A tool for processing silicon wafers is housed within

Chapter 13, Problem 13.95

(choose chapter or problem)

A tool for processing silicon wafers is housed within avacuum chamber whose walls are black and maintainedby a coolant at Tvc?300 K. The thin silicon wafer is mounted close to, but not touching, a chuck, which iselectrically heated and maintained at the temperature Tc. The surface of the chuck facing the wafer is black. Thewafer temperature is Tw?700 K, and its surface is dif-fuse and gray with an emissivity of ?w?0.6. The func-tion of the grid, a thin metallic foil positioned coaxialwith the wafer and of the same diameter, is to controlthe power of the ion beam reaching the wafer. The gridsurface is black with a temperature of Tg?500 K. Theeffect of the ion beam striking the wafer is to apply auniform heat flux of . The top surfaceof the wafer is subjected to the flow of a process gas forwhich T??500 K and h?10 W/m2?K. Since the gapbetween the wafer and chuck, , is very small, flow ofthe process gas in this region may be neglected.(a) Represent the wafer schematically, showing acontrol surface and all relevant thermal processes.(b) Perform an energy balance on the wafer anddetermine the chuck temperature Tc.