In the thermal processing of semiconductor materials, annealing is accomplished by heating a silicon wafer according to a temperature-time recipe and then maintaining a fixed elevated temperature for a prescribed period of time. For the process tool arrangement shown as follows, the wafer is in an evacuated chamber whose walls are maintained at 27°C and within which heating lamps maintain a radiant flux qw/s at its upper surface. The wafer is 0.78 mm thick, has a thermal conductivity of 30 W/m ∙ K, and an emissivity that equals its absorptivity to the radiant flux (ε = a_l = 0.65). For qn/s = 3.0 x 10⁵ W/m², the temperature on its lower surface is measured by a radiation thermometer and found to have a value of T_w,l  = 997°C.

To avoid warping the wafer and inducing slip planes in the crystal structure, the temperature difference across the thickness of the wafer must be less than 2°C. Is this condition being met?

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Ta= 27°C Heating lamps 4"= 3x 10 wim? Wafer, k,,a L=0,78 mm = 997°C