Computational Modeling of Silicon Nanoparticle Synthesis: I. A General Two-Dimensional Model

REFERENCES

• Barrett , J. C. and Webb , N. A. 1998 . A Comparison of Some Approximate Methods for Solving the Aerosol General Dynamic Equation . J. Aerosol Sci. , 29 : 31 – 39 .
   Web of Science ®Google Scholar
• Becerra , R. and Walsh , R. 1992 . Some Mechanistic Problems in the Kinetic Modeling of Monosilane Pyrolysis . J. Phys. Chem. , 96 : 10856 – 10862 .
   Google Scholar
• Brenan , K. E. , Campbell , S. L. and Petzold , L. R. 1989 . Numerical Solution of Initial Value Problems in Differential-Algebraic Equations , New York : Elsevier Science .
   Google Scholar
• Coltrin , M. E. , Kee , R. J. and Evans , G. H. 1989 . A Mathematical-Model of the Fluid-Mechanics and Gas-Phase Chemistry in a Rotating-Disc Chemical Vapor-Deposition Reactor . J. Electrochem. Soc. , 136 : 819 – 829 .
   Web of Science ®Google Scholar
• Coltrin , M. E. , Kee , R. J. and Miller , J. A. 1984 . A Mathematical-Model of the Coupled Fluid-Mechanics and Chemical-Kinetics in a Chemical Vapor-Deposition Reactor . J. Electrochem. Soc. , 131 : 425 – 434 .
   Web of Science ®Google Scholar
• Coltrin , M. E. , Kee , R. J. and Miller , J. A. 1986 . A Mathematical-Model of Silicon Chemical Vapor-Deposition—Further Refinements and the Effects of Thermal-Diffusion . J. Electrochem. Soc. , 133 : 1206 – 1213 .
   Web of Science ®Google Scholar
• Coltrin , M. E. , Kee , R. J. , Rupley , F. M. and Meeks , E. 1996 . National Laboratories Report . SAND96-8216
   Google Scholar
• Frenklach , M. 2002 . Method of Moments with Interpolative Closure . Chem. Eng. Sci. , 57 : 2229 – 2239 .
   Web of Science ®Google Scholar
• Frenklach , M. and Harris , S. J. 1987 . Aerosol Dynamics Modeling Using the Method of Moments . J. Colloid Interface Sci. , 118 : 252 – 261 .
   Web of Science ®Google Scholar
• Friedlander , S. K. 2000 . Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics , Oxford : Oxford University Press .
   Google Scholar
• Gelbard , F. , Tambour , Y. and Seinfeld , J. H. 1980 . Sectional Representations for Simulating Aerosol Dynamics . J. Colloid Interface Sci. , 76 : 541 – 556 .
   Web of Science ®Google Scholar
• Girshick , S. L. , Swihart , M. T. , Suh , S. M. , Mahajan , M. R. and Nijhawan , S. 2000 . Numerical Modeling of Gas-Phase Nucleation and Particle Growth During Chemical Vapor Deposition of Silicon . J. Electrochem. Soc. , 147 : 2303 – 2311 .
   Google Scholar
• Ho , P. , Coltrin , M. E. and Breiland , W. G. 1994 . Laser-Induced Fluorescence Measurements and Kinetic-Analysis of Si Atom Formation in a Rotating-Disc Chemical-Vapor-Deposition Reactor . J. Phys. Chem. , 98 : 10138 – 10147 .
   Web of Science ®Google Scholar
• Hounslow , M. J. , Ryall , R. L. and Marshall , V. R. 1988 . A Discretized Population Balance for Nucleation, Growth, and Aggregation . AIChE J. , 34 : 1821 – 1832 .
   Web of Science ®Google Scholar
• Kee , R. J. , Dixon-Lewis , G. , Warnatz , J. , Coltrin , M. E. , Miller , J. A. and Moffat , H. K. 1986 . National Laboratories Report . SAND86-8246B
   Google Scholar
• Kee , R. J. , Rupley , R. M. , Meeks , E. and Miller , J. A. 1996 . National Laboratories Report . SAND96-8216
   Google Scholar
• Kiss , L. B. , Soderlund , J. , Niklasson , G. A. and Granqvist , C. G. 1999 . The Real Origin of Lognormal Size Distributions of Nanoparticles in Vapor Growth Processes . Nanostructured Materials , 12 : 327 – 332 .
