Heat treatment is common in processing of semiconductor material. A 200-mm-diameter silicon wafer with thickness of 725 µm is being heat treated in a vacuum chamber by infrared heat. The surrounding walls of the chamber have a uniform temperature of 310 K. The infrared heater provides an incident radiation flux of 200?kW/m2 on the upper surface of the wafer, and the emissivity and absorptivity of the wafer surface are 0.70. Using a pyrometer, the lower surface temperature of the wafer is measured to be 1000 K. Assuming there is no radiation exchange between the lower surface of the wafer and the surroundings, determine the upper surface temperature of the wafer. (Note: A pyrometer is a noncontacting device that intercepts and measures thermal radiation. This device can be used to

Question

determine the temperature of an object’s surface.)

Answer 1

The upper surface temperature of a silicon wafer undergoing heat treatment in a vacuum chamber by infrared heater is to be determined.

Assumptions 1 Steady operating conditions exist. 2 Radiation heat transfer between upper wafer surface and surroundings is between a small object and a large enclosure. 3 One-dimensional conduction in wafer. 4 The silicon wafer has constant properties. 5 No hot spot exists on the wafer.

Properties The thermal conductivity of silicon at 1000 K is 31.2 W/m ? K (Table A-3).



Analysis The heat transfer through the thickness of the wafer by conduction is equal to net heat transfer at the upper wafer surface:



Copy the following line and paste on a blank EES screen to solve the above equation:



Solving by EES software, the upper surface temperature of silicon wafer is



Discussion Excessive temperature difference across the wafer thickness will cause warping in the silicon wafer.