MEMS device uncertainty analysis method based on Nataf transformation

Abstract

The invention discloses an MEMS device uncertainty analysis method based on Nataf transformation, and the method comprises the following steps: building a Gaussian mixture model according to the obtained multi-dimensional discrete data of technological deviation, and obtaining a joint density function and an edge cumulative distribution function of the Gaussian mixture model; carrying out Nataf transformation on the Gaussian mixture model; analyzing time consumed by the random point collocation method under different expansion orders and corresponding precision, and performing Nataf inverse transformation on the grid points to obtain multi-dimensional configuration points suitable for the Gaussian mixture model; defining an output parameter according to a specific device, and solving an expansion coefficient; and obtaining numerical information of the output parameter according to a calculation result. The method is high in operation speed and high in result precision; moreover, the uncertainty analysis of the MEMS device under the associated process deviation can be effectively completed, and the distribution of the device performance parameter deviation caused by the associated process deviation can be accurately and quickly obtained, which has practical significance for the design, development, manufacturing and application of the MEMS device.

Description

technical field [0001] The invention belongs to the field of micro-electro-mechanical system (MEMS) computer simulation, in particular to a method for analyzing the uncertainty of MEMS devices based on Nataf transformation under the condition of associated process deviation. Background technique [0002] For the micromachining process, due to the complex and delicate manufacturing process, process control is very difficult. Such as the over-etching phenomenon in the etching process and the alignment deviation during photolithography may cause deviations in the dimensional parameters of the device. In addition, the MEMS process often involves the growth and sputtering of multiple materials, which may introduce deviations in material parameters, such as the uncertainty of Young's modulus. Usually, compared with the macroscopic machining process, the relative deviation of the process introduced by the MEMS process is much larger, which limits the high-precision performance of ...

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Problems solved by technology

[0004] In addition, the distribution of actual process deviations often does not satisfy the most common Gaussian distribution, and its specific distribution form is difficult to express in an analytical form, and only some discrete parameter data can be obtained through actual testing or process simulation.

In view of this situation, there is still a lack of in-depth research on how to perform efficient uncertainty analysis under the premise of considering the associated process deviation.

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