Tian Shiang Yang

A Novel Semianalytical Approach for Finding Pull-In Voltages of Micro Cantilever Beams Subjected to Electrostatic Loads and Residual Stress Gradients

Beam structures are widely used in microelectromechanical systems (MEMS) sensors and actuators, and modeling of pull-in behavior of beams subjected to electrostatic force is essential for MEMS actuators. However, from a fabrication perspective, MEMS microbeams are usually curled due to residual stress gradients, and this causes difficulties to accurately estimate the pull-in voltages. As a result, the characteristics of microbeams subjected to both residual stress gradients and electrostatic forces must be investigated to provide accurate information for the design of sensors and actuators. In this paper, a novel semianalytical formulation for computing the pull-in voltage of a curled cantilever beam due to residual stress gradients is proposed. By assuming an admissible deformation shape and using the energy method to determine the coefficients of the shape functions, it is possible to find the pull-in characteristics of the curled cantilevers. Detailed parametric studies are subsequently performed to quantify the influence of various geometry and processing parameters on the pull-in characteristics of those microbeams. Finally, we present a fitted formula for MEMS engineers to estimate pull-in voltages for beams with residual stress gradients for design optimization. The proposed method can also be extended for handling bilayered curled cantilever beams due to thermomechanical mismatches. Therefore, the method and results presented in this paper should be useful in micro sensor and actuator design.

Residual Vibration Suppression for Duffing Nonlinear Systems With Electromagnetical Actuation Using Nonlinear Command Shaping Techniques

Residual vibration control is crucial for numerous applications in precision machinery with negligible damping such as magnetically actuated systems. In certain magnetically actuated applications, the systems could also be highly nonlinear and conditionally stable. Although traditional command shaping techniques work well for linear and weakly nonlinear systems, they show little effects for dealing with systems with both strong structural and actuation nonlinearities. In this paper, a general input shaper design methodology for single degree of freedom systems with both Duffing spring and electromagnetic forcing nonlinearities is successfully devised using an energy approach. Following this method, two-step and three-step shapers are developed, which in the linear limit reduce to the traditional zero-vibration (ZV) and zero-vibration-and-derivative (ZVD) shapers, respectively. The robustness of these nonlinear shapers is investigated numerically through several case studies and the results show that the three-step shaper is sufficiently robust to resist significant amounts of parameter variations without exciting significant residual vibration. The two-step shaper, however, is somewhat less robust with respect to parameter variations. Meanwhile, an electromagnetically driven Duffing mechanical system is also constructed so that the performances and robustness of the nonlinear shapers in vibration suppression can be examined. It is shown that the nonlinear shapers result in a significant improvement in residual vibration suppression and settling time reduction in comparison with the traditional linearized ZV and ZVD shapers.

Effects of Pad Grooves on Chemical Mechanical Planarization

Chemical mechanical planarization (CMP) has played an enabling role in producing near-perfect planarity of interconnection and metal layers in ultralarge scale integrated devices. For stable and high performance of CMP, it is important to ensure uniform slurry flow at the pad-wafer interface, hence necessitating the use of grooved pads that help discharge debris and prevent subsequent particle loading effects. Here, using two-dimensional lubrication theory and contact mechanics models, we examine the effects of pad groove designs (viz. their width, depth, and spacing) on slurry flow in CMP. It is found that the presence of pad grooves generally increases the slurry flow rate (which clearly facilitates debris discharge) and the magnitude of the subambient fluid pressure (i.e., suction) on the pad-wafer interface. The increased suction implies higher contact stress on the pad-wafer interface, and hence the local material removal rate is expected to increase as well. However, our numerical results suggest that, as a grooved pad has less contact area for effective interaction with the wafer, the overall material removal rate is expected to increase as well. However, our numerical results suggest that, as a grooved pad has less contact area for effective interaction with the wafer, the overall material removal rate is decreased by the presence of pad grooves. There is therefore a trade-off between slurry flow rate enhancement and material removal rate reduction in pad groove design.

Fast Positioning and Impact Minimizing of MEMS Devices by Suppression of Motion-Induced Vibration by Command-Shaping Method

Electrostatic (ES) force is one of the most important actuation mechanisms for microelectromechanical systems (MEMS) devices. However, residual vibration of microstructures induced by ES actuation can bring various problems that degrade dynamic performance and device longevity, such as long settling time, dynamic pull-in, and contact fatigue. By suppressing this undesirable effect, it is expected that both the dynamic performance and device reliability can be effectively enhanced. This paper presents a command-shaping-based scheme with experiment validation for both fast positioning and reduced contact impact of MEMS devices by the suppression of motion-induced vibrations. The scheme was developed by applying energy conservation, force equilibrium, and elliptical integrals. Simulink simulations indicate that both the impact force and settling time can be effectively reduced. In order to count the possible parameter variation and unmodeled dynamics, an online tuning scheme is also proposed and verified through simulation. Finally, spring-plate specimens fabricated using SU-8 with a metallic coating and a test bed containing a laser positioning sensor and a high voltage source are designed to further demonstrate the performance of the proposed scheme; the test results indicate that the proposed approach can effectively enhance the dynamic performance of MEMS devices such as grating light valves and RF switches.

