#
Stochastic Mechanical Characterization of Polysilicon MEMS: A Deep Learning Approach^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Effective Properties of Polysilicon Films: Homogenization Approach

## 3. Effective Properties of Polysilicon Films: Neural Network Approach

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Gad-el-Hak, M. (Ed.) The Mems Handbook; CRC Press: Boca Raton, FL, USA, 2002. [Google Scholar]
- KO, W. Trends and frontiers of MEMS. Sens. Actuators A Phys.
**2007**, 136, 62–67. [Google Scholar] [CrossRef] - Corigliano, A.; Ardito, R.; Comi, C.; Frangi, A.; Ghisi, A.; Mariani, S. Mechanics of Microsystems; John Wiley and Sons: Hoboken, NJ, USA, 2018. [Google Scholar]
- Corigliano, A.; De Masi, B.; Frangi, A.; Comi, C.; Villa, A.; Marchi, M. Mechanical characterization of polysilicon through on-chip tensile tests. J. Microelectromech. Syst.
**2004**, 13, 200–219. [Google Scholar] [CrossRef] - Bagherinia, M.; Mariani, S.; Corigliano, A.; Lasalandra, E. Stochastic effects on the dynamics of a resonant MEMS magnetometer: A Monte Carlo investigation. In Proceedings of the 1st International Electronic Conference on Sensors and Applications (ECSA-1), Basel, Switzerland, 1–16 June 2014. [Google Scholar]
- Weinberg, M.S.; Kourepenis, A. Error sources in in-plane silicon tuning-fork MEMS gyroscopes. J. Microelectromech. Syst.
**2006**, 15, 479–491. [Google Scholar] [CrossRef] - Bagherinia, M.; Mariani, S. Stochastic Effects on the Dynamics of the Resonant Structure of a Lorentz Force MEMS Magnetometer. Actuators
**2019**, 8, 36. [Google Scholar] [CrossRef] - Mariani, S.; Ghisi, A.; Corigliano, A.; Zerbini, S. Multi-scale analysis of MEMS sensors subject to drop impacts. Sensors
**2007**, 7, 1817–1833. [Google Scholar] [CrossRef] - Ghisi, A.; Fachin, F.; Mariani, S.; Zerbini, S. Multi-scale analysis of polysilicon MEMS sensors subject to accidental drops: Effect of packaging. Microelectron. Reliab.
**2009**, 49, 340–349. [Google Scholar] [CrossRef] - Ghisi, A.; Kalicinski, S.; Mariani, S.; De Wolf, I.; Corigliano, A. Polysilicon MEMS accelerometers exposed to shocks: Numerical-experimental investigation. J. Micromech. Microeng.
**2009**, 19, 035023. [Google Scholar] [CrossRef] - Mariani, S.; Ghisi, A.; Corigliano, A.; Zerbini, S. Modeling impact-induced failure of polysilicon MEMS: A multi-scale approach. Sensors
**2009**, 9, 556–567. [Google Scholar] [CrossRef] - Mariani, S.; Martini, R.; Ghisi, A.; Corigliano, A.; Simoni, B. Monte Carlo simulation of micro-cracking in polysilicon MEMS exposed to shocks. Int. J. Fract.
**2011**, 167, 83–101. [Google Scholar] [CrossRef] - Mariani, S.; Martini, R.; Corigliano, A.; Beghi, M. Overall elastic domain of thin polysilicon films. Comput. Mater. Sci.
**2011**, 50, 2993–3004. [Google Scholar] [CrossRef] - Mariani, S.; Martini, R.; Ghisi, A.; Corigliano, A.; Beghi, M. Overall elastic properties of polysilicon films: A statistical investigation of the effects of polycrystal morphology. Int. J. Multiscale Comput. Eng.
**2011**, 9, 327–346. [Google Scholar] [CrossRef] - Bagherinia, M.; Bruggi, M.; Corigliano, A.; Mariani, S.; Lasalandra, E. Geometry optimization of a Lorentz force, resonating MEMS magnetometer. Microelectron. Reliab.
**2014**, 54, 1192–1199. [Google Scholar] [CrossRef] - Bagherinia, M.; Bruggi, M.; Corigliano, A.; Mariani, S.; Horsley, D.A.; Li, M.; Lasalandra, E. An efficient earth magnetic field MEMS sensor: Modeling, experimental results and optimization. J. Microelectromech. Syst.
**2015**, 24, 887–895. [Google Scholar] [CrossRef] - Mirzazadeh, R.; Eftekhar Azam, S.; Mariani, S. Micromechanical characterization of polysilicon films through on-chip tests. Sensors
**2016**, 16, 1191. [Google Scholar] [CrossRef] [PubMed] - Mirzazadeh, R.; Mariani, S. Uncertainty quantification of microstructure-governed properties of polysilicon MEMS. Micromachines
**2017**, 8, 248. [Google Scholar] [CrossRef] - Mirzazadeh, R.; Eftekhar Azam, S.; Mariani, S. Mechanical characterization of polysilicon MEMS: A hybrid TMCMC/POD-kriging approach. Sensors
**2018**, 18, 1243. [Google Scholar] [CrossRef] - Mariani, S.; Ghisi, A.; Mirzazadeh, R.; Eftekhar Azam, S. On-Chip testing: A miniaturized lab to assess sub-micron uncertainties in polysilicon MEMS. Micro Nanosyst.
**2018**, 10, 84–93. [Google Scholar] [CrossRef] - Capellari, G.; Chatzi, E.; Mariani, S. Structural Health Monitoring Sensor Network Optimization through Bayesian Experimental Design. ASCE ASME J. Risk Uncertain. Eng. Syst. Part A Civ. Eng.
**2018**, 4, 04018016. [Google Scholar] [CrossRef] - Bishop, C.M. Pattern Recognition and Machine Learning; Springer: New York, NY, USA, 2006. [Google Scholar]
- LeCun, Y.; Bottou, L.; Bengio, Y.; Haffner, P. Gradient-based learning applied to document recognition. Proc. IEEE
**1998**, 86, 11, 2278–2324. [Google Scholar] - He, K.; Zhang, X.; Ren, S.; Sun, J. Deep residual learning for image recognition. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA, 27–30 June 2016; pp. 770–778. [Google Scholar]
- Homer, E.R.; Hensley, D.M.; Rosenbrock, C.W.; Nguyen, A.H.; Hart, G.L.W. Machine-Learning informed representations for grain boundary structures. Front. Mater.
**2019**, 6, 168. [Google Scholar] [CrossRef] - Liu, Z.; Wu, C.T.; Koishi, M. A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials. Comput. Methods Appl. Mech. Eng.
**2019**, 345, 1138–1168. [Google Scholar] [CrossRef] - Ghisi, A.; Mariani, S. Effect of imperfections due to material heterogeneity on the offset of polysilicon MEMS structures. Sensors
**2019**, 19, 3256. [Google Scholar] [CrossRef] [PubMed] - Keskar, N.S.; Mudigere, D.; Nocedal, J.; Smelyanskiy, M.; Tang, P.T.P. On large-batch training for deep learning: Generalization gap and sharp minima. arXiv
**2016**, arXiv:1609.04836. [Google Scholar]

