Using inverse modeling to estimate the incident heat flux required to achieve temperature uniformity across a circular disk

This article presents a systematic inverse modeling analysis for estimating the incident heat flux required to achieve temperature uniformity across a circular disk during thermal processing. A one-dimensional thermal model, temperature-dependent thermal properties of silicon, and a future-time algo rithm of inverse heat transfer method are used. Vertical and lateral edge-h eat compensations on the perimeter are discussed. The required edge-heat co mpensations for maintaining uniform temperature across 100-mm-diameter (0.6 -min-thick), 150-mm-diameter (0.675-mm-thick), 200-mm-diameter (0.725-mm-th ick), and 300-mm-diameter (0.775-mm-thick) silicon disks are evaluated intu itively using inverse modeling. Our numerical results show that temperature uniformity can be efficiently achieved using inverse modeling. The resulti ng maximum temperature differences in our present study were only 0.279, 0. 583, 0.989, and 0.178 degreesC across 100-, 150-, 200- and 300-mm-diameter disks, respectively.