Numerical simulations of rarefied gas flows in thin film processes

Many processes exist in which a thin film is deposited from the gas phase, e.g. Chemical Vapor Deposition (CVD). These processes are operated at ever decreasing reactor operating pressures and with ever decreasing wafer feature dimensions, reaching into the rarefied flow regime. As numerical simulation tools are frequently used to design and improve reactors, there is a need for numerical simulation tools capable of modeling rarefied internal gas flows. To fulfill this need, the Direct Simulation Monte Carlo (DSMC) method was implemented in the 2D STARS and 3D X-Stream codes. The DSMC method was developed for high speed rarefied flow simulations in space applications, but is also suitable for low speed rarefied gas flows as e.g. found inside deposition reactors. After the implementation, validation of both codes was performed on a wide variety of problems, including a thin film deposition experiment that was designed and performed especially for the validation of the codes. The numerical results of the developed codes were very satisfactory in all cases, leading to the conclusion that the DSMC method in general, and the STARS and X-Stream codes specifically, are a very promising tool for use in internal rarefied gas flows, including thin film deposition processes. Finally, the developed codes were used for calculations on three applications in the thin film industry, namely the heat transfer in a stagnation flow CVD reactor, thin film deposition through a shadow mask and the reaction rate of a gas at a surface with a reactive sticking coefficient.

[1]  Graeme A. Bird,et al.  Molecular Gas Dynamics , 1976 .

[2]  Michio Nishida,et al.  DSMC Simulation of Parallel, Oblique and Normal Free Jet Impingements on a Flat Plate , 2000 .

[3]  Francis J. Alexander,et al.  Cell size dependence of transport coefficients in stochastic particle algorithms , 1998 .

[4]  Edward S. Piekos,et al.  DSMC modeling of micromechanical devices , 1995 .

[5]  G. B..  The Dynamical Theory of Gases , 1916, Nature.

[6]  Jong-Shinn Wu,et al.  Parallel DSMC method using dynamic domain decomposition , 2005 .

[7]  D. Russell.  Density Disturbance ahead of a Sphere in Rarefied Supersonic Flow , 1968 .

[8]  Cornelis Vuik,et al.  The Deflation Accelerated Schwarz Method for CFD , 2005, International Conference on Computational Science.

[9]  C. Shen,et al.  Rarefied Gas Flows in Micro‐Channels , 2002 .

[10]  T. J. Mountziaris,et al.  Gas-phase and surface reaction mechanisms in MOCVD of GaAs with trimethyl-gallium and arsine , 1991 .

[11]  Alejandro L. Garcia,et al.  Statistical error in particle simulations of hydrodynamic phenomena , 2002, cond-mat/0207430.

[12]  T. Bartel,et al.  Experimental validation of a direct simulation by Monte Carlo molecular gas flow model , 1995 .

[13]  Iain D. Boyd,et al.  New Discrete Vibrational Energy Model for the Direct Simulation Monte Carlo Method. , 1994 .

[14]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[15]  Jing Fan,et al.  Validation of a Hybrid Grid Scheme of DSMC in Simulating Three-Dimensional Rarefied Gas Flows , 2003 .

[16]  Graeme A. Bird,et al.  Definition of mean free path for real gases , 1983 .

[17]  Michail A. Gallis,et al.  Direct simulation Monte Carlo convergence behavior of the hard-sphere-gas thermal conductivity for Fourier heat flow , 2006 .

[18]  I. A. Sadarjoen.  Extraction and visualization of geometries in fluid flow fields. , 1999 .

[19]  Graeme A. Bird,et al.  MONTE-CARLO SIMULATION IN AN ENGINEERING CONTEXT , 1980 .

[20]  David A. Lane,et al.  Interactive Time-Dependent Particle Tracing Using Tetrahedral Decomposition , 1996, IEEE Trans. Vis. Comput. Graph..

[21]  Hiroaki Matsumoto,et al.  Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential , 1991 .

[22]  W. Steckelmacher.  Molecular gas dynamics and the direct simulation of gas flows , 1996 .

[23]  C. Kleijn,et al.  A General Correction to Surface Reaction Models Based on Reactive Sticking Coefficients , 2007 .

[24]  Iain D. Boyd,et al.  Conservative Species Weighting Scheme for the Direct Simulation Monte Carlo Method , 1996 .

[25]  Graeme A. Bird,et al.  Direct Simulation and the Boltzmann Equation , 1970 .

