O. Rezvanian

The viability and limitations of percolation theory in modeling the electrical behavior of carbon nanotube-polymer composites.

A new modeling method has been proposed to investigate how the electrical conductivity of carbon nanotube (CNT) reinforced polymer composites are affected by tunneling distance, volume fraction, and tube aspect ratios. A search algorithm and an electrical junction identification method was developed with a percolation approach to determine conductive paths for three-dimensional (3D) carbon nanotube arrangements and to account for electron tunneling effects. The predicted results are used to understand the limitations of percolation theory and experimental measurements and observations, and why percolation theory breaks down for specific CNT arrangements.

Temperature dependence of asperity contact and contact resistance in gold RF MEMS switches

Experimental measurements and modeling predictions were obtained to characterize the electro-mechanical response of two different gold contact radio frequency microelectromechanical system (RF MEMS) switches due to variations in the temperature and applied contact voltage. A three-dimensional surface roughness profile from AFM measurements of the top contact surface of a sample RF MEMS switch was used to obtain modeling predictions of the time-dependent deformation of the asperity microcontacts, real areas of contact, number of asperity microcontacts and constriction resistance. The experimental data indicated a decrease in the overall resistance and a decrease in the creep mechanism at 77 K and 5.6 K when compared to measurements at 293 K. At 293 K, there is more contact area per unit time, and the resistance drop from the increase in real contact area dominates the resistance increase due to asperity heating. At 77 K, the creep rate is reduced, and fewer asperities are in contact. At 5.6 K, the change in contact area over time is small, and the contact resistance measurement is dominated by the Joule heating. The data presented and constriction resistance modeling for gold RF MEMS switches show that temperature plays a significant role in the creep deformation and heating of switch contacts.

Statistically stored, geometrically necessary and grain boundary dislocation densities: microstructural representation and modelling

A unified physically based microstructural representation of f.c.c. crystalline materials has been developed and implemented to investigate the microstructural behaviour of f.c.c. crystalline aggregates under inelastic deformations. The proposed framework is based on coupling a multiple-slip crystal plasticity formulation to three distinct dislocation densities, which pertain to statistically stored dislocations (SSDs), geometrically necessary dislocations (GNDs) and grain boundary dislocations. This interrelated dislocation density formulation is then coupled to a specialized finite element framework to study the evolving heterogeneous microstructure and the localized phenomena that can contribute to failure initiation as a function of inelastic crystalline deformation. The GND densities are used to understand where crystallographic, non-crystallographic and cellular microstructures form and the nature of their dislocation composition. The SSD densities are formulated to represent dislocation cell microstructures to obtain predictions related to the inhomogeneous distribution of SSDs. The effects of the lattice misorientations at the grain boundaries (GBs) have been included by accounting for the densities of the misfit dislocations at the GBs that accommodate these misorientations. By directly accounting for the misfit dislocations, the strength of the boundary regions can be more accurately represented to account for phenomena associated with the effects of the GB strength on intergranular deformation heterogeneities, stress localization and the nucleation of failure surfaces at critical regions, such as triple junctions.

The role of creep in the time-dependent resistance of Ohmic gold contacts in radio frequency microelectromechanical system devices

It is shown that measured and calculated time-dependent electrical resistances of closed gold Ohmic switches in radio frequency microelectromechanical system (rf-MEMS) devices are well described by a power law that can be derived from a single asperity creep model. The analysis reveals that the exponent and prefactor in the power law arise, respectively, from the coefficient relating creep rate to applied stress and the initial surface roughness. The analysis also shows that resistance plateaus are not, in fact, limiting resistances but rather result from the small coefficient in the power law. The model predicts that it will take a longer time for the contact resistance to attain a power law relation with each successive closing of the switch due to asperity blunting. Analysis of the first few seconds of the measured resistance for three successive openings and closings of one of the MEMS devices supports this prediction. This work thus provides guidance toward the rational design of Ohmic contacts with ...

