Size effects in the elastic properties of polycrystalline silicon

verfasst von: 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.
Externe Organisation(en): Otto-von-Guericke-Universität Magdeburg
Typ: Artikel
Journal: Applied Research
Band: 3
ISSN: 2702-4288
Publikationsdatum: 06.02.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Allgemein
Elektronische Version(en): https://doi.org/10.1002/appl.202300014 (Zugang: Offen)

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 {von Zabiensky}, Max 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",
}