Transport Simulation in Microelectronics
Published on 27. January 1995
Book
Hardback
235 pages
978-3-7643-5168-7 (ISBN)
Description
Computer simulation of semiconductor processing equipment and devices requires the use of a wide variety of numerical methods. Of these methods, the Monte Carlo approach is perhaps most fundamentally suited to mod- eling physical events occurring on microscopic scales which are intricately connected to the particle structure of nature. Here physical phenomena can be simulated by following simulation particles (such as electrons, molecules, photons, etc. ) through a statistical sampling of scattering events. Monte Carlo is, however, generally looked on as a last resort due to the extremely slow convergence of these methods. It is of interest, then, to examine when in microelectronics it is necessary to use Monte Carlo methods, how such methods may be improved, and what are the alternatives. This book ad- dresses three general areas of simulation which frequently arise in semicon- ductor modeling where Monte Carlo methods playa significant role. In the first chapter the basic mathematical theory of the Boltzmann equation for particle transport is presented. The following chapters are devoted to the modeling of the transport processes and the associated Monte Carlo meth- ods.
Specific examples of industrial applications illustrate the effectiveness and importance of these methods. Two of these areas concern simulation of physical particles which may be assigned a time dependent position and velocity. This includes the molecules of a dilute gas used in such processing equipment as chemi- cal vapor decomposition reactors and sputtering reactors. We also consider charged particles moving within a semiconductor lattice.
Specific examples of industrial applications illustrate the effectiveness and importance of these methods. Two of these areas concern simulation of physical particles which may be assigned a time dependent position and velocity. This includes the molecules of a dilute gas used in such processing equipment as chemi- cal vapor decomposition reactors and sputtering reactors. We also consider charged particles moving within a semiconductor lattice.
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Alfred Kersch | William J. Morokoff
Transport Simulation in Microelectronics
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Content
Content.- 1 The Boltzmann Equation.- 1.1 The Liouville Equation.- 1.2 Rarefied Gases.- 1.2.1 Equilibrium.- 1.2.2 Knudsen Number and Fluid Equations.- 1.2.3 Multiple Species.- 1.2.4 Boundary Conditions.- 1.3 Radiation Transport.- 1.3.1 The Radiation Transport Equation.- 1.3.2 Boundary Conditions.- 1.4 Electron Transport.- 1.4.1 Classical Vlasov-Poisson.- 1.4.2 Semi-Classical Vlasov-Poisson.- 1.4.3 Semi-Classical Boltzmann Equation.- 1.4.4 Equilibrium.- 1.4.5 Hydrodynamic Equations.- 1.4.6 Electrons and Holes.- 1.4.7 Boundary Conditions.- 1.5 Summary.- 2 Modeling of Gas Flow.- 2.1 Typical Reactors.- 2.2 Hydrodynamic Equations.- 2.2.1 Balance Equations.- 2.2.2 Generalized Forces.- 2.3 Near Hydrodynamic Flows.- 2.3.1 Estimates of Transport Coefficients.- 2.3.2 Slip Boundary Conditions.- 2.4 Transition Regime Flows.- 2.4.1 Scattering Angle Models.- 2.4.2 Boundary Conditions.- 2.5 Free Molecular Flow.- 3 Numerical Methods for Rarefied Gas Dynamics.- 3.1 Direct Simulation Monte Carlo.- 3.1.1 Spatial Discretization.- 3.1.2 Time Step.- 3.1.3 Collision Step.- 3.1.4 Convection Step.- 3.1.5 Boundaries.- 3.2 Computing Results.- 3.3 Extensions.- 3.3.1 Multiple Species.- 3.3.2 Axisymmetric Flow.- 3.3.3 Gas Phase Chemical Reactions.- 3.4 Simplified Flows.- 3.4.1 Test Particle Method.- 3.4.2 Free Molecular Flow.- 4 Gas Transport Simulations.- 4.1 Near Hydrodynamic Effects.- 4.1.1 Determination of Slip Coefficients.- 4.1.2 The Diffusion Coefficient.- 4.2 UHV-CVD Reactor.- 4.3 Sputtering Reactors.- 4.3.1 The Reactor Model.- 4.3.2 Velocity Distributions.- 4.3.3 Collimated Sputtering.- 5 Modeling of Radiative Heat Transfer.- 5.1 Rapid Thermal Processing.- 5.2 Semi-transparent Materials.- 5.2.1 The McMahon Approximation.- 5.2.2 Example: Single Coating Layer.- 5.3 Optical Properties of Surfaces.- 5.4 Solution of the Integral Equation.- 5.4.1 The Series Solution.- 5.4.2 Specular Reflection.- 5.4.3 Diffuse Reflection.- 5.5 The Rendering Equation.- 6 Monte Carlo for Radiation Transport.- 6.1 Monte Carlo Solution Procedure.- 6.2 Quasi-Monte Carlo Methods.- 6.2.1 Discrepancy.- 6.2.2 Quasi-Random Sequences.- 6.2.3 Integration and Discrepancy.- 6.3 Coupling Radiation and Gas Transport.- 7 Radiation Transport Simulations.- 7.1 Case Study of an RTP Reactor.- 7.1.1 A Simplified Radiative Heat Transfer Reactor.- 7.1.2 Numerical Experiment.- 7.1.3 Numerical Results.- 7.1.4 Conclusions.- 7.2 Scalar Control RTCVD-reactor.- 7.3 Multi-variable Control RTCVD-reactor.- 8 Modeling of Charge Transport.- 8.1 Numerical Methods for Linear Transport.- 8.1.1 Event Based Monte Carlo.- 8.1.2 History Based Monte Carlo.- 8.2 Further Comparisons.- 8.2.1 Distribution Functions.- 8.2.2 Mass and Charge Currents.- A Monte Carlo Methods.- References.