Publication Date

2-13-2014

Abstract

Microelectromechanical systems (MEMS) are part of every modern technological advance. Electrodeposited thin nickel (Ni) polycrystalline films in MEMS often show fiber texture resulting in transverse isotropic elastic properties. It is of interest to determine these elastic properties, in particular the in-plane Young's modulus, since it plays a fundamental role in device performance. The fabrication process of MEMS films introduces uncertainties in the microstructure geometry, crystallographic texture, the crystal elastic constants, the physical film dimensions and other parameters. In this thesis the numerical value of the in-plane Young's modulus of thin Ni polycrystalline films is predicted. The predicted values lie between the Reuss-Voigt averages, a result that is consistent with theory. Additionally the uncertainties of the predictions of the in-plane Young's moduli are quantified by taking into account the uncertainties in microstructure geometry, crystallographic texture, and the numerical values of the Ni single-crystal constants. Representative volumes of the microstructure geometry are modeled with Voronoi diagrams. The crystallographic texture is numerically generated from real X-ray diffraction experimental data by using a texture discretization algorithm. The Young's modulus is estimated by simulating uniaxial stress tests on the numerically generated microstructures with a self-consistent fast Fourier transform (FFT) method. The uncertainties in microstructure geometry, crystallographic texture, and single-crystal elastic constant values are treated as epistemic due to the lack of available experimental data. The sensitivity of the in-plane Young's modulus is examined with respect to the three uncertainties addressed above. The study of the propagation of uncertainties throughout the model lead us to the conclusion that the in-plane Young's modulus of the electrodeposited thin Ni films is extremely sensitive only with respect to the uncertainties in the Ni crystal constants. A Voronoi based algorithm that attempts to simulate the complete polycrystalline film microstructure geometry is also developed for future large-scale simulations. Finally a J2 plasticity model that attempts to decribe the overall mechanical response of the Ni film is developed. The J2 model is based on a phase-field dislocation model developed by Koslowski and it includes the Hall-Petch size effect. The numerical predictions of the J2 model are compared with real tensile stress experiments performed on as-deposited and annealed Ni samples. The J2 model predictions show good agreement with phase-field simulations, and capture aspects of size effects.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Deborah Sulsky

Second Committee Member

Evangelos A. Coutsias

Third Committee Member

Jens Lorenz

Fourth Committee Member

Yu-Lin Shen

Project Sponsors

This work was supported in part by the NNSA Center for the Prediction of Reliability, Integrity, and Survivability of Microsystems and in part by the U.S. Department of Energy under Award DE-FC52-08NA28617

Language

English

Keywords

Texture Analysis, In-plane Young's Modulus, MEMS, Crystal Plasticity, ODF

Document Type

Dissertation

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