(53c) A Comparison of Various Free Energy Models for Oxide Precipitation in Crystalline Silicon

Continuum modeling of point defect aggregation during silicon crystal growth and wafer annealing has a long-standing history of success. Numerous studies have shown that these models are able to capture, at least qualitatively, the essential features of point defect diffusion and clustering under a variety of crystal growth and wafer annealing conditions, especially in the case of homogeneous vacancy clustering [1,2,3,4].

On the other hand, process modeling of oxygen precipitation in Czochralski-grown (CZ) crystals has been more challenging due to the inherent complexity of oxygen precipitation and its strong coupling to the point defect distributions (e.g. ref. [5]). Oxygen precipitation is a critically important process because bulk oxide precipitates provide essential gettering, or trapping, sites for metallic atoms that are introduced during wafer processing. It is therefore essential to ensure that these precipitates are present in the bulk region of the wafer before metallic elements are introduced, but also that they are not located at the device-active surface region.

We present a comprehensive continuum model of coupled vacancy aggregation and oxide precipitation, based on a hybrid Master-Fokker Planck equation formulation. This model is an extension of a recently developed model for vacancy aggregation, which has been demonstrated to provide a quantitatively accurate picture of void formation under a wide range of operating conditions during both crystal growth and wafer annealing [1]. Several free energy model descriptions for oxide precipitation are compared and contrasted [5, 6, 7, 8]. A new free energy model has been developed that keeps track of the point defect population in the O cluster, thus eliminating the need for assuming instant equilibration of the O clusters with the local point defect concentration. The O precipitates are assumed to be oblate spheroids, thus allowing us to probe the effect of temperature and point defect concentration on the O precipitate morphology. The coupling physics between oxide precipitation and vacancy aggregation is probed in detail and the results from various models are compared to experimental measurements for wafer thermal annealing treatment.

[1] Thomas A. Frewen, Sumeet S. Kapur, Walter Haeckl, Wilfried von Ammon, Talid Sinno, ``A microscopically accurate continuum model for void formation during semiconductor silicon processing'', J. Crystal Growth 279 (2005) 258-271.

[2] Talid Sinno, Robert A. Brown, ``Modeling microdefect formation in Czochralski silicon'', J. Electrochem. Soc. 146 (1999) 2300-2312.

[3] Milind S. Kulkarni, ``A selective review of the quantification of defect dynamics in growing Czochralski silicon crystals'', Ind. Eng. Res. 44 (2005) 6246-6263.

[4] Masanori Akatsuka, Masahiko Okui, Shigeru Umeno, Koji Sueoka, ``Calculation of size distribution of void defects in CZ silicon'', J. Electrochem. Soc. 150 (2003) G587-G590.

[5] Koji Sueoka, Masanori Akatsuka, Masahiko Okui, Hisashi Katahama, ``Computer simulation for morphology, size, and density of oxide precipitates in CZ silicon'', J. Electrochem. Soc. 150 (2003) G469-G475.

[6] Z. Wang, ?Modeling Microdefects Formation in Crystalline Silicon-The Roles of Point Defects and Oxygen?, PhD Thesis, MIT, (2002).

[7] Taylor, W. J., Gösele, U. M. and Tan, T. Y., ?Precipitate strain relief via point defect interaction: models for SiO2 in silicon?, Mater. Chem. and Phys., 34 (1993), 166.

[8] Senkader, S., Esfandyari, J., Hobler, G., ?A model for oxygen precipitation in silicon including bulk stacking fault growth?, J. Appl. Phys., 78 (1995), 6469.