Thermal uniformity of 12-in silicon wafer in linearly ramped-temperature transient rapid thermal processing

This paper presents a systematic method for estimating the dynamic incident-heat-flux profiles required to achieve thermal uniformity in 12-in silicon wafers during linearly ramped-temperature transient rapid thermal processing using the inverse heat-transfer method. A two-dimensional thermal model and temperature-dependent silicon wafer thermal properties are adopted in this study. The results show that thermal nonuniformities on the wafer surfaces occur during ramped increases in direct proportion to the ramp-up rate. The maximum temperature differences in the present study are 0.835°C, 1.174°C, and 1.516°C, respectively, for linear 100°C/s, 200°C/s, and 300°C/s ramp-up rates. Although a linear ramp-up rate of 300°C/s was used and measurement errors did reach 3.864°C, the surface temperature was maintained within 1.6°C of the center of the wafer surface when the incident-heat-flux profiles were dynamically controlled according to the inverse-method approach. These thermal nonuniformities could be acceptable in rapid thermal processing systems