Chapter 13, Problem 13.95P

A tool for processing silicon waters is housed within a vacuum chamber whose walls are black and maintained by a coolant at $T_{\text{ve}}=300\text{K}$ . The thin silicon wafer is mounted close to, but not touching, a chuck, which is electrically heated and maintained at the temperature $T_c$ .

The surface of the chuck facing the wafer is black. The wafer temperature is $T_w=700\text{K}$ , and its surface is diffuse and gray with an emissivity of ${\epsilon }_w=0.6$ . The function of the grid, a thin metallic foil positioned coaxial with the wafer and of the same diameter, is to control the power of the ion beam reaching the wafer. The grid surface is black with a temperature of $T_g=500\text{K}$ . The effect of the ion beam striking the wafer is to apply a uniform heat flux of ${q^{″}}_{\text{ib}}=600{\text{W/m}}^{\text{2}}$ . The top surface of the wafer is subjected to the (low of a process gas for which $T_{\infty }=500\text{K}$ and $h=10{\text{W/m}}^{\text{2}}\cdot \text{K}$ . Since the gap between the wafer and chuck, $\delta$ , is very small, flow of the process gas in this region may be neglected.

(a) Represent the wafer schematically, showing a control surface and all relevant thermal processes.
(b) Perform an energy balance on the wafer and determine the chuck temperature $T_c$ .