**Figure 1.**Exemplary morphologies of 2 × 2 μm

^{2}statistical volume elements (SVEs), where each color represents a different grain.

**Figure 3.**Stochastic homogenization, 2 × 2 μm

^{2}SVE: Cumulative distribution functions of the bounds on the homogenized in-plane Young’s modulus $E$ of a polysilicon film featuring ${s}_{g}=0.5$ μm.

**Figure 5.**Effective Young’s modulus predicted by the neural network (NN) against the ground-truth data: (

**left**) Training set; (

**right**) validation set.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Molina, J.P.Q.; Rosafalco, L.; Mariani, S.
Stochastic Mechanical Characterization of Polysilicon MEMS: A Deep Learning Approach. *Proceedings* **2020**, *42*, 8.
https://doi.org/10.3390/ecsa-6-06574

**AMA Style**

Molina JPQ, Rosafalco L, Mariani S.
Stochastic Mechanical Characterization of Polysilicon MEMS: A Deep Learning Approach. *Proceedings*. 2020; 42(1):8.
https://doi.org/10.3390/ecsa-6-06574

**Chicago/Turabian Style**

Molina, José Pablo Quesada, Luca Rosafalco, and Stefano Mariani.
2020. "Stochastic Mechanical Characterization of Polysilicon MEMS: A Deep Learning Approach" *Proceedings* 42, no. 1: 8.
https://doi.org/10.3390/ecsa-6-06574