Yuh-Chung Hu

Review on the Modeling of Electrostatic MEMS

Electrostatic-driven microelectromechanical systems devices, in most cases, consist of couplings of such energy domains as electromechanics, optical electricity, thermoelectricity, and electromagnetism. Their nonlinear working state makes their analysis complex and complicated. This article introduces the physical model of pull-in voltage, dynamic characteristic analysis, air damping effect, reliability, numerical modeling method, and application of electrostatic-driven MEMS devices.

Closed form solutions for the pull-in voltage of micro curled beams subjected to electrostatic loads

This paper derives three analytical models, namely the full-order, the fourth-order and the third-order models, and the corresponding closed form solutions for the pull-in voltages of micro curled beams subjected to electrostatic loads. The analytical models are derived based on the Euler–Bernoulli beam theory and Taylors series expansion and are then solved by the energy method. The accuracy of the present models is verified through comparing with former analytical models and the experimentally measured data conducted in former works. It is verified that the present closed form solutions are more accurate than past works. This paper also compares three commonly used assumed deflection shape functions and shows that the natural mode of the beam is the best choice in predicting the pull-in voltage. The present closed form solutions for the pull-in voltage are very convenient and accurate enough for implementation in device design.

An analytical model considering the fringing fields for calculating the pull-in voltage of micro curled cantilever beams

This paper derives a high precision analytical solution to determine the pull-in voltages of a micro curled beam subjected to electrostatic loads. The analytical model considers the fringing fields between the micro curled beam and the ground plane as well as the initial curling induced by the stress gradient. Furthermore, the electromechanical coupling effects are also involved in the present analytical model. Then the analytical solution of pull-in voltage is obtained by the energy method. By comparing with the other published analytical models as well as the experimentally measured data, the accuracy of the present analytical solution is verified to be more accurate than the other published works. The present analytical solution can determine the pull-in voltage with a maximum deviation of 1% from the experimentally measured results as the ratio of the beam length to the width is greater than 5.

Enhance the Pyroelectricity of Polyvinylidene Fluoride by Graphene-Oxide Doping

The high quality properties and benefits of graphene-oxide have generated an active area of research where many investigations have shown potential applications in various technological fields. This paper proposes a methodology for enhancing the pyro-electricity of PVDF by graphene-oxide doping. The PVDF film with graphene-oxide is prepared by the sol-gel method. Firstly, PVDF and graphene-oxide powders are dispersed into dimethylformamide as solvent to form a sol solution. Secondly, the sol solution is deposited on a flexible ITO/PET substrate by spin-coating. Thirdly, the particles in the sol solution are polymerized through baking off the solvent to produce a gel in a state of a continuous network of PVDF and graphene-oxide. The final annealing process pyrolyzes the gel and form a β-phase PVDF film with graphene-oxide doping. A complete study on the process of the graphene oxide doping of PVDF is accomplished. Some key points about the process are addressed based on experiments. The solutions to some key issues are found in this work, such as the porosity of film, the annealing temperature limitation by the use of flexible PET substrate, and the concentrations of PVDF and graphene-oxide.

The fabrication of silicon-based PZT microstructures using an aerosol deposition method

This paper presents a series of processes for fabricating lead-zirconate-titanate (PZT) microstructures on a silicon substrate. An aerosol deposition method was used to deposit PZT thick film at room temperature. The low temperature deposition enabled a special lift-off process for patterning thick PZT films using a THB-151N photoresist. The milling rate of THB-151N by PZT particles was found to be the same as the PZT deposition rate of 5 μm h−1. Using this patterning technique, complex configurations of PZT microstructures have been demonstrated. Suspended multi-layer PZT microstructures have also been realized in this work.

Fabrication of micro nickel/diamond abrasive pellet array lapping tools using a LIGA-like technology

A manufacturing process of micro nickel/diamond abrasive pellet array lapping tools using a LIGA-like technology is reported here. The thickness of JSR THB-151N resist coated on an aluminum alloy substrate for micro lithography can reach up to 110 µm. During the lithography, different geometrical photomasks were used to create specific design patterns of the resist mold on the substrate. Micro roots, made by electrolytic machining on the substrate with guidance of the resist mold, can improve the adhesion of micro nickel abrasive pellets electroplated on the substrate. During the composite electroforming, the desired hardness of the nickel matrix inside the micro diamond abrasive pellets can be obtained by the addition of leveling and stress reducing agents. At moderate blade agitation and ultrasonic oscillation, higher concentration and more uniform dispersion of diamond powders deposited in the nickel matrix can be achieved. With these optimal experiment conditions of this fabrication process, the production of micro nickel/diamond abrasive pellet array lapping tools is demonstrated.

An approximate analytical solution to the pull-in voltage of a micro bridge with an elastic boundary

This paper derives an approximate analytical solution to the pull-in voltage of a micro bridge with elastic boundaries. The analytical model considers the elastic boundary effect, fringing field capacitance, residual stresses and the distributed flexibility of the bridge. The accuracy of the present approximate analytical solution is verified by comparison with the simulation results of commercial FEM packages and other published closed-form solutions as well as experimental measured data. The deviation of the present approximate analytical solution is within 5% for a wide beam and a narrow beam in a small deflection regime. The present approximate analytical solution has explicit physical meaning and is highly accurate for device design.

Electromechanical behavior of the curled cantilever beam

We propose an approximate analytical solution to the pull-in voltage of a microcurled cantilever beam. The analytical model considers the realistic situations, which include stress gradient, nonideal boundary conditions, and fringing field capacitance. The proposed analytical model can be used at wafer level for extracting the Youngs modulus of the thin film of which the cantilever beam is made. The approximate analytical solution is obtained based on the Eulers beam model and the minimum energy method. The accuracy of the proposed model is verified to be more accurate than the other published models. The model presented in this work can be used for wafer-level evaluation of the material properties through simple electrical testing and is also expected to find use in the design of microelectromechanical devices.

A method for mechanical characterization of capacitive devices at wafer level via detecting the pull-in voltages of two test bridges with different lengths

The paper aims at developing a wafer-level testing method to examine Youngs modulus and residual stress of structural materials of capacitive micro-devices by detecting the pull-in voltages of micro test beams made of the materials to be tested. We derive a formula that correlates the Youngs modulus, residual stress and pull-in voltage of the micro test beams. The analytical model considers the fringing field capacitance, the distributed characteristics of the micro test beams and the electromechanical coupling effect. By the present method, one can extract Youngs modulus and residual stress simultaneously by detecting the pull-in voltages of two test beams of different lengths. Three common structural materials used in micro-devices are demonstrated: mono-crystalline silicon, poly-silicon and aluminum. The extracted Youngs moduli and residual stresses agree very well with the experimental measurement. The present method is expected to be applicable to the wafer-level testing in MEMS device manufacture and compatible with the wafer-level testing in IC industry since the test and the pickup signals are both electrical.

The fringe capacitance formula of microstructures

This paper presents a fringe capacitance formula of microstructures. The formula is derived by curve fitting on ANSYS simulation results. Compared with the ANSYS and experimental results, the deviation is within ±2%. The application to determine the pull-in voltage of an electrostatic micro-beam is demonstrated, which agrees very well with the experimental data. The formula presented is very accurate, yields explicit physical meanings and is applicable to common dimension ranges for MEMS devices.