1. Determination of elastic parameters of Si3N4 thin films by means of a numerical approach and bulge tests
- Author
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Zdeněk Buchta, Alice Chlupová, J. Holzer, Tomáš Kruml, Pavel Hutař, Hector A. Tinoco, Tomáš Pikálek, and Josef Lazar
- Subjects
010302 applied physics ,Materials science ,Mathematical analysis ,Metals and Alloys ,Modulus ,02 engineering and technology ,Surfaces and Interfaces ,021001 nanoscience & nanotechnology ,01 natural sciences ,Finite element method ,Intersection (Euclidean geometry) ,Square (algebra) ,Surfaces, Coatings and Films ,Electronic, Optical and Magnetic Materials ,chemistry.chemical_compound ,Error function ,Membrane ,Silicon nitride ,chemistry ,0103 physical sciences ,Materials Chemistry ,Thin film ,0210 nano-technology - Abstract
This paper describes and applies a methodology to determine the elastic properties of freestanding thin membranes by means of a bulge test and a numerical approach. The numerical procedure is based on the combination of two standard methods i.e. finite element analysis and classical analytical solutions to calculate elastic properties of thin films. Bulge tests were conducted on silicon nitride (Si3N4) monolayer of 2 × 2 mm (square) and 3.5 × 1.5mm (rectangular) membranes with the aim to determine elastics properties (Young's modulus (E) and Poison's ratio (v)) that define the load-deflection curves of both membranes. With this purpose, an error function was constructed for each membrane which involved finite element solutions, analytical solutions and experimental measurements. Error functions were found and minimized by mapping a set of elastic parameters for the two membranes (square and rectangular). A unique solution was determined in the intersection of both linear approximations, obtaining 236 GPa for E and 0.264 for v. It is well known that in a traditional bulge test analysis only one of both biaxial modulus can be determined and not a combination of E and v. Numerical results show that calculated load-deflection curves agree well with the measurements obtained for both square and rectangular membranes experimentally. The proposed methodology is only applicable in thin films with elastic behavior, however generalization for more complicated geometries is possible.
- Published
- 2019
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