Search Results (8)

This work presents a multi-scale one-way-coupled thermo-mechanical method to determine the residual stress in an Atmospheric Plasma Spray (APS) process. The model uses three submodelling scale levels that range from the entire component (macroscopic) to a splat coating layer (microscopic) dimension. The three-level scale temperature and stress evolutions of an Al₂O₃ coating material on a flat aluminium substrate were analysed. The quenching stress for different substrate preheating temperatures up to 600 K at the end of the APS coating process was discussed and validated through an experimental in situ curvature method and Stoney’s quenching stress equation. Full article

The successful handling of large semiconductor wafers is crucial for scaling up their production. Early-stage warpage control allows the prevention of undesirable asymmetric warpage, known as wafer bifurcation or buckling. Indeed, even in a gravity-free environment, thinning an 8″ or 12″ semiconductor wafer can result in warpage and bifurcation. To mitigate this issue, the taiko method, which involves creating a thicker ring region around the rim of the wafer, has been widely used. Previous research has focused on the theoretical factors affecting the warpage of a backside metalized taiko wafer. This work extends the case to a front-side metalized taiko wafer and introduces the concept of the equivalent thickness of a taiko wafer. The equivalent thickness of a taiko wafer, influenced by the ring region, lies in between the thickness of the central region and that of the annular region. Because of the limited number of taiko wafers that can be produced on a production line, modelling can be beneficial. In this work we compared the results of a developed analytical model with those obtained from a finite element analysis (FEA) approach with ANSYSY^® Mechanical Enterprise 2022/R2 software to model the equivalent thickness of a taiko wafer. We investigated the curvature as a function of the stress of the metal layer, considering key design factors such as the substrate region thickness, the thickness of the thin metal film, the step height, and the width of the ring region. By systematically varying the thickness of the central region of the taiko wafer, we explored the curvature as a function of stress induced by thermal load in the linear regime and determined the slopes in the linear region of the curvature vs. stress curves. The aim of this study is to identify regularities and similarities with the Stoney equation and investigate the validity of the analytical approach for the case of a taiko substrate. The results show that there is a good agreement between the analytical model of a taiko wafer and the numerical analysis gained by the FEA methods. Full article

Precision machining (e.g., fine grinding, polishing) induced residual stress is very small and often not constant across the wafer and it is difficult to be directly obtained by stress testing equipment or Stoney equation. The residual stress could be obtained theoretically based on the principle of superposition in which the entire wafer deformation is taken as the sum of all deformations induced by the residual stresses of different positions on the wafer surface. However, the solved residual stress is affected greatly by deformation measurement errors and fluctuates greatly across the wafer surface. To solve the problem, a regularization method with continuity constraints was proposed in this study. The mechanisms for the discontinuity of the residual stress distribution and the sensitivity of calculation results to the measurement errors were studied. The influences of the number of subareas of the silicon wafer were investigated and the continuity constraint term was constructed based on the positional relationship of different subareas. Stable and continuous residual stress distribution was successfully obtained after using the proposed regularization method. The method may also be applied to estimate the residual stress from surface deformation for thin substrate plates of other materials. Full article

Polyhydroxybutyrate (PHB) is a bio-based, biodegradable and commercially used polymer, which in its native form is unfortunately not generally applicable. A widely used technique to adapt polymers to a wider range of applications is the surface modification with amorphous hydrogenated carbon (a-C:H) layers, realized by plasma-enhanced chemical vapor deposition (PE-CVD). However, this process creates intrinsic stress in the layer–polymer system which can even lead to full layer failure. The aim of this study was to investigate how the carbon layer is affected when the basic polymer film to be coated can follow the stress and bend (single side attachment) and when it cannot do so because it is firmly clamped (full attachment). For both attachment methods, the a-C:H layers were simultaneously deposited on PHB samples. Ex-situ characterization was performed using a scanning electron microscope (SEM) for surface morphology and contact angle (CA) measurements for wettability. In addition, the stress prevailing in the layer was calculated using the Stoney equation. Diffuse reflectance infrared Fourier transform spectroscopy (DRIFT) measurements were used to investigate the chemical composition of the coating surface. Full article

The silicon wafers for solar cells on which the paste is deposited experience a bowing phenomenon. The thickness of commonly used c-Si wafers is 180 μm or more. When fabricating c-Si solar cells with this wafer thickness, the bowing value is 3 mm or less and the problem does not occur. However, for the thin c-Si solar cells which are being studied recently, the output reduction due to failure during manufacture and cracking are attributed to bowing. In generally, it is known that the bowing phenomenon arises mainly from the paste applied to the back side electrode of c-Si solar cells and the effects of SiNx (silicon nitride) and the paste on the front side are not considered significant. The bowing phenomenon is caused by a difference in the coefficient of expansion between heterogeneous materials, there is the effect of bowing on the front electrode and ARC. In this paper, a partially processed c-Si solar cell was fabricated and a bowing phenomenon variation according to the wafer thicknesses was confirmed. As a result of the experiment, the measured bow value after the firing process suggests that the paste on the front-side indicates a direction different from that of the back-side paste. The bow value increases when Al paste is deposited on SiNx. The fabricated c-Si solar cell was analyzed on basis of the correlation between the bowing phenomenon of the materials and the c-Si wafer using Stoney’s equation, which is capable of analyzing the relationship between bowing and stress. As a result, the bowing phenomenon of the c-Si solar cell estimated through the experiment that the back side electrode is the important element, but also the front electrode and ARC influence the bowing phenomenon when fabricating c-Si solar cells using thin c-Si wafers. Full article

Rapid progress in the reduction of substrate thickness for silicon-based microelectronics leads to a significant reduction of the device bending stiffness and the need to address its implication for the thermo-mechanical fatigue behavior of metallization layers. Results on 5 µm thick Cu films reveal a strong substrate thickness-dependent microstructural evolution. Substrates with h_s = 323 and 220 µm showed that the Cu microstructure exhibits accelerated grain growth and surface roughening. Moreover, curvature-strain data indicates that Stoney’s simplified curvature-stress relation is not valid for thin substrates with regard to the expected strains, but can be addressed using more sophisticated plate bending theories. Full article

This study proposes a new microcantilever design with a rectangular hole at the fixed end of the cantilever that is more sensitive than conventional ones. A commercial finite element analysis software ANSYS is used to analyze it. The Stoney equation is first used to calculate the surface stress induced moment, and then applied to the microcantilever free end to produce deflection. The stress analysis of the proposed and conventional designs is performed, followed by dynamic analysis of the proposed design. We found that the Sader equation is more accurate than Stoney in predicting cantilever deflections, and that for increasing the sensitivity of a microcantilever biosensor increasing the cantilever thickness is more practical. Full article

An analytical model for predicting the deflection and force of a bimaterialcantilever is presented. We introduce the clamping effect characterised by an axial loadupon temperature changes. This new approach predicts a non linear thermal dependence ofcantilever strain. A profilometry technique was used to measure the thermal strain.Comparison with experimental results is used to verify the model. The concordance of theanalytical model presented with experimental measurements is better than 10% Full article