A novel semi-analytical approach for micro beams subjected to electrostatic loads and residual stress gradients

Beam structures are widely used in MEMS sensors and actuators. MEMS micro beams are usually curled due to residual stresses and the characteristics of micro beams subjected to both residual stress gradients and electrostatic forces must be investigated for providing accuracy information for designing sensors and actuators. In this work, a novel semi-analytical formulation to address the above needs is proposed. By assuming an admissible deformation shape and utilizing energy method to determine the coefficients of the shape functions, it is possible to find the pull-in characteristics of the curled cantilevers. Detail parametric studies are subsequently performed to quantify the influence of various geometry and processing parameters on the pull-in characteristics of those micro beams. The method and results presented in this work would be very useful for related micro sensors and actuator designs.Copyright

Optimization of Wafer-Back Pressure Profile in Chemical Mechanical Planarization

In chemical mechanical planarization, a rotating wafer is pressed facedown against a rotating pad, while a slurry is dragged into the pad-wafer interface to assist in planarizing the wafer surface. Due to stress concentration, the interfacial contact stress near the wafer edge generally is much higher than that near the wafer center, resulting in a spatially nonuniform material removal rate and hence an imperfect planarity of the wafer surface. Here, integrating theories of fluid film lubrication and two-dimensional contact mechanics, we calculate the interfacial contact stress and slurry pressure distributions. In particular, the possibility of using a multizone (i.e., piecewise constant) wafer-back pressure profile to improve the contact stress uniformity is examined by studying a particular case with realistic parameter settings. The numerical results indicate that using a two-zone wafer-back pressure profile with optimized zonal sizes and pressures can increase the usable wafer surface area (within which the average contact stress nonuniformity is below 0.1%) by as much as 12%. Using an optimized three-zone wafer-back pressure profile, however, does not increase the usable wafer surface area much further.

Thermal Analysis of a Laser Peeling Technique for Removing Micro Edge Cracks of Ultrathin Glass Substrates for Web Processing

Ultrathin glass is a promising substrate material for web processing (also called roll-to-roll processing) of flexible electronics, but is highly susceptible to breaking and cracking due to the almost inevitable presence of substrate-edge defects. Recently, a novel technique for removing the micro cracks on the edges of ultrathin glass substrates was devised at ITRI. It amounts to shining a CO2 laser on one edge of a substrate, which induces spontaneous peeling of a thin layer containing preexisting cracks on the edge from the substrate, resulting in an essentially crack-free new substrate edge. Exploiting the thinness of ultrathin glass substrates, here we propose a simplified two-dimensional thermal model for the laser peeling process, and obtain an analytic expression for the transient temperature variation in a substrate being peeled. This enables us to locate the “thermally affected zone” in the substrate, which turns out to be impressively similar in size and shape to the substrate-edge peels observed in experiments. Moreover, a quantitative criterion for the minimum cooling rate required for the progression of the peeling process is obtained. The results here thus provide useful insights into the laser peeling mechanism, and can be used to expedite the optimization of process parameters. Some preliminary purely numerical results using a finite element method (FEM) based software also are briefly discussed here.Copyright

Thermo-mechanical analysis of laser peeling of ultrathin glass for removing edge flaws in web processing applications

Laser peeling is an efficient method for removing edge defects on ultra-thin glass for enabling the subsequent roll-to-roll glass processing for display applications. This process involves complicated interaction in various fields such as heat transfer, stress, fracture, and material properties variations. In order to guide the process design for optimizing the laser peeling process, it is important to conduct necessary analyses. In this work, the laser peeling process is modelled as a moving heat source and the corresponding heat transfer, thermal stress, and crack propagation are then simulated. Problems observed during experiments are firstly explained based on simulation results. Finally, essential parametric studied are also performed for providing recommendation for process optimization.

Analysis of Experimental Data for Metallic Impurity Out-Diffusion from Deep-UV Photoresist

In a previous study [J. Electrochem, Soc., 146, 3455 (1999)]. the radioactive tracer technique was employed to determine the percentages of manganese and zinc impurities diffused from a deep UV photoresist to various underlying substrates at different baking temperatures. For the same baking time, it was found that such diffusion ratios do not increase monotonically with temperature. Instead, as the baking temperature increases, the diffusion ratios may first increase and then decrease, first decrease and then increase, or simply decrease monotonically, depending upon the specific impurity/substrate combination. Here, to explain the various temperature dependences of the impurity diffusion ratios, we propose a theory that supplements the Ficks diffusion law with the Arrhenius law, which relates the diffusivities and interfacial segregation coefficients of the metallic impurities to the baking temperature. The theory also makes it possible to extract the values of important physicochemical parameters from raw experimental data, and the methodology is demonstrated in the paper by attempting to analyze the aforementioned experimental data.

Effects of Wafer Carrier Design on Contact Stress Uniformity in CMP

Here we use 2-D models of fluid film lubrication and contact mechanics to calculate the contact stress and fluid (i.e., slurry) pressure distributions on the wafer–pad interface in CMP. In particular, the effective rigidity of the wafer (determined by the wafer carrier structure), the retaining ring width and its back pressure are taken to be the design parameters. The purpose is to study the synergetic effects of such parameters on the contact stress non-uniformity (NU), which directly affects the spatial non-uniformity of the material removal rate on the wafer surface. Our numerical results indicate that, for a given wafer rigidity, one may choose a particular combination of the retaining ring parameters to minimize NU. Also, the corresponding minimum NU decreases with the effective wafer rigidity, suggesting that it is beneficial to use a soft (e.g., floating-type) wafer carrier. Moreover, for a soft wafer carrier, the presence of the retaining ring also reduces NU to some extent, but the use of a multi-zone wafer-back pressure profile would be more effective in this regard.