Intrinsic Stress Gradients Research Articles

Estimation of the Young's Modulus of Nanometer-Thick Films Using Residual Stress-Driven Bilayer Cantilevers.

Precise prediction of mechanical behavior of thin films at the nanoscale requires techniques that consider size effects and fabrication-related issues. Here, we propose a test methodology to estimate the Young’s modulus of nanometer-thick films using micromachined bilayer cantilevers. The bilayer cantilevers which comprise a well-known reference layer and a tested film deflect due to the relief of the residual stresses generated during the fabrication process. The mechanical relationship between the measured residual stresses and the corresponding deflections was used to characterize the tested film. Residual stresses and deflections were related using analytical and finite element models that consider intrinsic stress gradients and the use of adherence layers. The proposed methodology was applied to low pressure chemical vapor deposited silicon nitride tested films with thicknesses ranging from 46 nm to 288 nm. The estimated Young’s modulus values varying between 213.9 GPa and 288.3 GPa were consistent with nanoindentation and alternative residual stress-driven techniques. In addition, the dependence of the results on the thickness and the intrinsic stress gradient of the materials was confirmed. The proposed methodology is simple and can be used to characterize diverse materials deposited under different fabrication conditions.

Cobalt-Iron-Manganese Electrodeposition for High Performance Magnetoelastic Resonators

Magnetostrictive Co-Fe-Mn films were investigated for their use in fabricating magnetoelastic resonators. Electrodepositing these films enables batch fabrication of resonators with varying geometries and therefore, resonant frequencies, while controlling the film stoichiometry and crystallography. Boron, phosphorous, and molybdenum were used to increase the electrical resistivity and control film texture. Additionally, ascorbic acid and TMAB were used as “oxygen scavengers” to control the chemistry’s stability and limit the oxidation of the Fe2+ to Fe3+. As suggested by Osaka et al, Fe(OH)3 is formed and included into the film resulting in a decrease of the saturation magnetic flux density (Bs) value as the Fe cation is oxidized[1,2]. Additives, such as Saccharin and Sorbitol, were added as grain refiners and stress reducers, enabling flat cantilever structures that did not bend out of plain due to intrinsic stress gradients. The composition and phase of the deposited films were controlled by temperature, agitation, concentrations in the electrodeposition chemistry, current density, and duty cycle of the pulsing regime. The samples were analyzed with EDS to determine the composition and XRD to look at film texture. Magnetic testing was performed using super conducting quantum interference device (SQUID) magnetometry, as well as visual inspection of the displacement on a deposit stress analyzer as a magnetic field was applied to the films. The magnetostriction was then correlated to EDS and XRD results to identify phase, stoichiometry and the plating parameters to produce improved magnetostriction while maintaining low intrinsic stress. Annealing studies of these films were performed using a tube furnace with inert gas to heat past the Curie temperature and then cool in the presence of an applied magnetic field. The applied magnetic field direction and its correlation with magnetic properties and phase will be discussed. Acknowledgement Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. References Osaka, T., et al., A high moment CoFe soft magnetic thin film prepared by electrodeposition. Electrochemical and Solid State Letters, 2003. 6(4): p. C53-C55.Elhalawaty, S., et al., Oxygen Incorporation into Electrodeposited CoFe Films: Consequences for Structure and Magnetic Properties. Journal of the Electrochemical Society, 2011. 158(11): p. D641-D646.

Microstructure and mechanical properties of stress-tailored piezoelectric AlN thin films for electro-acoustic devices

Nanoindentation measurements along with atomic force microscopy, X-ray diffraction, and residual stress analyses on the basis of Raman measurements have been performed to characterize stress-tailored AlN thin films grown using reactive RF magnetron sputtering. The intrinsic stress gradient caused by the growing in-plane grain size along film thickness was minimized by increasing the N2 concentration in the Ar/N2 gas mixture during the growth process. The increase of N2 concentration did not degrade the device-relevant material properties such as crystallographic orientation, surface morphology, piezoelectric response, or indentation modulus. Due to comparable crystallographic film properties for all investigated samples it was concluded that mainly the AlN crystallites contribute to the mechanical film properties such as indentation modulus and hardness, while the film stress or grain boundaries had only a minor influence. Therefore, by tailoring the stress gradient in the AlN films, device performance, fabrication yield, and the design flexibility of electro-acoustic devices can be greatly improved.

