Silicon wafer is susceptible to warping when the wafer is subjected to a temperature difference across its thickness. Thus, steps needed to be taken to prevent the temperature gradient across the wafer thickness from getting large. As an engineer in a semiconductor company, your task is to determine the maximum allowable heat flux on the bottom surface of the wafer while maintaining the upper surface temperature at 27°C. To prevent the wafer from warping, the temperature difference across its thickness of 500??m cannot exceed 1°C.

Question

Answer 1

To prevent a silicon wafer from warping, the temperature difference across its thickness cannot exceed 1°C. The maximum allowable heat flux on the bottom surface of the wafer is to be determined.



Assumptions 1 Heat conduction is steady and one-dimensional. 2 There is no heat generation. 3 Thermal conductivity is constant.

Properties The thermal conductivity of silicon at 27°C (300 K) is 148 W/m?K (Table A-3).

Analysis For steady heat transfer, the Fourier’s law of heat conduction can be expressed as



Discussion With the upper surface of the wafer maintained at 27°C, if the bottom surface of the wafer is exposed to a flux greater than 2.96×105 W/m2, the temperature gradient across the wafer thickness could be significant enough to cause warping.