Electrothermomechanical Finite-Element Modeling of Metal Microcontacts in MEMS

Three-dimensional fractal representations of surface roughness are incorporated into a finite-element framework to obtain the electrothermomechanical behavior of ohmic contacts in radio frequency (RF) microelectromechanical systems (MEMS) switches. Fractal surfaces are generated from the Weierstrass-Mandelbrot function and are representatives of atomic force microscope surface roughness measurements of contact surfaces in fabricated RF MEMS switches with metal contacts. A specialized finite-element scheme is developed, which couples the thermomechanical asperity creep deformations with the electromechanical contact characteristics to obtain predictions of contact parameters and their evolution as a function of time and loading. A dislocation-density-based crystal plasticity framework is also used to investigate microstructure evolution at microcontacts and its effects on contact parameters. Using this approach, simulations are made to investigate how surface roughness, initial residual strains, and operating temperature can affect asperity contact behavior. Based on these predictions, tribological design guidelines can be obtained to increase the lifetime of low-contact-resistance RF MEMS switches by limiting stiction and electrical resistance increase.

Electro-mechanical modeling of the piezoresistive response of carbon nanotube polymer composites

A coupled electro-mechanical FE approach was developed to investigate the piezoresistive response of carbon nanotube polymer composites. Gauge factors (GFs) and resistance variations of CNT–polymer composite systems were obtained by coupling Maxwell equations to mechanical loads and deformations through initial piezoresistive coefficients of the CNTs, the epoxy, and the tunnel regions, for different arrangements, percolated paths, tunnel distances, and tensile, compressive, and bending loading conditions. A scaling relation between GFs and applied strains was obtained to understand how variations in loading conditions and CNT arrangements affect sensing capabilities and piezoresistive carbon nanotube polymer composite behavior. These variations in GFs were then used to understand how the coupled strains, stresses and current densities vary for aligned and percolated paths for the different loading conditions, CNT arrangements, and tunnel distances. For the percolated path under tensile loading conditions, elastic strains as high as 16% and electrical conductivities that were four orders in magnitude greater than the initial matrix conductivity were obtained. Results for the three loading conditions clearly demonstrate that electrical conductivity and sensing capabilities can be optimized as a function of percolation paths, tunneling distance, orientation, and loading conditions for piezoresistive applications with large elastic strains and conductivities.

Inelastic Contact Behavior of Crystalline Asperities in rf MEMS Devices

Microelectromechanical systems (MEMS), particularly those with radio frequency (rf) applications, have demonstrated significantly better performance over current electromechanical and solid-state technologies. Surface roughness and asperity microcontacts are critical factors that can affect contact behavior at scales ranging from the nano to the micro in MEMS devices. Recent investigations at the continuum level have underscored the importance of microstructural effects on the inelastic behavior of asperity microcontacts. Hence, a microstructurally based approach that accounts for the inhomogeneous deformation of the asperity microcontacts under cyclic loading and that is directly related to asperity physical scales and anisotropies can provide a detailed understanding of the deformation mechanisms associated with asperity microcontacts so that guidelines can be incorporated in the design and fabrication process to effectively size critical components and forces for significantly improved device durability and performance. A physically based microstructural representation of fcc crystalline materials that couples a multiple-slip crystal plasticity formulation to dislocation densities is used in a specialized finite-element modeling framework. The asperity model and the loading conditions are based on realistic service conditions consistent with rf MEMS with metallic normal contacts. The evolving microstructure, stress fields, contact width, hardness, residual effects, and the localized phenomena that can contribute to failure initiation and evolution in the flattening of single crystal gold asperity microcontacts are characterized for a loading-unloading cycle. It is shown that the nonuniform loading conditions due to asperity geometry and contact loading and the size effects due to asperity dimensions result in significant contribution of the geometrically necessary dislocation densities to stress, deformation, and microstructural evolution of crystalline asperities. This is not captured in modeling efforts based on von Mises continuum plasticity formulations. Residual strains and stresses are shown to develop during the cyclic loading. Localized tensile stress regions are shown to develop due to stress reversal and strain hardening during both loading and unloading regimes. Hardness predictions also indicate that nano-indentation hardness values of the contact material can overestimate the contact force in cases, where a rigid flat surface is pressed on a surface roughness asperity.

Computational Modeling and Design of Adaptive Thin-Film Composite Coatings

The tailoring of thin film coatings comprised of high strength constituents, such as diamond like carbon and partially stabilized zirconia and ductile constituents, such as gold and molybdenum is investigated by new microstructurally-based finite-element techniques for applications related to the wear, durability, and performance of these coatings over a broad range of temperatures and loading conditions. The effects of contact transfer films, grain-shape sizes and distributions, grain-boundary structure and sliding, texture, and strength are used to determine the optimal thin film coating compositions. Comparisons are made with experimental measurements and observations, and guidelines for optimal thin film composite coatings are proposed.