Nanoscale Weibull Statistics

In this paper a modification of the classical Weibull Statistics is developed for nanoscale applications. It is called Nanoscale Weibull Statistics. A comparison between Nanoscale and classical Weibull Statistics applied to experimental results on fracture strength of carbon nanotubes clearly shows the effectiveness of the proposed modification. A Weibull's modulus around 3 is, for the first time, deduced for nanotubes. The approach can treat (also) a small number of structural defects, as required for nearly defect free structures (e.g., nanotubes) as well as a quantized crack propagation (e.g., as a consequence of the discrete nature of matter), allowing to remove the paradoxes caused by the presence of stress-intensifications

Determination of residual stress in glass frit bonded MEMS by finite element analysis

Glass frit bonding is an universal technique with intermediate glass layer for the packaging of Micro-Electro-Mechanical Systems (MEMS). The joining of two wafers is required to protect surfaced micro-machined structures during fabrication and use. The object of this paper is to investigate numerically the influence of the bonding process on the generated residual stress in the glass frit layer of a typical chip. The residual stresses are caused by different coefficients of thermal expansion of the frit glass and the silicon wafer. A determination of the stress level is required, since the residual stress can influence the properties of the capped micro-machined structures and also the long-term reliability of the bond frame. A parameterized Finite Element (FE) model of a typical chip structure was developed which consists of a silicon device wafer, the glass frit layer and a silicon cap wafer with a cavity. Frame width and thickness of the glass, also called seal glass were varied. It was shown, that significant stresses (a bout 100MPa) occur in the plane of seal glass in cause of cooling after bonding. The influence of bond pressure is rather small. The residual stresses have to consider if further mechanical stresses are investigated. So a tension test normal to the seal glass plane was superposed with the residual stresses. The location of maximum stresses could be shown and it was in agreement with experimental results