Evaluating the effects of thin film patterns on the temperature distribution of silicon wafers during radiant processing

A numerical model was developed to find the temperature distributions during radiant heating of a silicon wafer with SiO2 thin film patterns. The radiative properties of silicon and the film structure were found by considering the effects of partial transparency and thin film interference. The average total properties over simple patterns with feature sizes of the order of a few micrometers were found, using an average of the properties of each region within the pattern, weighted by their relative areas. In general, wafers with a single SiO2 film or pattern reach a higher steady state temperature than a plain Si wafer due to higher total absorptivity. This applies to thin films of any thickness below several micrometers, where coherent effects are dominant. The temperature of patterned wafers vary nonlinearly with film thickness, with the highest temperature discrepancy from Si wafer occurring at film thickness of approximately 0.2 μm. For wafers with complex patterns, the temperature distributions can be estimated by the average of temperatures for simpler patterns, weighted by their respective areas. Due to limitations in the computational domain, the radiative processing of 3-in. wafers was modeled; however, results were confirmed for the 12-in. wafer for limited cases