On modelling thermal oxidation of silicon II: Numerical aspects

International Journal for Numerical Methods in Engineering

Volumn 47, Issue 1-3, 2000, Pages 359-377

  Rao, Vinay S ^a,b   Hughes, Thomas J R ^a   Garikipati, Krishna ^a  

^a Stanford University   (United States)

^b SCHLUMBERGER CAMBRIDGE RESEARCH   (United Kingdom)

Author keywords

Continuum mechanics; Discontinuous interpolations; Finite elements; Levelset methods; Thermal oxidation

Indexed keywords

COMPUTER SIMULATION; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; INTERFACES (MATERIALS); INTERPOLATION; SILICA; SILICON; THERMOOXIDATION;

CONTINUUM MECHANICS; LEVELSET METHODS;

MATHEMATICAL MODELS;

EID: 0033897651     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0207(20000110/30)47:1/3<359::aid-nme775>3.0.co;2-7     Document Type: Article

References (29)

1. Rafferty CS. Stress effects in silicon oxidation-simulation and experiments. Ph.D. Thesis, Stanford University, 1989.
2. Peng JP, Chidambarrao D, Srinivasan GR. Novel. A nonlinear viscoelastic model for thermal oxidation of silicon. COMPEL 1991; 10(4):341-353.
3. Deal BE, Grove AS. General relationship for the thermal oxidation of silicon. Journal of Applied Physics 1965; 36(12):3370-3378.
4. Yu C-L, Flinn PA, Bravman JC. In-situ measurement of viscous flow of thermal silicon dioxide thin films at high temperature. Personal Communication.
5. Technology Modeling Associates, Inc., Sunnyvale, CA. TSUPREM-4 Two-Dimensional Process Simulation Program, Verson 6.4, User's Manual, October 1996.
6. Law ME. Grid adaption near moving boundaries in two dimensions for ic process simulation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 1995; 14(10):1223-1230.
7. Rueda HA, Cea S, Law ME. Mechanical stress modeling for silicon fabrication processes. In International Conference on Simulation of Semiconductor Processes and Devices, SISPAD, IEEE, Piscataway, NJ, USA, 1997; 53-56.
8. Chadwick P. Continuum Mechanics: Concise Theory and Problems. Wiley: New York, 1976.
9. Hughes TJR. Numerical implementation of constitutive models: rate independent deviatoric plasticity. In Theoretical Foundations for Large Scale Computations of Nonlinear Material Behavior, Asaro R, Nemat-Nasser S, Hegemier G (eds). Martinus Nijhoff Publishers: The Netherlands, 1984.
10. Zienkiewicz OC, Taylor RL. The Finite Element Method, vol-I, II. McGraw-Hill: U.K., 1989.
11. Sethian JA. Level Set Methods. Cambridge University Press: Cambridge, 1996.
12. Hughes TJR, Mallet M. A new finite element formulation for computational fluid dynamics: III. The generalized streamline operator for multidimensional advective-diffusive flows. Computer Methods in Applied Mechanics and Engineering 1986; 58(3):305-328.
13. Hughes TJR. The Finite Element Method, Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
14. Brooks AN, Hughes TJR. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32:199-259.
15. Hughes TJR, Franca L, Hulbert GM. A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares methods for advective-diffusive equations. Computer Methods in Applied Mechanics and Engineering 1989; 73:173-189.
16. Hughes TJR, Franca L, Mallet M. A new finite element formulation for computational fluid dynamics: VII. Convergence analysis of the generalized SUPG formulation for linear time-dependent multidimensional advective-diffusive systems. Computer Methods in Applied Mechanics and Engineering 1987; 63(1):97-112.
17. Taylor RL, Simo JC, Zienkiewicz OC, Chan AC. The patch test: a condition for assessing finite element convergence. International Journal for Numerical Methods in Engineering 1986; 22:39-62.
18. Simo JC, Rifai MS. A class of mixed assumed strain methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering 1990; 29:1595-1638.
19. Armero F, Garikipati K. An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. International Journal of Solids and Structures 1996; 33(20-22):2863-2885.
20. Simo JC, Oliver J, Armero F. An analysis of strong discontinuities induced by softening in solids. Computational Mechanics 1993; 12:277-296.
21. Simo JC. On a fully three-dimensional finite strain viscoelastic damage model: formulation and computational aspects. Computer Methods in Applied Mechanics and Engineering 1985; 60:153-173.
22. Simo JC, Hughes TJR. Computational Inelasticity. Springer: New York, 1998.
23. Lu SCH, Pister KS. Decomposition of deformation gradient and representation of the free energy function for isotropic solids. International Journal of Solids and Structures 1975; 11(7-8):927-934.
24. Lee EH, Liu DT. Finite strain elastic-plastic theory particularly for plane wave analysis. Journal of Applied Physics 1967; 38:19.
25. Simo JC, Taylor RL, Pister KS. Variational and projection methods for the volume constraint in finite deformation plasticity. Computer Methods in Applied Mechanics and Engineering 1985; 51:177-208.
26. Renardy M, Rogers RC. An Introduction to Partial Differential Equations. Springer: Berlin, 1993.
27. Nagtegaal JC, Parks DM, Rice JR. On numerically accurate finite element solutions in the fully plastic range. Computer Methods in Applied Mechanics and Engineering 1974; 4:153-177.
28. Garikipati K, Rao VS, Hao MY, Ibok E, DeWolf I, Dutton RW. Modelling, calibration and validation of contributions to stress in the shallow trench isolation process sequence. 1999, to appear in Computer Modeling and Simulation in Engineering.
29. Kao D-B. Two dimensional oxidation effects in silicon - experiments and theory. Ph.D. Thesis, Stanford University, June 1986.