Conjugate heat transfer analysis of 300-mm bake station

Abstract

An exhaustive heat-transfer analysis of 200-mm and 300-mm bake equipment has been conducted to infer the temperature uniformity on the wafer from the time it is set on the plate until the end of the bake process. The objective of the analysis was to gain insight into the heat transport to the wafer and improve the thermal uniformity of the wafer. During the soft, hard and post-exposure bake processes, the temperatures to which the wafer is heated can range from 50 degrees to 250 degrees C. The influence of the variables that contribute to the temperature nonuniformity, namely the height of the proximity pins, wafer warp and bow, heater thickness, insulation of the bake plate, and lid material, have been analyzed. The analysis has been carried out using computational fluid dynamics packages, FLUENT/UNS and FIDAP. The accuracy of the numerical simulations has been verified through analytical solution is presented which provides a closed-form expression for the temperature of the wafer in terms of Biot number, a dimensionless parameter. The temperature rise of the wafer based on this simple expression compares very favorably with the detailed axisymmetric numerical solution that was carried out using variable material properties and the complex boundary conditions for the geometry of a 200-mm bake plate. The radial temperature variation on the wafer after 100 seconds on the bake plate also matches very well with the measurements. Based on the success of the modeling results with the 200-mm bake plates, a 300-mm bake plate analysis was conducted to determine if the temperature uniformity would be within specifications. The analysis revealed some key factors that caused temperature nonuniformity and the design was then altered to improve the temperature uniformity. Subsequent measurements confirmed the improvement of the temperature uniformity.