Extension of the Stoney Equation for a Taiko Wafer (Si and SiC)

An extension of the Stoney formula for the case of a back side metallized 8” silicon taiko wafer has been developed, in the elastic regime, within the frame of the theory of elasticity. A good correlation between the calculated warpage, determined by the stress released by a given back side metallization (BSM), and the corresponding experimental warpages of the same thick metal layers deposited on an 8” silicon taiko wafer provides evidences of the correctness of the developed theory. This development suggests the possibility to extend this approach to the case of 8” taiko wafers based on a wide band gap semiconductor such as silicon carbide (SiC).

Study of nanostructured HfN coatings using layers arrangement

ABSTRACTIn the present investigation, nanostructured ceramic HfN coatings were deposited onto silicon (100) wafer by magnetron sputtering DC method, from a metallic Hf target. The deposition process followed by a similar pattern as the multilayer film deposition, using cycles with the nitrogen gas turned on for 90 s and turned off for 15 s; four sets of samples were obtained using 5, 10, 15 and 20 cycles. The X ray diffraction (XRD) identified the presence of two different cubic crystalline phases of HfN, corroborated by Rietveld analysis. The Vickers hardness test showed that the hardness values increases with more cycles, due to a higher compressive stress evaluated by Stoney formula. All samples were investigated with no visible fracture until 10 grf for the 5 cycles sample; however, no fractures were visible at all for the 15 and 20 cycle samples for that given load, instead fractures started to appear at 25grf for the 10 and 15 cycles coating. Eventually it is distinguished that, the thickness and morphology of the coatings were measured by field emission scanning electron microscopy FE-SEM. As well as, the thickness increased from 0.4 µm to almost 1.33 µm as the number of cycles also increased, where we can observe the formation of columnar growth, moreover it is possible to distinguish the formation of two different clusters which might be related to different phases.

Stoney Formula: Investigation of Curvature Measurements by Optical Profilometer

Thin films’ residual stress is often determined by the Stoney formula, using the measurements of the substrate curvature, even if the required hypotheses are not completely respected. In this study, a 2.2 µm titanium nitride coating was deposited by reactive sputtering on a silicon substrate. The Stoney formula was used in order to calculate the residual stress of the film. The radius of curvature was measured, before and after coating by optical profilometer, considering the whole surface of the sample. The effect of the substrate shape (square and rectangular) with various dimensions was investigated. We showed that the shape of the substrate influence strongly the deformation. Moreover, it was highlighted that the choice of the radius (maximum value, minimum value, mean value, with or without initial curvature correction) is critical to the determination of the stress.

A METHOD FOR DEFINING INITIAL STRESS IN PROGRESSIVELY DEPOSITED FILM ON A SUBSTRATE

The initial stress is induced during film formation and is partially counterbalanced through curvature changes. Therefore, it is commonly evaluated by the measured residual stress. Initial stress may directly affect the film formation rather than residual stress in progressively deposited films. In the present work, we introduced a multiple layer model for progressively deposited films to obtain a quantitative solution for estimating the initial stress. The results showed that residual stress in the last layer is equal to the initial stress when layer number approaches infinity. In particular, the initial stress, σi in deposited film could be determined using the equation, σi = σSt/β, in which σSt is the averaged residual stress in films calculated by Stoney formula and β is the correction factor. The value of β varied between 0 and 1, depending on relative modulus and relative thickness of film and substrate. Finally, using element birth and death technique, a finite element model was presented to verify the analytical multiple layer model. Good agreement was obtained between the analytical and FE results.