Optimization of Process Parameter and Temperature Uniformity on Wafers for Rapid Thermal Processing
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interest in the semiconductor industry. Several efforts have been made to improve equipment performance: - The constructive design of the process chamber was improved incrementally by changing the number of lamps used. Their position and direction were optimized to fulfill requirements for different wafer sizes and applications. - Additional arrangements inside the process chamber (edge guard ring, susceptors), specially shaped reflectors, paint patterns at the reflectors and also scratched patterns on a quartz window were introduced. - The design of the process (heatup rate, prestabilization steps, independent top and bottom heater bank control, gas flow) has a major impact on the resulting process uniformity. Therefore a compromise between yield requirements and wafer throughput had to be found. In todays semiconductor fabrication mostly standard recipes with fixed settings for ramp-up rate and gas flow are used. As mentioned in [15] the only variable set of parameters to influence process parameter uniformity in an already installed RTP system is the power supplied to each single lamp (independent lamp control) or to groups of lamps (lamp bank or multizone control). The adjustment of such a lamp correction table by conventional trial-and-error methods is both timeand wafer consuming. The motivation of this work was the development of a very fast algorithm which generates an optimum solution of a lamp correction table for a given process. In other 275 Mat. Res. Soc. Symp. Proc. Vol. 389 ©1995 Materials Research Society
words, the global minimum of the standard deviation of the process parameter distribution should be achieved. THE MODEL - LAMBERT SOLVER
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The model described in [14] will be used in the following considerations without modifications. Its main features will be outlined briefly: The model is characterized by the calculation of the intensity distribution of each single lamp on the wafer using raytracing. Furthermore, the intensity distributions of the backreflected wafer radiation and the ring radiation at a given temperature are calculated. These time-consuming calculations must be done prior to the use of this model, but only for a given system configuration. Based on a lamp correction table the intensity distribution on the wafer resulting from all lamps is calculated. The total absorbed intensity distribution on the wafer is calculated by adding the intensity distributions of the three heat sources: lamps, wafer and silicon ring. Therefore the target temperature has to be known. The numerical solution of the heat conduction equation leads to the resulting temperature distribution. Based on experimental results the temperature distribution can be converted to a parameter distribution. This needs to be added by the "correction" distribution (obtained as a difference between one measured and associated calculated parameter distribution). Fig. 1 shows an overview of the used model, implemented in the LAMdBERT Solver' (LAmp radiation Model Based Equipment control for RTP)t.
Fig. I
Overview of
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