Zai-Fa Zhou

A simple method for extracting material parameters of multilayered MEMS structures using resonance frequency measurements

Multilayered structures are increasingly used in MEMS. Based on the resonant frequency of the doubly–clamped multilayered beam, the Youngs modulus and residual stress for an individual layer have been measured by designing beam test structures for each layer with different widths. Taking into account the buckling or no buckling problem of the multilayered beam, this paper introduces a model for the resonant frequency of the beam. An approach to extract the Youngs modulus and residual stress for the individual layer is developed. The validity of this approach has been studied using finite element modeling. As a multilayered example, test structures for a gold/polysilicon bilayer beam were fabricated. A scanning laser Doppler vibrometer system was used to measure the resonant frequency of the beam. The extracted parameters are that the average value of Youngs modulus of polysilicon and gold are 133.7 GPa and 78.6 GPa with standard deviation being 4.2 GPa and 11.5 GPa, respectively; the average value of residual stress of polysilicon and gold are 13.9 MPa (compressive) and 19.7 MPa (tensile) with standard deviation being 0.47 MPa and 4.4 MPa, respectively.

An online test structure for the thermal expansion coefficient of surface micromachined polysilicon beams by a pull-in approach

An online test structure for measuring the thermal expansion coefficient (TEC) of surface micromachined polysilicon beams is presented by using clamped–clamped beams. In this structure, the polysilicon beam is heated by applying direct current voltage between two anchors, causing it to expand. The thermal expansion of the beam is restricted due to the clamped–clamped boundary, while the pull-in voltage is measured by applying the other varying voltage between the beams and substrate. Based on the electrothermal properties of the test structure and the pull-in approach, an analytical model and an extracting method for the TEC are developed. Validation of the analytical model has been confirmed by FEM simulation and experiments. In the experiments, current–voltage measurements are only required, and all measurements can be carried out in free air. Measured average value of the TEC is (2.49 ± 0.03) × 10−6 K−1 with temperature ranging from 300 to 350 K.

In situ test structures for the thermal expansion coefficient and residual stress of polysilicon thin films

In this research, micromachined devices consisting of four micro-rotating structures for the in situ determination of the thermal expansion coefficient (TEC), tensile and compressive residual stress of polysilicon thin films are studied. The structures are heated electrically and deflect due to the thermal expansion. The lateral displacements of the devices are related to the thermal stress and residual stress of the test beams. The micro-rotating structures are arranged, so that the lateral displacements are designed to be either a constant value which is used to determine the TEC of the thin film or a variable value that changes with the residual stress of the thin film. An analytical model of the test structure is presented. The finite element software ANSYS is used to verify the analytical model and provide guidelines for the structure design. Experimental results with a surface micromachined polysilicon thin film are used to demonstrate the proposed method. In the experiments, a current–voltage measurement system only is required. The TEC for the polysilicon thin film is obtained to be (2.61 ± 0.04)xa0× 10−6xa0K−1xa0from 400 to 420xa0K and the residual stress is measured asxa0−(10.15 ± 0.70)xa0MPa.

A Modified 3D fast marching simulation for thick photoresists lithography

Fast marching methods (FMM) can solve many problems on tracking and capturing moving interface, even some sharp corners and topology changes are being developed. As the well performance in dealing with evolving surface, the FMM has been improved and introduced into three-dimensional (3D) lithography simulation of thick photoresists such as SU-8 photoresist. A stationary level set formulation of lithography simulation has been established, and solved at an extremely fast speed. A hash table has been applied to reduce the storage memory of the algorithm by 23% at least without any precision loss. As a result, the 3D lithography simulation of thick SU-8 has been successfully implemented and the obtained results indicate that the modified fast marching method can be used as an effective tool to accelerate the thick photoresists lithography simulations.

A Simple Extraction Method of Young’s Modulus for Multilayer Films in MEMS Applications

Based on the first resonance frequency measurement of multilayer beams, a simple extraction method has been developed to extract the Young’s modulus of individual layers. To verify this method, the double-layer cantilever, as a typical example, is analyzed to simplify the situation and finite element modeling (FEM) is used in consideration of the buckling and unbuckling situation of cantilevers. The first resonance frequencies, which are obtained by ANSYS (15.0, ANSYS Inc., Pittsburgh, PA, USA) with a group of thirteen setting values of Young’s modulus in the polysilicon layer are brought into the theoretical formulas to obtain a new group of Young’s modulus in the polysilicon layer. The reliability and feasibility of the theoretical method are confirmed, according to the slight differences between the setting values and the results of the theoretical model. In the experiment, a series of polysilicon-metal double-layer cantilevers were fabricated. Digital holographic microscopy (DHM) (Lyncée Tech, Lausanne, Switzerland) is used to distinguish the buckled from the unbuckled. A scanning laser Doppler vibrometer (LDV) (Polytech GmbH, Berlin, Germany) system is used to measure the first resonance frequencies of them. After applying the measurement results into the theoretical modulus, the average values of Young’s modulus in the polysilicon and gold layers are 151.78 GPa and 75.72 GPa, respectively. The extracted parameters are all within the rational ranges, compared with the available results.

