Coupled system of PDEs to predict the sensitivity of some materials constituents of FOUP with the AMCs cross-contamination

 
 
 
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  • Abstract


    This paper deals a predictive model using modeling and computational methods to investigate the sensitivity of some materials constituents of the FOUP with the AMCs cross contamination. Required numerical tools which are employed in order to study the AMCs cross-contamination transfer phenomena between wafers and FOUPs were developed. Numerical optimization and finite elements formulation in transient analysis were established. Analytical solution of one dimensional problem was developed and the calibration process of physical constants was performed. This mode was used to study the sensitivity of some material with the cross contamination. The behavior of the AMCs in transient analysis was determined. The model framework preserves the classical forms of the diffusion and convection-diffusion equations and yields to consistent form of the Fick's law. The adsorption kinetics of the contaminant on the surface (interface contaminant/polymer) was assumed. The adsorption process and the surface roughness effect were also traduced as a boundary condition using the switch condition Dirichlet to Neumann and the interface condition. Many tests of contamination processes were assumed in order to study the sensitivity of the materials. Optimization methods with analytical solution were used to define physical constants for each material versus contaminant. Finite element methods including adsorption kinetic were also used and by using Henry law on the interface and the switch of Dirichlet to Neumann conditions.

    Keywords: Cross-contamination, FOUP, mathematical modeling, finite element method, sensitivity study.


  • References


    1. Thi Quynh Nguyen, Herv Fontaine, Yannick Borde, Vronique Jacob, Identification and quantification of FOUP molecular contaminants inducing defects in integrated circuits manufacturing, Microelectronic Engineering, vol. 105, 2013, pp. 124-129.
    2. Paola Gonzlez-Aguirre, Herv Fontaine, Carlos Beitia, Jim Ohlsen, Jorgen Lundgren, Poshin Lee,A comparative study of the HF sorption and outgas singability of different Entegris FOUP platforms and materials, Microelectronic Engineering, vol. 105, 2013, pp. 113-118.
    3. Herv Fontaine, H. Feldis, A. Danel, S. Cetre, C. Ailhas, Impact of the volatile Acid Contaminant on Copper Interconnects, Electrical Performances. ECS Transactions, 25(5), 2009, pp. 78-86.
    4. Shih-Cheng Hu, Tzong-Ming Wu ,Hong-Chong Lin , Kwen Hsu, Design and evaluation of a nitrogen purge system for the front opening unifed pod (FOUP), Applied Thermal Engineering, vol. 27, pp. 1386-1393. 2007.
    5. Alemayeuhu Ambaw, Randolph Beaudry, Inge Bulens, Mulugeta Admasu Delele, Q. Tri Ho, Ann Schenk, Bart M. Nicolai, Pieter Verboven, Modeling the diffusion adsorption kinetics of 1-methylcyclopropene (1-MCP) in apple fruit and nontarget materials in storage rooms, Journal of Food Engineering, vol.102, 2011, pp. 257-265.
    6. Anli Geng, Kai-Chee Loh, Effects of adsoprtion kinetics and surface heterogeneity on band spreading in perfusion chromatography-a network model analysis, Chemical Engineering Science, vol. 59, 2004, pp. 2447-2465.
    7. J. A. Boscoboinik, S.J. Manzi, V.D. Pereyra Adsorption-desorption kinetics of monomer-dimer mixture, Physics A, vol. 389, 2010, pp. 1317.1328.
    8. H.Denny Kamaruddin, William J.Koros, Some observation about the application of Fick's first law for membrane separation of multicomponent mixtures, Journal of Membrane Science, vol. 135, 1997, pp. 147.159.
    9. Rico F. Tabor, Julian Eastoe, Peter J. Dowding, A two-step model for surfactant adsorption at solid surfaces, Journal of Colloid and Interface Science, vol. 346, 2010, pp. 424-428.
    10. Hiroki Nagaoka and Toyoko Imae, Ananlytical investigation of two-step adsorption kinetics on surfaces, Journal of Colloid and Interface Science vol. 264, 2003, pp. 335-342.
    11. Shengping Ding, William T. Petuskey, Solutions to Ficks second law of diffusion with a sinusoidal excitation, Solide State Ionics, vol. 109, 1998, pp. 101-110.
    12. K.J.Kuijlaars, C.R.Kleijin, H.E.A. van den Akker, Multi-component diffusion phenomena in multiple-wafer chemical vapor deposition reactors, The chemical Engineering Journal, vol. 57, 1995, pp. 127-136.
    13. Juergen Siepmann, Florence Siepmann, Modeling of diffusion controlled drug delivery,Journal of Controlled Release, vol. 161, 2012, pp. 351-362.
    14. J. Crank, The mathematics of diffusion, second edition, 1975 Clarendon Press, Oxford.
    15. Baptiste, Hiriart, Urruty, Optimisation et analyse convexe, Puf, 1998, page 11-12.
    16. R.Hirsch, C.C.Muller-Goymann, Fitting of diffusion coefficients in a three compartment sustained release drug formulation using a geneticalgorithm, International Journal of Pharmaceutics, vol. 120, 1995, pp. 229-234.
    17. Jacob Fish and Ted Belytschko, A first course of finite elements, north western university, USA, John Wiley and sons, Ltd, 2007.
    18. O.C. Zienkiewicz and R.L Taylor, The finite elements methods, volume 2, solid mechanics, fith edition, 2000.

 

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Article ID: 2829
 
DOI: 10.14419/ijamr.v3i3.2829




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