A resonant method for determining the residual stress and elastic modulus of a thin film

Abstract

By measuring the resonant frequencies of the first two symmetric vibration modes of a circular thin-film diaphragm and solving the Rayleigh-Ritz equation analytically, the residual stress and elastic modulus of the film were determined simultaneously. The results obtained employing this method are in excellent agreement with those obtained numerically in finite element modelling when tested using freestanding circular SiC diaphragms with residual tensile stress. The stress and modulus values are also in reasonably good agreement with those obtained from nanoindentation and wafer curvature measurements, respectively.

Fracture Strain of SiC Nanowires and Direct Evidence of Electron‐Beam Induced Amorphisation in the Strained Nanowires

“…The drawback of this material in bulk form is its high brittleness or low ductility, which has somehow hindered its widespread applications. In the past two or three decades, researchers have shown that some materials in the form of nanostructures exhibited novel properties in comparison to their bulk counterparts . SiC nanorods was found being fractured at an extremely high strain of approximately 10%, which is close to the theoretical prediction, in a bending test performed on an atomic force microscope and SiC nanowires could experience a strain up to 4.5% prior to brittle fracture during the tensile test performed in an scanning electron microscope (SEM).…”

Investigation of the Young’s Modulus and the Residual Stress of 4H-SiC Circular Membranes on 4H-SiC Substrates

“…The resonance peaks for asymmetric modes (1, 1), (2, 1), (3, 1), and (1, 2) seem to be splitted with lower magnitude peaks. The fabrication process led to a geometric asymmetry of the diaphragm, as previously shown in Figure 1, resulting in the creation of nondegenerated modes in asymmetric vibration modes [39,40]. Moreover, Fartash et al reported that the presence of an anisotropic tension, due to internal stress or tension after mounting the sample, could also cause the splitting of degenerated modes.…”

“…This technique is very suitable to create thin suspended square and rectangular membranes but does not allow the achievement of vertical sidewalls. In addition, the realization of circular membrane geometry is more complex, that's why, dry etching using plasma is recommended [39]. With this method, the Si wafer/3C-SiC epilayer interface can act as an etch-stop to define a 3C-SiC membrane.…”

A two-step load-deflection procedure applicable to extract the Young's modulus and the residual tensile stress of circularly shaped thin-film diaphragms

“…30,35 In terms of dynamic measurement principles, a paper has been recently published where the resonance frequencies of the first two symmetric vibration modes of a circular thinfilm diaphragm were measured and compared to an analytically derived equation in order to determine E and r 0 . 36 This method is simple and has versatile potential when applied to structures with a well-known mass density like the investigated epitaxial 3C-SiC diaphragms. 36 However, it suffers from the same drawback as other resonant techniques because it requires knowledge of the mass density of the thin a) film which can differ considerably from bulk properties and is thus often also unknown.…”

“…36 This method is simple and has versatile potential when applied to structures with a well-known mass density like the investigated epitaxial 3C-SiC diaphragms. 36 However, it suffers from the same drawback as other resonant techniques because it requires knowledge of the mass density of the thin a) film which can differ considerably from bulk properties and is thus often also unknown. [25][26][27] This paper focuses solely on bulge testing because it is the most versatile method.…”