Size effects in the elastic properties of polycrystalline silicon

authored by: Marcus Aßmus, Max von Zabiensky, Martin Weber, Holm Altenbach
Abstract: Polycrystalline silicon has a wide range of applications in the semiconductor industry. Instead of components whose dimensions are of the same order of magnitude in all three spatial directions, thin slices are primarily used there. Deviating mechanical properties have been noticed among such thin configurations. In this work, we systematically investigate the size‐dependent effective elastic properties of polycrystalline silicon. This is realized by gradually reducing the thickness of such components, starting from a structure usually referred to as representative volume element. Based on the framework of continuum mechanics, we specify unit cell problems for aggregates whose microstructures are build artificially based on first‐order properties through tessellations. The effective responses of virtual material tests are determined by the aid of the finite element method. Based on a larger number of computational simulations with different but equivalent microstructures, the effective elastic properties of silicon polycrystals are evaluated statistically. The findings are examined with regard to geometrically‐induced symmetries by several methods. For the unconstrained configurations examined here, results show an increase in the scattering of the results where the average stiffness decreases with decreasing structural thickness. These outcomes are also compared to analytical estimates for silicon bulk configurations. This comparison indicates that the average stiffness varies in between a reasonable mean and the isotropic first‐order lower bound of the silicon bulk. Compared to experimental findings, admissible bounds of the stiffnesses are clearly outlined.
External Organisation(s): Otto-von-Guericke University Magdeburg
Type: Article
Journal: Applied Research
Volume: 3
ISSN: 2702-4288
Publication date: 06.02.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: General
Electronic version(s): https://doi.org/10.1002/appl.202300014 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{12e30877b9884d299c6d5626913b94dd,
title = "Size effects in the elastic properties of polycrystalline silicon",
abstract = "Polycrystalline silicon has a wide range of applications in the semiconductor industry. Instead of components whose dimensions are of the same order of magnitude in all three spatial directions, thin slices are primarily used there. Deviating mechanical properties have been noticed among such thin configurations. In this work, we systematically investigate the size‐dependent effective elastic properties of polycrystalline silicon. This is realized by gradually reducing the thickness of such components, starting from a structure usually referred to as representative volume element. Based on the framework of continuum mechanics, we specify unit cell problems for aggregates whose microstructures are build artificially based on first‐order properties through tessellations. The effective responses of virtual material tests are determined by the aid of the finite element method. Based on a larger number of computational simulations with different but equivalent microstructures, the effective elastic properties of silicon polycrystals are evaluated statistically. The findings are examined with regard to geometrically‐induced symmetries by several methods. For the unconstrained configurations examined here, results show an increase in the scattering of the results where the average stiffness decreases with decreasing structural thickness. These outcomes are also compared to analytical estimates for silicon bulk configurations. This comparison indicates that the average stiffness varies in between a reasonable mean and the isotropic first‐order lower bound of the silicon bulk. Compared to experimental findings, admissible bounds of the stiffnesses are clearly outlined.",
keywords = "cubic silicon, elastic properties, homogenization, polycrystalline aggregate, size effect",
author = "Marcus A{\ss}mus and Zabiensky, {Max von} and Martin Weber and Holm Altenbach",
note = "Publisher Copyright: {\textcopyright} 2023 The Authors. Applied Research published by Wiley-VCH GmbH.",
year = "2024",
month = feb,
day = "6",
doi = "10.1002/appl.202300014",
language = "English",
volume = "3",
journal = "Applied Research",
issn = "2702-4288",
number = "1",
}