半導体製造用縦型拡散炉で熱処理されるウェーハ列の温度分布履歴の数値シミュレーション

概要

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More than hundred circular wafers in a row are loaded into an inner tube inside a vertical pipe furnace, heated, and unloaded. During the whole process, the wafer temperature plays a dominant role. For example, the wafer temperature dominates thermal oxidation or diffusion rate. A drastic radial temperature variation sets up thermal stresses in each wafer, and often causes plastic deformation. This paper numerically simulates the temperature distribution in the wafer row during the whole process. The radiosity method is employed to analyze radiative heat transfer among the tube surfaces and wafers. The zoning method is used to reduce the number of the geometrical factors, where the inner space inside the tube are divided into a number of subspaces by setting imaginary planes. Then, the energy conservation equation for the wafers is derived based on the radiative heat flux and thermal conduction in the wafers. This equation is solved using a finite difference scheme to obtain the temperature distribution in the wafer row. Finally, the time history of temperature distribution for 164-wafer row is simulated, and compared with the experiment.
日本シミュレーション学会の論文
1994-12-15