Statistical mechanical model for crack growth.

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. Here, an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

Determining Stress in Metallic Conducting Layers of Microelectronics Devices Using High Resolution Electron Backscatter Diffraction and Finite Element Analysis.

Delayed failure due to stress voiding is a concern with some aging microelectronics, as these voids can grow large enough to cause an open circuit. Local measurements of stress in the metallic layers are crucial to understanding and predicting this failure, but such measurements are complicated by the fact that exposing the aluminum conducting lines will relieve most of their stress. In this study, we instead mechanically thin the device substrate and measure distortions on the thinned surface using high resolution electron backscatter diffraction (HREBSD). These measurements are then related to the stresses in the metallic layers through elastic simulations. This study found that in legacy components that had no obvious voids, the stresses were comparable to the theoretical stresses at the time of manufacture (≈300 MPa). Distortion fields in the substrate were also determined around known voids, which may be directly compared to stress voiding models. The technique presented here for stress determination, HREBSD coupled with finite element analysis to infer subsurface stresses, is a valuable tool for assessing failure in layered microelectronics devices.

Freely jointed chain models with extensible links.

Analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.

Actuation of higher harmonics in large arrays of micromechanical cantilevers for expanded resonant peak separation.

A large array of elastically coupled micro cantilevers of variable length is studied experimentally and numerically. Full-scale finite element modal analysis is implemented to determine the spectral behavior of the array and to extract a global coupling matrix. A compact reduced order model is used for numerical investigation of the array's dynamic response. Our model results show that at a given excitation frequency within a propagation band, only a finite number of beams respond. Spectral characteristics of individual cantilevers, inertially excited by an external piezoelectric actuator, were measured in vacuum using laser interferometry. The theoretical and experimental results collectively show that the resonant peaks corresponding to individual beams are clearly separated when operating in vacuum at the 3rd harmonic. Distinct resonant peak separation, coupled with the spatially-confined modal response, make higher harmonic operation of tailored, variable-length cantilever arrays well suited for a variety of resonant based sensing applications.

Nondegenerate Parametric Resonance in Large Ensembles of Coupled Micromechanical Cantilevers with Varying Natural Frequencies.

We investigate the collective dynamics and nondegenerate parametric resonance (NPR) of coplanar, interdigitated arrays of microcantilevers distinguished by their cantilevers having linearly expanding lengths and thus varying natural frequencies. Within a certain excitation frequency range, the resonators begin oscillating via NPR across the entire array consisting of 200 single-crystal silicon cantilevers. Tunable coupling generated from fringing electrostatic fields provides a mechanism to vary the scope of the NPR. Our experimental results are supported by a reduced-order model that reproduces the leading features of our data including the NPR band. The potential for tailoring the coupled response of suspended mechanical structures using NPR presents new possibilities in mass, force, and energy sensing applications, energy harvesting devices, and optomechanical systems.

Accurate spring constant calibration for very stiff atomic force microscopy cantilevers.

There are many atomic force microscopy (AFM) applications that rely on quantifying the force between the AFM cantilever tip and the sample. The AFM does not explicitly measure force, however, so in such cases knowledge of the cantilever stiffness is required. In most cases, the forces of interest are very small, thus compliant cantilevers are used. A number of methods have been developed that are well suited to measuring low stiffness values. However, in some cases a cantilever with much greater stiffness is required. Thus, a direct, traceable method for calibrating very stiff (approximately 200 N/m) cantilevers is presented here. The method uses an instrumented and calibrated nanoindenter to determine the stiffness of a reference cantilever. This reference cantilever is then used to measure the stiffness of a number of AFM test cantilevers. This method is shown to have much smaller uncertainty than previously proposed methods. An example application to fracture testing of nanoscale silicon beam specimens is included.

Zn cluster drifting effect for the formation of ZnO 3D nanoarchitecture.

Metal catalysts are widely used for nanowire (NW) growth and are one of the essential parameters that dictate the crystal growth phenomena, thus controlling the NW's morphology. Although extensive research has been conducted on catalyst effects, the catalyst drifting effect is generally underestimated for controlling the morphology of nanostructures grown at a relatively high temperature. In this paper, we report a discovery of Zn cluster drifting phenomenon during ZnO vapor deposition. Because of the deposition of ZnO along the drifting path, the dynamic process of cluster drifting could be visualized after the growth. This phenomenon provides a sound explanation of the formation of randomly orientated ZnO nanowall networks. The cluster drifting direction could be intentionally directed by designing the surface inclination, through which a partially parallel aligned ZnO vertical nanofin array was created. This 3D nanoarchitecture would possibly provide a novel configuration for designing high performance integrated nanodevices. The drifting of Zn clusters could be a general phenomenon for most metal catalysts and would provide a new insight into nanofabrication and nanodevice development.