The Extended Range of Reaction-layer Fatigue Susceptibility of Polycrystalline Silicon Thin Films

Abstract

A linear elastic fracture mechanics analysis of a silicon dioxide-polycrystalline silicon (SiO 2 -Si) bimaterial system was performed to assess the vulnerability of micron-scale silicon structures, such as microelectromechanical systems, to fatigue in ambient air. Previous research has shown that fatigue of silicon films is due to a "reaction-layer fatigue" process where silicon structural films fail due to the sequential, mechanically induced thickening and environmentally assisted cracking of the silicon dioxide reaction layer which forms on the surface upon exposure to air. This work specifically considered the stability of a crack reaching the SiO 2 -Si interface. This analysis revealed a significant overestimate in the oxide thicknesses susceptible to reaction-layer fatigue reported in our previous studies. Instead, a surface oxide layer as thin as 15 nm may activate this fatigue mechanism for a polycrystalline silicon thin film whose fracture strength exceeds 5 GPa.

Very high-cycle fatigue failure in micron-scale polycrystalline silicon films: Effects of environment and surface oxide thickness

“…Here unstable cracking can only commence when the crack reaches the silicon/oxide interface, which allows for reaction-layer mechanism to occur in oxide layers down to ϳ15 nm. 49 Note that in both of these fatigue scenarios the only crack growth occurring in the silicon is of an unstable nature, which is consistent with the notion that bulk silicon does not fatigue, but micron-scale silicon does.…”

“…Whereas notch-root oxides up to 100 nm thick were found in failed MUMPs devices, they were typically on the order of 20 nm thick in the SUMMiT V™ devices. Recently, Pierron and Muhlstein 49 have proposed that reaction-layer fatigue can occur in two different scenarios: ͑i͒ the crack can stably grow inside the oxide until it reaches the critical crack size a c , i.e., the stress intensity for unstable crack propagation into the entire device is exceeded ͑a c ഛ h͒, or ͑ii͒ the crack can grow stably toward the silicon/oxide interface and change to unstable growth as it reaches this interface ͑h = a c ͒. In this second scenario the critical crack size is shorter than in the first scenario because of an additional driving force for unstable crack advancement as it reaches the silicon/oxide interface.…”

“…In this second scenario the critical crack size is shorter than in the first scenario because of an additional driving force for unstable crack advancement as it reaches the silicon/oxide interface. 49 For the MUMPs devices that have relatively thick initial ͑post-release͒ oxides ͑ϳ15-30 nm͒ which grow with cycling up to 100 nm, the first scenario applies because critical crack lengths of ϳ50 nm will be reached within the oxide before the crack reaches the interface. 46,49 The SUMMiT V™ devices, conversely, have thinner initial oxides ͑3-6 nm͒ which grow to a maximum of ϳ20 nm thick.…”

“…49 For the MUMPs devices that have relatively thick initial ͑post-release͒ oxides ͑ϳ15-30 nm͒ which grow with cycling up to 100 nm, the first scenario applies because critical crack lengths of ϳ50 nm will be reached within the oxide before the crack reaches the interface. 46,49 The SUMMiT V™ devices, conversely, have thinner initial oxides ͑3-6 nm͒ which grow to a maximum of ϳ20 nm thick. Here unstable cracking can only commence when the crack reaches the silicon/oxide interface, which allows for reaction-layer mechanism to occur in oxide layers down to ϳ15 nm.…”

Mechanisms for Fatigue of Micron‐Scale Silicon Structural Films

“…Since the crack in the oxide layer must cause failure of the entire structure, the criterion for this mechanism is that the thickness of the oxide layer, h, must be greater than or equal to the critical crack size, a c , to fail the entire structure, i.e., when a c < h. Because the oxide layer thickness in bulk silicon will only be a tiny fraction of the material, the beauty of this mechanism is that it provides an explanation as to why no delayed failure would occur by fatigue in bulk silicon as a growing crack in the oxide layer could never get large enough to break the entire structure i.e., as a c > h. Using a fracture-mechanics analysis, Mulhstein and Ritchie [43] defined the range of oxide thicknesses where reaction-layer fatigue would be viable; their calculations suggested that a oxide thickness of ~50 nm was required. Subsequent work by Pierron and Muhlstein [47] expanded this numerical model to account for an alternative failure scenario where stable crack growth in the oxide changes to unstable crack growth when the crack hits the silicon/oxide interface, i.e., when a c = h; this lowered the oxide thickness that is potentially susceptible to reaction-layer fatigue to ~15 nm. The mechanism also explained the decreasing growth rates observed for cracks propagating within the oxide layer; as these cracks approach the SiO 2 /Si interface (with its three-fold modulus mismatch), fracturemechanics calculations of the crack-driving force showed that it decreased as cracks got closer to the interface [43] .…”