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A control scheme to achieve wafer-to-wafer temperature uniformity in the reaction tube used for oxidation, diffusion, or annealing during semiconductor processes is proposed. In the analytical model, self-radiation loss, radiation between neighboring wafers, radiation from the tube wall, and thermal diffusion on a wafer surface are taken into account. The temperature monitoring points were the inlet, middle, and outlet of the reaction tube. The analysis indicates that if the tube wall temperatures at the inlet and outlet are 6 percent higher than that at the center of the tube, the wafer-to-wafer temperature becomes uniform. In the experiment, taking the silica tube temperature as the tube wall temperature, the increase in the temperatures at the inlet and outlet must be 5.6 percent to achieve wafer-to-wafer temperature uniformity, while it should be 6.9 percent if the temperature of the secondary tube is considered to be the tube wall temperature. Experiment results verify the effectiveness of the model. At the same time, the tube wall temperature is assumed to be influenced not only by the temperature of the silica tube but also by that of the secondary tube. The model predicts that the wafer temperature increased by 1°C if the tube wall temperature is increased as described in the foregoing. However, in the experiment, the wafer temperature increases by 1.6°C at most [ABSTRACT FROM AUTHOR]

The nonuniform temperatures that develop over silicon wafers on insertion and removal from the furnaces used in the oxidation and diffusion processes of semiconductor fabrication are one factor in reduced yields. For example, because of temperature differences in the oxidation process there are thermal stresses and differing thermal hystereses over the wafer surface which degrade the uniformity of the oxide layer formed. The most pronounced temperature differences, occurring when the wafers are inserted into the furnace, develop mainly because of the effect of the boat μg which supports the wafers. Since the heat capacity of the boat is much greater than that of the wafers, during the slower rise in the boat temperature radiant heat exchange with the wafer bottoms keeps the temperature of the bottoms lower than the temperature of the wafer tops, which are almost unaffected by the boat. This transient in the wafer temperature depends on such process parameters as the boat insertion speed, the ratio between the wafer and furnace reactor tube diameters, and the wafer spacing. In order to analyze this temperature characteristic the process is modelled and the results of numerical simulation are compared with experiment. The model for the wafer temperatures inside the furnace is a system of coupled partial differential equations for the mostly radiant heat fluxes of the boat and wafers. With an insertion speed of 2 m/sec, both the experimental data and the model give a maximum temperature difference over the wafer surface of 230°C near the end of insertion, thus confirming the model. [ABSTRACT FROM AUTHOR]