Celler, G. K., and Sorin Cristoloveanu. "Frontiers of Silicon-on-Insulator." Journal of Applied Physics 93 (May 1, 2003): 4955-4978.
Miller, David C., Brad L. Boyce, Michael T. Dugger, Thomas E. Buchheit, and Ken Gall. "Characteristics of a Commercially Available Silicon-on-Insulator MEMS Materials." Sensors and Actuators A 138 (2007): 130-144.
Ghasemi-Nejhad, Mehrdad N., Chiling Pan, and Hongwei Feng. "Intrinsic Strain Modeling and Residual Stress Analysis for Thin-Film Processing of Layered Structures." Journal of Electronic Packaging 125 (March 2003): 4-17.
(a) Miller, et al. noted the use of wafer curvature to infer stresses within thin films such as SOI. Derive the stress-curvature relationship given in Eq. 1, also known as the Stoney formula in the thin-film limit.
(b) Graphically represent the structure of Si in SOI, at the unit cell and micrometer-scale level, and separately indicate the closest packed plane and direction in that plane for this structure.
(c) During wafer bonding, blisters can occur at the wafer interfaces (Celler, Fig. 9). State the full tensorial stress state at the location of such a blister, and quantify the strains you would expect to correspond to this state in the adjacent Si.
(b) Nejhad, et al. present an analysis of retained internal stresses, and an associated elastic analysis in Eq. (8). Justify the form of Eq. (8) in terms of crystal structure of the two film materials of interest, and the origin of the strain terms.
(c) After Eq. (10), the authors state that there are so many contributors of intrinsic strain that it is difficult to consider them quantitatively. Rank-order the sources they list in terms of relative amount of stress contribution for this system, and justify your answer.
(d) Determine the % of residual stress in terms of the tensile and compressive failure strength of these two film materials. In other words, how closely does the residual stress in films or lines approach the failure stress of the bulk forms of these same materials?
(b) Silicon on insulator delamination can be modeled by fracture between two dissimilar interfaces: Si and SiO2, for example. Assume that the interface blister you considered earlier is now an initial crack at the interface, and compute the fracture stress required to delaminate the film under Mode I loading. You can cite any required properties to implement a simple fracture theory such as Griffith's.
(c) In section 4 of the Frontiers paper, the authors discuss Bruel's innovation as leading to the realization that fracture could be induced by shearing. What kind of mode of loading is this, and will the stress required to initiate fracture for a given material be lower in this mode than in Mode I?
"Plasticity and fracture of microelectronic thin films [SOI - Silicon on Insulator.]" (PDF)
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