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

Ananya Roy¹, Francesco Rizzini², Gabriele Gattere²

¹Department of Civil and Environmental Engineering, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.

|March 6, 2025

Summary

Quantifying geometric uncertainties is crucial for microelectromechanical systems (MEMS) miniaturization. This study presents a novel method using genetic algorithms and proper orthogonal decomposition to predict over-etch variations in MEMS devices, improving manufacturing accuracy.

Keywords:

genetic algorithm (GA)kriging interpolation micro electro-mechanical systems (MEMS)over-etching proper orthogonal decomposition (POD)uncertainty quantification

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Area of Science:

Engineering
Materials Science
Nanotechnology

Background:

Microelectromechanical systems (MEMS) miniaturization faces challenges in quantifying geometric uncertainties.
Variations in MEMS device geometry, even under identical manufacturing conditions, lead to different responses.
Over-etch measures represent a critical geometric uncertainty in MEMS fabrication.

Purpose of the Study:

To develop and validate an accurate method for predicting over-etch measures in MEMS devices.
To quantify geometric uncertainties within and between MEMS dies.
To establish a link between capacitance-voltage response and geometric variations.

Main Methods:

A hybrid approach combining genetic algorithms (GAs), proper orthogonal decomposition (POD), and kriging surrogate modeling.
Utilizing an on-chip test device to measure capacitance-voltage response.
Statistical analysis of a batch of tested MEMS devices.

Main Results:

The proposed method accurately predicts over-etch measures using only capacitance-voltage data.
Geometric uncertainties (over-etch values) vary significantly both between and within MEMS dies.
Quantified mean over-etch values: +12.2% at comb fingers, +10.0% at supporting springs, and -4.8% at stoppers.
Demonstrated noteworthy environmental influence on MEMS variability.

Conclusions:

The developed method offers an effective alternative for estimating uncertainties in MEMS devices.
Accurate quantification of geometric uncertainties is essential for reliable MEMS performance.
Understanding and controlling over-etch variations are key to advancing MEMS technology.