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 processi ng using the inverse heat-transfer method, A two-dimensional thermal model and temperature-dependent silicon wafer thermal properties are adopted in t his study. The results show that thermal nonuniformities on the wafer surfa ces occur during ramped increases in direct proportion to the ramp-up rate. The maximum temperature differences in the present study are 0.835 degrees C, 1.174 degreesC, and 1.516 degreesC, respectively, for linear 100 degrees C/s, 200 degreesC/s, and 300 degreesC/s ramp-up rates, Although a linear ra mp-up rate of 300 degreesC/s was used and measurement errors did reach 3.86 4 degreesC, the surface temperature was maintained within 1.6 degreesC of t he center of the wafer surface when the incident-heat-flux profiles were dy namically controlled according to the inverse-method approach. These therma l nonuniforimities could be acceptable in rapid thermal processing systems.