Thin film stress calculated from wafer bow measurements

bow1       bow at the center of the wafer before deposition in m
bow2       bow at the center of the wafer after deposition in m
tflm         thickness of film in m
tsub        thickness of substrate or wafer in m
dwfr        diameter of wafer in mm
ymod      Young's modulus of substrate in GPa
pois         Poisson's ratio of substrate
sel           Film stress


When thin films are deposited at high temperature or annealed at high temperature, intrinsic stresses develop in the film due to mismatch of thermal expansion coefficients between the film and substrate material. The wafer will visibly bow or bend to a measurable degree based on the stress developed in the film. If the bow or radius of curvature of the wafer can be reliably measured, the stress developed in the film can be found out. Tensile stress will bow the wafer down making it concave while compressive stress will bow the wafer up making it convex.

The design interface can be used to determine the stress in the film if the bow of the wafer is known before and after measurement. A positive bow is considered wafer bending up and a negative bow is considered bending down. If the change in bow (bow2-bow1) is negative, the stress is negative and tensile, while a positive stress is compressive.


-The film thickness is uniform.
-The substrate is much thicker than the deposited film.
-The influence of the orientation of the silicon substrate on the deposited film stress is not considered. 
-Film stress is constant across the crossection of the film.
-Temperature of the film and substrate is uniform.

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