On the derivation of heterogeneous reaction kinetics from a homogeneous reaction model

SIAM Journal on Applied Mathematics

Volumn 60, Issue 6, 2000, Pages 1977-1996

  Evans, J D ^a   King, J R ^b  

^a University of Bath   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; MATHEMATICAL MODELS; OXIDATION; SILICON;

DIFFUSIVITY; STEFAN PROBLEMS;

REACTION KINETICS;

EID: 0034481839     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S003613999834649X     Document Type: Article

References (36)

1. R.B. BECK AND B. MAJKUSIAK, The initial growth rate of thermal silicon dioxide, Phys. Stat. Sol. (a), 116 (1989), pp. 313-329.
2. J. BLANC, A revised model for the oxidation of silicon by oxygen, Appl. Phys. Lett., 33 (1978), pp. 424-426.
3. J. BLANC, The oxidation of silicon by dry oxygen. Can we distinguish between models?, Phil. Mag. B, 55 (1987), pp. 685-710.
4. G. CAGINALP, Conserved-phase field system: Implications for kinetic undercooling, Phys. Rev. B, 38 (1988), pp. 789-791.
5. D.S. COHEN AND T. ERNEUX, Free boundary problems in controlled release pharmaceuticals. I: Diffusion in glassy polymers, SIAM J. Appl. Math., 48 (1988), pp. 1451-1465.
6. B.E. DEAL AND A.S. GROVE, General relationship for the thermal oxidation of silicon, J. Appl. Phys., 36 (1965), pp. 3770-3778.
7. J.D. EVANS, Control of Stress Fields in Silicon Device Fabrication, D. Phil. thesis, Oxford University, Oxford, 1992.
8. J.D. EVANS AND J.R. KING, Asymptotic results for the Stefan problem with kinetic undercooling, Quart. J. Mech. Appl. Math., in press.
9. R.B. FAIR, Diffusion and oxidation of silicon, Adv. Chemistry, 221 (1989), pp. 265-323.
10. A. FARGEIX, G. GHIBAUDO, AND G. KAMARINOS, A revised analysis of dry oxidation of silicon, J. Appl. Phys., 54 (1983), pp. 2878-2880.
11. A. FASANO, G.H. MEYER, AND M. PRIMICERIO, On a problem in the polymer industry: Theoretical and numerical investigation of swelling, SIAM J. Math. Anal., 17 (1986), pp. 945-960.
12. I.G. GÖTZ, W. MERZ, K. PULVERER, AND J. ZHANG, A fluid dynamical free boundary value problem for the oxidation process of silicon, Nonlin. World, 2 (1995), pp. 429-457.
13. K. GRÖGER AND N. STRECKER, A free boundary value problem modeling thermal oxidation of silicon, Z. Anal. Anwendungen., 7 (1988), pp. 57-66.
14. P.S. HAGAN, R.S. POLIZZOTTI, AND G. LUCKMAN, The effects of surface poisons on the oxidation of binary alloys, SIAM J. Appl. Math., 45 (1985), pp. 826-842.
15. S.M. HU, New oxide growth law and the thermal oxidation of silicon, Appl. Phys. Lett., 42 (1983), pp. 872-874.
16. E.A. IRENE, Models for the oxidation of silicon, CRC Critical Reviews in Solid State and Materials Sciences, 14 (1988), pp. 175-223.
17. L. JIANG AND W. MERZ, A free boundary value problem for the one dimensional oxidation process of silicon, Mat. Apl. Comput., 13 (1994), pp. 159-171.
18. J.R. KING, Mathematical Aspects of Semiconductor Process Modelling, D. Phil. thesis, Oxford University, Oxford, 1986.
19. J.R. KING, The isolation oxidation of silicon, SIAM J. Appl. Math., 49 (1989), pp. 264-280.
20. J.R. KING, T.E. SHARP, B. TUCK, AND T.G. ROGERS, Mathematical modelling of the interstitialcy diffusion mechanism, Proc. Roy. Soc. Lond. Ser. A, 450 (1995), pp. 623-649.
21. W. MERZ, K. PULVERER, AND B. STOTH Construction of an asymptotic model for the oxidation process of silicon, Z. Angew. Math. Mech., 78 (1998), pp. 711-720.
22. N.F. MOTT, On the oxidation of silicon, Phil. Mag. B., 55 (1987), pp. 117-129.
23. N.F. MOTT, S. RIGO, F. ROCHET AND A.M. STONEHAM, Oxidation of silicon, Phil. Mag. B., 60 (1989), pp. 189-212.
24. 2 growth, J. Appl. Phys., 60 (1986), pp. 2106-2114.
25. M.P. MURRELL, C.J. SOFIELD, AND S. SUGDEN, Silicon transport during oxidation, Phil. Mag. B., 63 (1991), pp. 1277-1287.
26. C.A. PAZ DE ARAUJO AND R.W. GALLEGOS, Kinetics of rapid thermal oxidation, J. Electrochem. Soc., 136 (1989), pp. 2673-2676.
27. E. RANK, A new finite element approach to the local oxidation of silicon, in Proceedings of Sixth International NASECODE Conference, J.J.H. Miller, ed., Boole Press Ltd., Dublin, Ireland, 1989.
28. E. RANK AND U. WEINERT, A simulation system for diffusive oxidation of silicon: a two-dimensional finite element approach, IEEE Trans. Computer-Aided Design, 9 (1990), pp. 543-550.
29. F.M. ROSS AND W.M. STOBBS, A study of the initial stages of the oxidation of silicon using the Fresnel method, Phil. Mag. A., 63 (1991), pp. 1-36.
30. A.M. STONEHAM, C.R.M. GROVENOR, AND A. CEREZO, Oxidation and the structure of the silicon/oxide interface, Phil. Mag. B., 55 (1987), pp. 201-210.
31. M. SUSA AND K. NAGATA, Thermal oxidation of silicon substrates through oxygen diffusion, Mat. Sci. Engrg. A, 146 (1991), pp. 51-62.
32. S.M. SZE, ED., VLSI Technology, McGraw-Hill, New York, 1983.
33. A.B. TAYLER AND J.R. KING, Free boundaries in semi-conductor fabrication, in Free Boundary Problems: Theory and Applications, K.H. Hoffman and J. Sprekels, eds., Vol. I, Pitman Res. Notes Math. Ser., Longman, London, 1990, pp. 243-259.
34. W.A. TILLER, On the kinetics of the thermal oxidation of silicon. IV. The two-layer film, J. Electrochem. Soc., 130 (1990), pp. 501-506.
35. L. VERDI, A. MIOTELLO, AND R. KELLY, Oxide growth at a Si surface, Thin Solid Films, 241 (1994), pp. 383-387.
36. U. WEINERT AND E. RANK, A simulation system for diffusive oxidation of silicon - One-dimensional analysis, Z. Naturforsch., 46a (1991), pp. 955-966.