In the thermal processing of semiconductor materials,

Chapter , Problem 1.56

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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 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 ( l 0.65). For 3.0 105 W/m2 , the temperature on its lower surface is measured by a radiation thermometer and found to have a value of Tw,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?