Electrically conducting ultrananocrystalline diamond for the development of a next generation of micro-actuators

The potential of ultrananocrystalline diamond (UNCD) as a structural material for complex micro-electro mechanical systems (MEMS) is enormous due to its excellent chemical, mechanical and electrical properties, but it has so far not been extensively explored, mostly due to intrinsic stress problems. We have fabricated, for the first time, an actuatable MEMS device based on nitrogen-incorporated ultrananocrystalline diamond (N-UNCD), which is electrically conducting and has low intrinsic stress gradient. We characterized the N-UNCD and verified its semiconducting nature by looking at its thermal and electrical properties. Fifteen pairs of oriented slender beams (from 90 to 200μm length) provide the driving force and are capable of generating a linear displacement on a central moving shuttle up to almost 2μm. An ‘in-house’ built optical-based detection system was used to assess the motion of the actuator, with an accuracy of 0.4nm. These results pave the way for development of diamond-based MEMS technology that could be applicable in many fields, including bio-medicine, optics, and sensors and actuators for space applications, where precision displacement is demanded along with robust materials, as well as general applications that require sliding surfaces.

Experimental Validation of Topology Optimization for RF MEMS Capacitive Switch Design

In this paper, we present 30 distinct RF MEMS capacitive switch designs that are the product of topology optimizations that control key mechanical properties such as stiffness, response to intrinsic stress gradients, and temperature sensitivity. The designs were evaluated with high-accuracy simulations prior to micro-fabrication. We built and tested more than 170 switches, including at least five per distinct design. Experimental results confirm that the finite element models are accurate and that the switches behave as intended by the different optimizations. Extensive testing results include actuation and release voltages as a function of temperature, switching times, capacitance ratios, fitted S-parameters, and profile measurements during actuation and over temperature. [2013-0203].

Estimation of bending of micromachined gold cantilever due to residual stress

Electroplated gold is widely used as the material for the micromachined beam structures due to its excellent electrical and mechanical properties. This work attempts to analyze the surface micromachined gold cantilever beams under inherently present stress gradient. The structure is analyzed by using finite element method simulation at different intrinsic stress gradients. The gold layers are deposited using cyanide electroplating bath operated at different current densities. Residual stresses in electroplated gold layers deposited on photoresist coated silicon samples are estimated by using X-ray diffraction technique. Cantilever beam structures are fabricated using surface micromachining technique. The tip deflections of the fabricated cantilever beams are found to be ~16 and 8 μm corresponding to the 1.0 and 0.7 mA/cm2 current densities (mean), respectively. The corresponding intrinsic stress gradients are estimated to be −13.9 and −7.2 MPa/μm, respectively. Simulated and measured values of residual stresses are well matched.

Variation of the intrinsic stress gradient in thin aluminum nitride films

The intrinsic stress gradient variation of thin aluminum nitride (AlN) films is the central objective in this paper. For the first time, significant influence parameters on the stress gradient are identified and varied during the deposition process. The process power induced in the plasma and the gas flow ratio of the sputter gases argon and nitrogen are the two major parameters for controlling the stress gradient of deposited AlN films. The controlled avoidance as well as the controlled generation of positive and negative gradients is shown. The stress gradient was investigated by analysis of released one-side clamped cantilever test structures.

Transient and steady-state shear banding in aging soft glassy materials

Transient and steady-state shear banding in a Laponite suspension were studied by particle imaging velocimetry in Couette and cone and plate flow geometries on samples with varying age. The time evolution of the velocity profile and shear stress was measured simultaneously as a fixed shear rate was imposed on the sample. By varying the aging time of the rejuvenated samples, we examined the effect of the stress overshoot on the shear banding behavior. Transient banding only occurred for aged samples that showed a stress overshoot. However, steady-state banding occurred when the imposed shear rate was below a critical value, even in the absence of a stress overshoot or transient banding. These results were consistent for independently prepared samples with vastly different overall ages, and in different flow geometries with varying intrinsic stress gradients. Different mechanisms for transient and steady-state shear banding will be discussed.

The interplay between boundary conditions and flow geometries in shear banding: Hysteresis, band configurations, and surface transitions

We study shear banding flows in models of wormlike micelles or polymer solutions, and explore the effects of different boundary conditions for the viscoelastic stress. These are needed because the equations of motion are inherently non-local and include “diffusive” or square-gradient terms. Using the diffusive Johnson–Segalman model and a variant of the Rolie-Poly model for entangled micelles or polymer solutions, we study the interplay between different boundary conditions and the intrinsic stress gradient imposed by the flow geometry. We consider prescribed gradient (Neumann) or value (Dirichlet) of the viscoelastic stress tensor at the boundary, as well as mixed boundary conditions in which an anchoring strength competes with the gradient contribution to the stress dynamics. We find that hysteresis during shear rate sweeps is suppressed if the boundary conditions favor the state that is induced by the sweep. For example, if the boundaries favor the high shear rate phase then hysteresis is suppressed at the low shear rate edges of the stress plateau. If the boundaries favor the low shear rate state, then the high shear rate band can lie in the center of the flow cell, leading to a three-band configuration. Sufficiently strong stress gradients due to curved flow geometries, such as that of cylindrical Couette flow, can convert this to a two-band state by forcing the high shear rate phase against the wall of higher stress, and can suppress the hysteresis loop observed during a shear rate sweep.

