System and method for determining nonlinear membrane stress

Abstract

The invention provides a system and method for determining nonlinear membrane stress. According to the invention, a membrane material is taken as a multilayer board shell structure to perform mechanic modeling so as to define the deflexion, cross section corner, middle plane internal displacement or curvature variation on the middle plane of the multilayer board shell structure as well as nonlinear geometric relationship to describe the deformation of the membrane material. Shape measuring equipment is adopted to measure the deformation of the membrane material caused by membrane stress, and the deformation is represented as the deflexion, cross section slope, middle plane internal displacement or curvature variation of the thin-film material. The finite elements of the multilayer board shell structure are adopted to discrete the geometrical model of a detected object, the measured values of degree of freedom of all or part of finite element nodes are given in a direct measurement or indirect interpolation manner, the least square fitting condition between the deformation generated by membrane stress at the nodes and the measured deformation is created, and the membrane stress is reversely solved through nonlinear iterative computations. As for membrane temperature mismatching stress belonging to part of the membrane stress, the nonlinear temperature mismatching stress of the membrane material with a deformed base body is calculated and considered at the same time under the condition of given temperature variation.

Description

technical field [0001] The invention pertains to measurement techniques used in the manufacture of integrated circuits and microelectromechanical systems (MEMS), which are used to measure thin film stress in thin film materials. Background technique [0002] Thin film materials are widely used in the manufacture of integrated circuits and microelectromechanical systems (MEMS). After chemical deposition (CVD) and physical deposition (PVD) techniques are used to form thin film materials with specific properties and functions on the surface of the substrate, the thin film materials can be processed into integrated circuits and microchips by using micromachining processes such as masks, photolithography, and corrosion. structure. Non-negligible stress inevitably occurs in the thin film material due to the crystal defects generated during the film formation process and the difference between the thermal expansion coefficients of the thin film material and the base material. Thi...

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Problems solved by technology

Although this method avoids the problem of using non-coordinated strain, it still has the following obvious defects: (1) It is generally impossible to measure the kinematic variables of all nodes, except for the nodes on the boundary, the internal nodes are not measurable , can only be obtained by interpolation; (2) It is difficult to ensure sufficient accuracy in the measurement of degrees of freedom such as rotation angles; (3) The coordination condition between the deformation of the substrate and the film is not conside

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