Method for solving stress of thin substrate

Abstract

The invention belongs to the technical field of precision measurement and analysis, and particularly relates to a method for solving the stress of a thin substrate, which comprises the following steps of: S1, acquiring basic parameters of the thin substrate of which the stress is to be analyzed; S2, establishing a finite element model of the thin substrate; S3, applying a unit stress load to each surface in the model in sequence, solving the finite element model, and outputting a solving result; S4, obtaining the center point coordinates of the surfaces to which the unit stress load is applied in the finite element model, and further constructing a matrix L including the center point distance relationship between the surfaces; S5, acquiring the surface shape of the real thin substrate, and drawing an accept-reject curve; and S6, solving the linear equation by adopting a regularization method, and calculating to obtain the real stress distribution of the thin substrate. The problems of discontinuous stress distribution and large fluctuation of the thin substrate caused by directly solving the equation set are solved, and extra physical damage is not introduced in the process of obtaining the stress distribution.

Description

technical field [0001] The invention belongs to the technical field of precision measurement and analysis, and in particular relates to a method for solving the stress of a thin substrate. Background technique [0002] The thin substrate is a thin plate in mechanics, the geometric feature is circular, and its thickness dimension is much smaller than the plane dimension. At present, large-size silicon wafers of 300mm are widely used, and their thickness is less than 0.2mm. Due to the difference in temperature between the upper and lower surfaces during processing, residual stress will be generated on the surface of the silicon wafer after processing. Residual stress will lead to subsurface damage, the greater the damage, the greater the residual stress, so the residual stress can be used to characterize the damage of the silicon wafer subsurface. At present, in practical applications, laser triangulation and laser interferometers can be used to complete the measurement of t...

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Problems solved by technology

However, in actual measurement, the Raman frequency shift will still be affected by the focal depth, laser heating effect and other temperature, and it does not have very high precision in the absence of effective calibration criteria; and due to the limited penetration depth of light waves, the obtained is the best The stress state of the surface layer, the micro-Raman measurement results reflect the changes in the microstructure of the processing damage, and the fluctuations of the measured values ​​​​at different positions are relatively large

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