TY - JOUR

T1 - Size effects in the elastic properties of polycrystalline silicon

AU - Aßmus, Marcus

AU - Zabiensky, Max von

AU - Weber, Martin

AU - Altenbach, Holm

N1 - Publisher Copyright: © 2023 The Authors. Applied Research published by Wiley-VCH GmbH.

PY - 2024/2/6

Y1 - 2024/2/6

N2 - 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.

AB - 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.

KW - cubic silicon

KW - elastic properties

KW - homogenization

KW - polycrystalline aggregate

KW - size effect

UR - http://www.scopus.com/inward/record.url?scp=85187877052&partnerID=8YFLogxK

U2 - 10.1002/appl.202300014

DO - 10.1002/appl.202300014

M3 - Article

VL - 3

JO - Applied Research

JF - Applied Research

SN - 2702-4288

IS - 1

M1 - e202300014

ER -