Effect of intrinsic stress gradient on the effective mode-I fracture toughness of amorphous diamond-like carbon films for MEMS

The influence of intrinsic stress gradient on the mode-I fracture of thin films with various thicknesses fabricated for Microelectromechanical Systems (MEMS) was investigated. The material system employed in this study was hydrogen-free tetrahedral amorphous diamond-like carbon (ta-C). Uniform gauge microscale specimens with thicknesses 0.5, 1, 2.2, and 3 μm, containing mathematically sharp edge pre-cracks were tested under mode-I loading in fixed grip configuration. The effective opening mode fracture toughness, as calculated from boundary force measurements, was 4.25±0.7 MPa√m for 0.5-μm thick specimens, 4.4±0.4 MPa√m for 1-μm specimens, 3.74±0.3 MPa√m for 2.2-μm specimens, and 3.06±0.17 MPa√m for 3-μm specimens. Thus, the apparent fracture toughness decreased with increasing film thickness. Local elastic property measurements showed no substantial change as a function of film thickness, which provided evidence for the stability of the sp 2/sp 3 carbon binding stoichiometry in films of different thicknesses. Detailed experiments and finite element analysis pointed out that the dependence of the effective fracture toughness on specimen thickness was due to the intrinsic stress gradient developed during fabrication and post-process annealing. This stress gradient is usually unaccounted for in mode-I fracture experiments with thin films. Thicker films, fabricated from multiple thin layers, underwent annealing for extended times, which resulted in a stress gradient across their thickness. This stress gradient caused an out-of-plane curvature upon film release from its substrate and, thus, combined bending and tensile mode-I loading at the crack tip under in-plane forces. Since the bending component cannot be isolated from the applied boundary force measurements, its contribution, becoming important for thick films, remains unaccounted for in the calculation of the critical stress intensity factor, thus resulting in reduced apparent fracture toughness that varies with film thickness and curvature. It was concluded that in the presence of a stress gradient, accounting only for the average intrinsic stresses could lead in an overestimate of the fracture resistance of a brittle film. Under these considerations the material fracture toughness of ta-C, as determined from specimens with negligible curvature, is K IC=4.4±0.4 MPa√m.

Determination of mechanical properties of PECVD silicon nitride thin films for tunable MEMS Fabry–Pérot optical filters

This paper reports an investigation on techniques for determining elastic modulus and intrinsic stress gradient in plasma-enhanced chemical vapor deposition (PECVD) silicon nitride thin films. The elastic property of the silicon nitride thin films was determined using the nanoindentation method on silicon nitride/silicon bilayer systems. A simple empirical formula was developed to deconvolute the film elastic modulus. The intrinsic stress gradient in the films was determined by using micrometric cantilever beams, cross-membrane structures and mechanical simulation. The deflections of the silicon nitride thin film cantilever beams and cross-membranes caused by in-thickness stress gradients were measured using optical interference microscopy. Finite-element beam models were built to compute the deflection induced by the stress gradient. Matching the deflection computed under a given gradient with that measured experimentally on fabricated samples allows the stress gradient of the PECVD silicon nitride thin films introduced from the fabrication process to be evaluated.

Electrostatic Actuators with Intrinsic Stress Gradient : I. Materials and Structures

Electrostatic actuators based on microelectromechanical systems (MEMS) have many attractive features for use as variable capacitors in high-frequency applications. The devices consist of two electrodes, one fixed and the other movable. In this study, a curved, cantilever beam was used as the movable electrode. A novel process has been developed for fabricating an all-gold, curved beam. The cantilever beams were curved due to an intrinsic stress gradient in the metal. Electroplating and conventional lithography were used to metallize the cantilever beam electrodes. The internal stress gradient in the gold was obtained by changing the electroplating conditions during fabrication. Stiction during release and operation of the variable capacitors was alleviated by treating the gold with an alkane thiol self-assembled monolayer. The intrinsic stress gradient and the stress-induced bending moment were calculated using a generalized model for the stress gradient in the films. Compared to bimetallic, cantilever beams, the curvature of the all-gold beam was found to be independent of temperature. This implies that the operation of the single-metal variable capacitor will be more reproducible and stable with temperature than a comparable bimetallic device. © 2002 The Electrochemical Society. All rights reserved.