   Google Scholar
• Kumar , S. and Ramkrishna , D. 1996a . On the solution of population balance equations by discretization. 1. A fixed pivot technique . Chem. Eng. Sci. , 51 : 1311 – 1332 .
   Web of Science ®Google Scholar
• Kumar , S. and Ramkrishna , D. 1996b . On the solution of population balance equations by discretization. 2. A moving pivot technique . Chem. Eng. Sci. , 51 : 1333 – 1342 .
   Web of Science ®Google Scholar
• Landgrebe , J. D. and Pratsinis , S. E. 1990 . A discrete-sectional model for particulate production by gas-phase chemical-reaction and aerosol coagulation in the free-molecular regime . J. Colloid Interface Sci. , 139 : 63 – 86 .
   Web of Science ®Google Scholar
• Lee , K. W. and Chen , H. 1984 . Coagulation rate of polydisperse particles . Aerosol Sci. Technol. , 3 : 327 – 334 .
   Web of Science ®Google Scholar
• Lee , K. W. , Chen , H. and Gieseke , J. A. 1984 . Log-normally Preserving Size Distribution for Brownian Coagulation in the Free-Molecule Regime . Aerosol Sci. Technol. , 3 : 53 – 62 .
   Web of Science ®Google Scholar
• Lee , K. W. and Liu , B. Y. H. 1980 . On the Minimum Efficiency and the Most Penetrating Particle-Size for Fibrous Filters . J. Air Pollution Control Association , 30 : 377 – 381 .
   Web of Science ®Google Scholar
• Li , X. G. , He , Y. Q. , Talukdar , S. S. and Swihart , M. T. 2003 . Process for Preparing Macroscopic Quantities of Brightly Photoluminescent Silicon Nanoparticles with Emission Spanning the Visible Spectrum . Langmuir , 19 : 8490 – 8496 .
   Web of Science ®Google Scholar
• Lister , J. D. , Smit , D. J. and Hounslow , M. J. 1995 . Adjustable Discretized Population Balance for Growth and Aggregation . AIChE J. , 41 : 591 – 603 .
   Google Scholar
• McGraw , R. 1997 . Description of Aerosol Dynamics by the Quadrature Method of Moments . Aerosol Sci. Technol. , 27 : 255 – 265 .
   Web of Science ®Google Scholar
• McGraw , R. , Nemesure , S. and Schwartz , S. E. 1998 . Properties and Evolution of Aerosols with Size Distributions having Identical Moments . J. Aerosol Sci. , 29 : 761 – 772 .
   Web of Science ®Google Scholar
• McGraw , R. and Wright , D. L. 2003 . Chemically Resolved Aerosol Dynamics for Internal Mixtures by the Quadrature Method of Moments . J. Aerosol Sci. , 34 : 189 – 209 .
   Web of Science ®Google Scholar
• Moffat , H. K. , Jensen , K. F. and Carr , R. W. 1992a . Determination of the Arrhenius Rate Parameters for Si2H6↔ SiH4+ SiH2 and ΔH° f (SiH2) by RRKM Analysis of Forward and Reverse Reaction-Rate Data . J. Phys. Chem. , 96 : 7683 – 7695 .
   Google Scholar
• Moffat , H. K. , Jensen , K. F. and Carr , R. W. 1992b . Estimation of Arrhenius Parameters for the 1,1 Elimination of H2 from Si2H6 and the Role of Chemically Activated Disilane in Silane Pyrolysis . J. Phys. Chem. , 96 : 7695 – 7703 .
   Google Scholar
• Nijhawan , S. , McMurry , P. H. , Swihart , M. T. , Suh , S. M. , Girshick , S. L. , Campbell , S. A. and Brockmann , J. E. 2003 . An Experimental and Numerical Study of Particle Nucleation and Growth During Low-Pressure Thermal Decomposition of Silane . J. Aerosol Sci. , 34 : 691 – 711 .
   Google Scholar
• Ostraat , M. L. , De , Blauwe, J. W. , Green , M. L. , Bell , L. D. , Atwater , H. A. and Flagan , R. C. 2001 . Ultraclean Two-Stage Aerosol Reactor for Production of Oxide-Passivated Silicon Nanoparticles for Novel Memory Devices . J. Electrochem. Soc. , 148 : G265 – G270 .
