

Multiple Species Diffusion: Dopant atoms occupy substitutional sites in the silicon crystal lattice, losing (donors such as arsenic and phosphorus) or gaining (acceptors such as boron) at the same time an electron. One fundamental interest in semiconductor devices modelling is to study the interaction of two unequally charged dopants and the influence of the chemical potential. Here, we select arsenic (As) and boron (B). In the following Figure, the shape of the initial dopant implantations at 950 oC is visualized. The solutions obtained after thirty minutes show that   the boron profile is mainly influenced by the chemical potential while the arsenic concentration is changed only slowly by diffusion. It can nicely be seen that  the dynamic mesh chosen by KARDOS is well-fitted to the local behaviour of the solution.
2dmulti-1 2dmulti-2
2dmulti-3 2dmulti-3

Phosphorus Diffusion: Here, we simulate phosphorus diffusion using a detailed par-diffusion model. Since a diffusion mechanism based only on the direct interchange with neighbouring silicon atoms turns out to be energetically unfavourable, native point defects called interstitials and vacancies  are taken into account. The phosphorus concentration shows its typical ''kink and tail`` behaviour, a phenomenon which is known as anomalous diffusion of phosphorus.
Snapshot at t=3min of total and substitutional phosphorus concentration,
interstitials and vacancies and 1D-cut of all

Last update: July 2007
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