[26]  Michael P. Garrity.  Raytracing irregular volume data , 1990, VVS.

[27]  Robert J. Kee,et al.  A Mathematical Model of the Fluid Mechanics and Gas‐Phase Chemistry in a Rotating Disk Chemical Vapor Deposition Reactor , 1989 .

[28]  W. Morokoff,et al.  Selfconsistent simulation of sputter deposition with the Monte Carlo method , 1994 .

[29]  Nicolas G. Hadjiconstantinou,et al.  Analysis of dis-cretization in the direct simulation Monte Carlo , 2000 .

[30]  Anthony Skjellum,et al.  A High-Performance, Portable Implementation of the MPI Message Passing Interface Standard , 1996, Parallel Comput..

[31]  Bernard S. Meyerson,et al.  Low‐temperature silicon epitaxy by ultrahigh vacuum/chemical vapor deposition , 1986 .

[32]  G. Thompson,et al.  The effect of fly-ash particulates on the atmospheric corrosion of zinc and mild steel , 1993 .

[33]  H. Wise,et al.  Diffusion and Heterogeneous Reaction. III. Atom Recombination at a Catalytic Boundary , 1960 .

[34]  C. F. Curtiss,et al.  Molecular Theory Of Gases And Liquids , 1954 .

[35]  Wang,et al.  Detailed surface and gas-phase chemical kinetics of diamond deposition. , 1991, Physical review. B, Condensed matter.

[36]  Full simulation of silicon chemical vapor deposition process , 2002 .

[37]  Alejandro L. Garcia.  ESTIMATING HYDRODYNAMIC QUANTITIES IN THE PRESENCE OF MICROSCOPIC FLUCTUATIONS , 2006 .

[38]  James N. Moss,et al.  Direct Simulation of Transitional Flow for Hypersonic Reentry Conditions , 2003 .

[39]  Claus Borgnakke,et al.  STATISTICAL COLLISION MODEL FOR SIMULATING POLYATOMIC GAS WITH RESTRICTED ENERGY EXCHANGE. , 1974 .

[40]  Gang Chen,et al.  Statistical Error Analysis for the Direct Simulation Monte Carlo Technique , 1996 .

[41]  H. Legge.  Plume Impingement Forces on Inclined Flat Plates , 1990 .

[42]  N. Shibata,et al.  A Boundary Layer Model for the MOCVD Process in a Vertical Cylinder Reactor , 1987 .

[43]  J. Thibault,et al.  Direct simulation Monte Carlo method for molecular and transitional flow regimes in vacuum components with static and moving surfaces , 1999 .

[44]  W. M. Haynes.  CRC Handbook of Chemistry and Physics , 1990 .

[45]  R. E. Oosterbroek,et al.  Fabrication of a high-temperature microreactor with integrated heater and sensor patterns on an ultrathin silicon membrane , 2005 .

[46]  Hiroaki Matsumoto,et al.  Variable soft sphere molecular model for air species , 1992 .

[47]  Leonardo Dagum,et al.  Models of thermal relaxation mechanics for particle simulation methods , 1993 .

[48]  C. Y. Lee,et al.  Estimation of Diffusion Coefficients for Gases and Vapors , 1955 .

[49]  Klavs F. Jensen,et al.  Chemical vapor deposition : principles and applications , 1993 .

[50]  K. Kobe.  The properties of gases and liquids , 1959 .

[51]  R. Gordon,et al.  Kinetic Modeling of the Chemical Vapor Deposition of Silicon Dioxide from Silane or Disilane and Nitrous Oxide , 1990 .

[52]  C. R. Kleijn,et al.  Zinc deposition experiments for validation of direct-simulation Monte Carlo calculations of rarefied internal gas flows , 2007 .

[53]  Claus Borgnakke,et al.  Statistical collision model for Monte Carlo simulation of polyatomic gas mixture , 1975 .

[54]  K.-C. Tseng,et al.  International Journal of Computational Fluid Dynamics , 2022 .

[55]  Robert J. Kee,et al.  A Model of Silicon Carbide Chemical Vapor Deposition , 1991 .

[56]  Alejandro L. Garcia,et al.  Time step truncation error in direct simulation , 2000 .

[57]  W. Wagner.  A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation , 1992 .

[58]  P. Wesseling.  Principles of Computational Fluid Dynamics , 2000 .