Fatigue of polycrystalline silicon for microelectromechanical system applications: crack growth and stability under resonant loading conditions

Although bulk silicon is not known to exhibit susceptibility to cyclic fatigue, micron-scale structures made from silicon films are known to be vulnerable to degradation by fatigue in ambient air environments, a phenomenon that has been recently modeled in terms of a mechanism of sequential oxidation and stress-corrosion cracking of the native oxide layer. To date, most stress-life (S/N) fatigue tests on such silicon films have been conducted using resonant-loaded specimens. Consequently, there is a need to establish the interaction between the dynamic loading and the driving force for fatigue-crack growth. In this paper, finite element models are used to establish the relationship between natural frequency, specimen compliance, and linear-elastic stress–intensity factor for a commonly used micron-scale, micromechanical fatigue characterization structure. These results are then incorporated into a general, lumped parameter model to evaluate the stability of fatigue cracks in resonant-loaded structures. It is well known that the applied stress amplitude and corresponding driving force for crack advance depend on the system damping, as well as sample geometry. Consequently, changes in damping caused by cycling in different environments can have a significant mechanical effect on the stability of fatigue cracks. In the case of the fatigue characterization structure used by the authors, the models show that tests conducted at atmospheric pressure subject cracks to a monotonically increasing driving force for crack advance. However, when the damping in the system is reduced (e.g., by testing in vacuo) fatigue cracks may arrest, independent of environmental effects on crack growth. Therefore, testing of structures loaded in resonance at a fixed natural frequency in vacuum should not be considered equivalent to an “inert” atmosphere. Finally, the finite element models are applied to polycrystalline silicon structural films to determine the critical crack lengths (∼5.5–66 nm) and an average fracture toughness (∼0.85 MPa√m) from specimens subjected to fatigue cycling at stress amplitudes ranging from ∼2.2 to 3.5 GPa.