A tool used for fabricating semiconductor devicesconsists

Chapter 5, Problem 5.13

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A tool used for fabricating semiconductor devicesconsists of a chuck (thick metallic, cylindrical disk)onto which a very thin silicon wafer (??2700 kg/m3,c?875 J/kg?K, k?177 W/m?K) is placed by arobotic arm. Once in position, an electric field in thechuck is energized, creating an electrostatic force thatholds the wafer firmly to the chuck. To ensure a repro-ducible thermal contact resistance between the chuckand the wafer from cycle to cycle, pressurized heliumgas is introduced at the center of the chuck and flows(very slowly) radially outward between the asperities ofthe interface region.An experiment has been performed under conditions forwhich the wafer, initially at a uniform temperatureTw,i?100C, is suddenly placed on the chuck, which is ata uniform and constant temperature Tc?23C. With thewafer in place, the electrostatic force and the helium gasflow are applied. After 15 s, the temperature of the waferis determined to be 33C. What is the thermal contactresistance (m2?K / W) between the wafer and chuck?Will the value of increase, decrease, or remain thesame if air, instead of helium, is used as the purge gas?

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