# An Assessment of Local Geometric Uncertainties in Polysilicon MEMS: A Genetic Algorithm and POD-Kriging Surrogate Modeling Approach

## TL;DR

This paper introduces a new method using genetic algorithms and surrogate modeling to assess geometric uncertainties in MEMS devices, revealing significant variability in over-etch measures.

## Contribution

The novel approach combines genetic algorithms with POD-Kriging to estimate MEMS uncertainties using capacitance-voltage responses, offering an alternative to traditional methods.

## Key findings

- MEMS devices on the same wafer showed different over-etch values depending on local geometry.
- Over-etch mean values were +12.2% at comb fingers, +10.0% at springs, and −4.8% at stoppers.
- The method enables uncertainty quantification based on capacitance-voltage responses alone.

## Abstract

On the way toward MEMS miniaturization, the quantification of geometric uncertainties stands as a primary challenge. In this paper, an approach that combines genetic algorithms and proper orthogonal decomposition with kriging surrogate modeling was proposed to accurately predict over-etch measures through an on-chip test device. Despite being fabricated on a single wafer under nominally identical manufacturing conditions, MEMS can display different responses under the same actuation, due to a different characteristic geometry. It is shown that the uncertainties, given in terms of over-etch values, were not only different from die to die but also within the same die, depending on the local geometric features of the device. Therefore, the proposed method provided an alternative solution to estimate the uncertainties in MEMS devices, relying only on the capacitance–voltage response. A statistical analysis was carried out based on a batch of devices tested in the laboratory. These tests and the estimation procedure allowed us to quantify the mean values of the over-etch relative to the target as +12.2 % at comb fingers, +10.0 % at the supporting springs, and −4.8 % at stoppers, showing noteworthy variability induced by the environment.