   Google Scholar
• Otto , E. , Fissan , H. , Park , S. H. and Lee , K. W. 1999 . The Log-Normal Size Distribution Theory of Brownian Aerosol Coagulation for the Entire Particle Size Range: Part II—Analytical Solution Using Dahneke's Coagulation Kernel . J. Aerosol Sci. , 30 : 17 – 34 .
   Web of Science ®Google Scholar
• Park , K. S. , Lee , B. W. and Choi , M. 1999a . An Analysis of Aerosol Dynamics in the Modified Chemical Vapor Deposition . Aerosol Sci. Technol. , 31 : 258 – 274 .
   Web of Science ®Google Scholar
• Park , S. H. , Lee , K. W. , Otto , E. and Fissan , H. 1999b . The Log-Normal Size Distribution Theory of Brownian Aerosol Coagulation for the Entire Particle Size Range: Part I—Analytical Solution Using the Harmonic Mean Coagulation kernel . J. Aerosol Sci. , 30 : 3 – 16 .
   Web of Science ®Google Scholar
• Pratsinis , S. E. 1988 . Simultaneous Nucleation, Condensation, and Coagulation in Aerosol Reactors . J. Colloid Interface Sci. , 124 : 416 – 427 .
   Web of Science ®Google Scholar
• Purnell , J. H. and Walsh , R. 1984 . Some Comments on Kinetics and Mechanism in the Pyrolysis of Monosilane . Chem. Phys. Lett. , 110 : 330 – 334 .
   Web of Science ®Google Scholar
• Randolph , A. D. and Larson , M. A. 1971 . Theory of Particulate Processes , New York : Academic Press .
   Google Scholar
• Seigneur , C. , Hudischewskyj , A. B. , Seinfeld , J. H. , Whitby , K. T. , Whitby , E. R. , Brock , J. R. and Barnes , H. M. 1986 . Simulation of Aerosol Dynamics—A Comparative Review of Mathematical-Models . Aerosol Sci. Technol. , 5 : 205 – 222 .
   Web of Science ®Google Scholar
• Seinfeld , J. H. 1986 . Atmospheric Chemistry and Physics of Air Pollution , New York : Wiley-Interscience .
   Google Scholar
• Serna , S. and Marquina , A. 2004 . Power ENO Methods: A Fifth-Order Accurate Weighted Power ENO Method . J. Comput. Phys. , 194 : 632 – 658 .
   Google Scholar
• Seto , T. , Kawakami , Y. , Suzuki , N. , Hirasawa , M. and Aya , N. 2001 . Laser Synthesis of Uniform Silicon Single Nanodots . Nano Lett. , 1 : 315 – 318 .
   Google Scholar
• Settumba , N. and Garrick , S. C. 2003 . Direct Numerical Simulation of Nanoparticle Coagulation in a Temporal Mixing Layer Via a Moment Method . J. Aerosol Sci. , 34 : 149 – 167 .
   Web of Science ®Google Scholar
• Swihart , M. T. and Girshick , S. L. 1999 . Thermochemistry and Kinetics of Silicon Hydride Cluster Formation During Thermal Decomposition of Silane . J. Phys. Chem. B , 103 : 64 – 76 .
   Google Scholar
• Talukdar , S. S. and Swihart , M. T. 2004 . Aerosol Dynamics Modeling of Silicon Nanoparticle Formation During Silane Pyrolysis: A Comparison of Three Solution Methods . J. Aerosol Sci. , 35 : 889 – 908 .
   Web of Science ®Google Scholar
• Tsantilis , S. , Kammler , H. K. and Pratsinis , S. E. 2002 . Population Balance Modeling of Flame Synthesis of Titania Nanoparticles . Chem. Eng. Sci. , 57 : 2139 – 2156 .
   Web of Science ®Google Scholar
• Waldmann , L. and Schmitt , K. H. 1966 . Aerosol Science , London : Academic Press .
   Google Scholar
• Wong , H. W. , Li , X. G. , Swihart , M. T. and Broadbelt , L. J. 2004 . Detailed Kinetic Modeling of Silicon Nanoparticle Formation Chemistry Via Automated Mechanism Generation . J. Phys. Chem. A , 108 : 10122 – 10132 .
   Google Scholar
• Zhang , Y. , Seigneur , C. , Seinfeld , J. H. , Jacobson , M. Z. and Binkowski , F. S. 1999 . Simulation of Aerosol Dynamics: A Comparative Review of Algorithms used in Air Quality Models . Aerosol Sci. Technol. , 31 : 487 – 514 .
   Web of Science ®Google Scholar