Chapter 12, Problem 12.97P

The equipment for heating a wafer during a semiconductor manufacturing process is shown schematically. The wafer is heated by an ion beam source (not shown) to a uniform, steady-state temperature. The large chamber contains the process gas, and its walls are at a uniform temperature of $T_{ch}=400k.\text{ A 5mm x 5mm}$ target area on the wafer is viewed by a radiometer, whose objective lens has a diameter of 25mm and is located 500mm from the wafer. The line-of-sight of the radiometer is ${\text{30}}^{\circ }$ off the wafer normal.

(a) In a preproduction test of the equipment, a black panel $\left(\epsilon \approx 1.0\right)$ is mounted in place of the wafer. Calculate the radiant power (W) received by the radiometer if the temperature of the panel is 800 K.

(b) The wafer, which is opaque, diffusegray with an emissivity of 0.7, is now placed in the equipment, and the ion beam is adjusted so that the power received by the radiometer is the same as that found for part (a). Calculate the temperature of the wafer for this heating condition.