| Pub. Date | : May, 2023 |
|---|---|
| Product Name | : The IUP Journal of Marketing Management |
| Product Type | : Article |
| Product Code | : IJMM040523 |
| Author Name | : A Landi and M Renna |
| Availability | : YES |
| Subject/Domain | : Marketing |
| Download Format | : PDF Format |
| No. of Pages | : 17 |
Internal stress in a film deposited on a plate-like substrate causes the film and substrate pair to warp until the mechanical equilibrium is reached. This condition is reached when both the net force and the resulting bending momenta reach a null value. In this paper, the analytical Lagrange-Kirchhoff model for the deformation of a coated Taiko plate silicon is proposed. Under the conditions of validity of the linear theory of thin plates, the model is in agreement with the experimental data. These results can be extended to other substrates, such as silicon carbide (SiC).
Internal stress in a film deposited on a plate-like substrate causes the film and substrate
pair to warp until the mechanical equilibrium is reached. This condition is reached
when both the net force and the resulting bending momenta reach a null value. A
plate-like or a disc-shaped substrate implies a simplification that the substrate thickness,
ts, is constant and small in comparison to its diameter D. From the curvature of
elastically deformed coated substrate the average film stress can be calculated. When
the thickness of the film, tf, is small comparted to that of the substrate, a simple
formula holds, which was first published by Stoney (1909).
Bifurcation is a nonlinear phenomenon which determines the emergence of an
abrupt degeneration in the symmetry of large wafers undergoing the large-scale
integration process of the semiconductor industry. Because of the stress induced by
the thin films manufactured upon the wafer, the warpage can degenerate and increase
asymmetrically, resulting in two main principal and different curvatures. The purpose
of processing is to contain the warpage and avoid the phenomenon of bifurcation.
However, an understanding of the occurrence of this phenomenon can be of help in
controlling the warpage of thinned wafers having large diameters. In this paper, the
Taiko wafer plate, Wafer plate, Annular plate, Die, Warpage, Curvature, Bifurcation