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

摘要

This paper presents a systematic method for estimating the dynamicnincident-heat-flux profiles required to achieve thermal uniformity inn12-in silicon wafers during linearly ramped-temperature transient rapidnthermal processing using the inverse heat-transfer method. Antwo-dimensional thermal model and temperature-dependent silicon wafernthermal properties are adopted in this study. The results show thatnthermal nonuniformities on the wafer surfaces occur during rampednincreases in direct proportion to the ramp-up rate. The maximumntemperature differences in the present study are 0.835°C,n1.174°C, and 1.516°C, respectively, for linear 100°C/s,n200°C/s, and 300°C/s ramp-up rates. Although a linear ramp-upnrate of 300°C/s was used and measurement errors did reachn3.864°C, the surface temperature was maintained within 1.6°C ofnthe center of the wafer surface when the incident-heat-flux profilesnwere dynamically controlled according to the inverse-method approach.nThese thermal nonuniformities could be acceptable in rapid thermalnprocessing systems