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 modยญ 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 adยญ dresses three general areas of simulation which frequently arise in semiconยญ 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 methยญ 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 chemiยญ cal vapor decomposition reactors and sputtering reactors. We also consider charged particles moving within a semiconductor lattice
CONTENT
Content -- 1 The Boltzmann Equation -- 1.1 The Liouville Equation -- 1.2 Rarefied Gases -- 1.3 Radiation Transport -- 1.4 Electron Transport -- 1.5 Summary -- 2 Modeling of Gas Flow -- 2.1 Typical Reactors -- 2.2 Hydrodynamic Equations -- 2.3 Near Hydrodynamic Flows -- 2.4 Transition Regime Flows -- 2.5 Free Molecular Flow -- 3 Numerical Methods for Rarefied Gas Dynamics -- 3.1 Direct Simulation Monte Carlo -- 3.2 Computing Results -- 3.3 Extensions -- 3.4 Simplified Flows -- 4 Gas Transport Simulations -- 4.1 Near Hydrodynamic Effects -- 4.2 UHV-CVD Reactor -- 4.3 Sputtering Reactors -- 5 Modeling of Radiative Heat Transfer -- 5.1 Rapid Thermal Processing -- 5.2 Semi-transparent Materials -- 5.3 Optical Properties of Surfaces -- 5.4 Solution of the Integral Equation -- 5.5 The Rendering Equation -- 6 Monte Carlo for Radiation Transport -- 6.1 Monte Carlo Solution Procedure -- 6.2 Quasi-Monte Carlo Methods -- 6.3 Coupling Radiation and Gas Transport -- 7 Radiation Transport Simulations -- 7.1 Case Study of an RTP Reactor -- 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 -- 8.2 Further Comparisons -- A Monte Carlo Methods -- References
