A comprehensive simulation capability to describe RTP related issues has been developed. The simulator describes: 1) The radiative heat transfer in 3D with cylindric symmetry by combined zonal-Monte-Carlo method for arbitrary geometry and for various boundary conditions. The spectrum of tungstenhalogen lamp is modeled realistically and the software allows for analysis of multivariable independent lamp control; 2) Conductive heat transfer in the patterned wafer as a function of patterns (3D representation -crucial for stress analysis) and in the chamber walls (important for temperature uniformity from run to run); 3) 3D wafer warpage and thermal stress analysis of the wafer treated as a laminated plate; 4) Electromagnetic wave interaction with the object of a size comparable to the wave length of radiation for multi-layered nonplanar structures including steps and trenches.; 5 ) Evaluation of emissivity of the wafer with deposited films for optical pyrometry. The software has been applied to various situations of which selected subsequent examples demonstrate its capability.A. Radiative Heat Transfer 3D radiative heat transfer in an RTP chamber with arbitrary shape of the chamber geometry, wafer (edge shape), reflecting shields, etc. (Fig.1) has been implemented. A hybrid zonal-MC numerical method is used; specular multiple reflections exchange factors and diffusive reflections view factors are employed. The exchange factors are updated at each time step to account for changing optical properties as a function of wave length, temperature and substrate doping. The model takes into account realistic spectral and temperature dependences of the optical properties of the wafer and chamber walls which may be opaque or semitransparent. In Fig.2 temperature nonuniformity as a function of radial position on the wafer for different time steps for two lamp powerings is shown. Chamber geometry and lamps configuration shown in Fig.1 were used. In both cases steady temperature of the center was 1023 K. During ramp-up, when thermal radiation from the wafer is considerably smaller than from the lamps, the center is colder than the edge due to more intense radiative heating of the edge. As the wafer is heated radiative losses from the wafer edge make the edge cooler than the center (steady state). The temperature has been studied for various lamp, shield ( Fig. 1) and wafer coating configurations. Diffusive reflections are more effective for wafer heating than specular reflections. This fact can be used in designing the chamber surfaces. However, correct data for the angular dependence of the diffusively reflective surfaces are needed. 0 0 Lamparrays 0 0 Qartz window Wafer Fig.1. Schematic sketch of cylindric RTP chamber.
SUMMARYThis paper describes the application of the boundary element method to solving two-dimensional steady slow viscous flow problems (creeping flow) in thermal silicon oxidation. The proposed method used the velocity-pressure formulation. The use of the incompressibility condition as a boundary condition and the application of the second Green's identity to transform the domain integral into a boundary integral result in a system of three boundary integral equations for velocity components and pressure. Solution of this system to be an ill-posed problem because of the presence of boundary conditions of the first kind. Two methods of regularization are employed. The numerical results for trench oxidation process are presented.
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