2021 Volume 6 Pages 33-38
This paper proposes a method to estimate stresses that cause the warpage of a silicon wafer from a deflection measurement. The deflection is measured by an optical method, a scan of a laser displacement sensor. A least-squares method with a finite element mesh is used for smoothing and differentiating the measurements. By applying this method, the surface strains of a silicon wafer are obtained as the 2nd derivatives of the deflection. The stresses that cause the warpage are estimated by assuming that the stresses are released and free in the warped wafer. The effectiveness of the method for obtaining surface strain from deflection is demonstrated by applying it to wafer simulation data and measured beam deflection. Results show that the surface strain can be properly obtained from the deflection measurement. Furthermore, the proposed method is applied to stress analysis of actual silicon wafers. This method is expected to be used to control quality of silicon wafers.