Weibull Fracture Probability for Silicon Wafer Bond Evaluation

Abstract

The phenomenon and the mechanisms of silicon to silicon direct bonding have been thoroughly studied. 1-4 Nevertheless, there is still a need for reliable evaluation methods to determine the quality of a bond due to different treatments. The widely used crack opening method, introduced by Maszara, is a fast and convenient method to determine the surface energy of a bond. 1 This technique is well suited to study bond mechanisms and surface chemistry, as the surface energy is the most relevant quantity characterizing these phenomena. However, there are severe problems connected to the crack opening technique, i.e., inaccuracy, insecure operator dependence, and the impossibility for its use on too strong bonds.The fracture strength of bonds needs to be evaluated in order to obtain mechanically reliable silicon microstructures. In this work, a new strategy toward a robust evaluation method is presented. It is based on fracture probability measurements on directly bonded structures. The strength of components, manufactured from brittle materials, depends on the combination of defect and stress distribution. When the stress around a defect reaches a critical level, fracture is initiated. If the stress is well defined and known, the fracture strength can be determined by the distribution of defects. This paper suggests a method to indirectly estimate the defect distribution at the interface of bonded silicon wafers. Thus, when the strength of a component is limited by the bond, the problem of finding the strength will be the problem of finding the stress distribution at the bonded interface. By the Weibull fracture probability analysis, it is hereafter possible to derive geometry-independent parameters, which makes comparisons and predictions of the fracture behavior for differently shaped and sized structures possible. The advantage of this method is that it applies to whole bonded wafers as well as to bonded micromachined components. Experimental All bonded structures were made from single-side polished 100 mm diam silicon wafers, 525 m thick. Bonded pairs with a cavity in one wafer and a gas inlet in the other were made. Series of these modules were burst, by applying a gas pressure between the bonded wafers. The resulting bond fracture probability was determined and correlated to different treatments and characteristics such as annealing temperature, cavity size, thermal cycling, and vibration tests. According to the theory below, the cavity depth is negligible to the bond fracture probability when it is kept sufficiently small, and it was arbitrarily chosen to 30 m. All structures were made by anisotropic wet etching in KOH. The wafers were bonded using hydrophilic fusion bonding 3 and hot nitric acid surface treatment prior to contacting. They were annealed until saturated bond strength values were reached: 90 h at 120 and 300ЊC, 5 and 3 h at 700, 800, and 1050ЊC.Two test series were subjected to one of the fatiguing procedures of vibration or thermal cycling, respectively. The fatiguing test parameters are given i...

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“…The mean of the distribution, F mean , which is related to F 0 through the shaping parameter and the gamma function may also be used for the comparison. This approach has been successfully used to analyze the reliability of bonded structures, joint fracture surface energy and defect distribution in ceramics and silicon wafers (Jonsson et al 2001; Köhler et al 2000). …”

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“…However, the experimental observation of the real system yields a fracture probability function, which in turn depends on the applied fracture pressure and geometric size and shape of the system. Fortunately, the Weibull fracture probability function allows for an expedient parametrization; using the known stress distribution, the parameters m (Weibull modulus) and σ fc (mean fracture uniform tensile stress of unit length) can be extracted [10]. These parameters are independent of geometry and load case.…”

“…The reliability of the bonded wafers is determined by a statistic analysis. This method has previously been used for evaluation of silicon-tosilicon fusion structures [10]. It has proven to be sensitive to small shifts in bond strength, yielding the fracture behaviour of the test sample series as an indirect measure of fracture surface energy and defect distribution.…”

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“…where the probability of fracture, p f , is expressed as a function of the stress along C with σ c (s) as the stress on C at position s [18][19]. σ 0 and m are characteristic stress and Weibull modulus, respectively.…”