Measurement of elastic modulus and residual stress of individual layers for composite films by resonant frequency of MEMS structures

This paper presents a direct and simple method to characterize the elastic modulus and residual stress of individual layers for composite films by measuring the resonant frequency. The structure is composed of the composite fixed-fixed beam. A model is developed to describe analytically elastic modulus and residual stress as a function of the resonant frequency of multi-layered fixed-fixed beams with different lengths and widths. FEM simulations are firstly implemented to validate the accuracy of the relationship between resonant frequency and mechanical properties. Experiments are then carried out by measuring the fundamental frequencies of the bilayer fixed-fixed beams with different lengths to extract the materials properties.

High-Voltage Flexible Microsupercapacitors Based on Laser-Induced Graphene

High-voltage energy-storage devices are quite commonly needed for robots and dielectric elastomers. This paper presents a flexible high-voltage microsupercapacitor (MSC) with a planar in-series architecture for the first time based on laser-induced graphene. The high-voltage devices are capable of supplying output voltages ranging from a few to thousands of volts. The measured capacitances for the 1, 3, and 6 V MSCs were 60.5, 20.7, and 10.0 μF, respectively, under an applied current of 1.0 μA. After the 5000-cycle charge-discharge test, the 6 V MSC retained about 97.8% of the initial capacitance. It also was recorded that the all-solid-state 209 V MSC could achieve a high capacitance of 0.43 μF at a low applied current of 0.2 μA and a capacitance of 0.18 μF even at a high applied current of 5.0 μA. We further demonstrate the robust function of our flexible high-voltage MSCs by using them to power a piezoresistive microsensor (6 V) and a walking robot (>2000 V). Considering the simple, direct, and cost-effective fabrication method of our laser-fabricated flexible high-voltage MSCs, this work paves the way and lays the foundation for high-voltage energy-storage devices.

On-line Test Microstructures of the Mechanical Properties for Micromachined Multilayered Films

Recently, multilayered structures have been utilized in MEMS applications, including infrared focal plane arrays, radio-frequency (RF) components, micromachined mirrors, etc. It is well known that MEMS devices are highly dependent on material parameters such as Young’s modulus and residual stress of the multilayered films. These properties determine both the final shape and the functionality of released microstructures and should therefore be accurately evaluated. Young’s modulus and residual stress for single-layer films have been widely studied by the cantilever deflections, wafer curvatures, displacements of variously designed microstructures, buckling lengths, membrane deflections, resonance frequency, pull-in voltages, and double-clamped beam deflections. However, these methods are not easily extended to multilayered films. Thus it is significantly expected to directly measure both Young’s modulus and residual stress for multilayer films simultaneously. This chapter presents some methods to characterize the material properties of the composite films by electrostatic pull-in testing and the resonance frequency testing approaches adopting the composite double-clamped beam or the cantilever beam. The analytical models are presented and test structures with different lengths and widths are designed. In situ methods for simultaneously extracting material properties (Young’s modulus and residual stress) of each layer for the composite films are reported. The extracting methods have been confirmed by FEM simulations and experiments.

In-Situ Testing of the Thermal Diffusivity of Polysilicon Thin Films

This paper presents an intuitive yet effective in-situ thermal diffusivity testing structure and testing method. The structure consists of two doubly clamped beams with the same width and thickness but different lengths. When the electric current is applied through two terminals of one beam, the beam serves as thermal resistor and the resistance R(t) varies as temperature rises. A delicate thermodynamic model considering thermal convection, thermal radiation, and film-to-substrate heat conduction was established for the testing structure. The presented in-situ thermal diffusivity testing structure can be fabricated by various commonly used micro electro mechanical systems (MEMS) fabrication methods, i.e., it requires no extra customized processes yet provides electrical input and output interfaces for in-situ testing. Meanwhile, the testing environment and equipment had no stringent restriction, measurements were carried out at normal temperatures and pressures, and the results are relatively accurate.

Three-dimensional modeling and simulation of the Bosch process with the level set method

A new approach for three-dimensional (3-D) simulation of the Bosch process with arbitrarily complex mask shape is presented. Its profile evolution algorithm is based on the 3-D narrow band level set method which is memory and computation efficient and also allows easy handling of topographic changes. A series of simulations and experiments have been conducted to verify the accuracy of the simulation system. After model parameter extraction from experiments, this simulator can be used to simulate several phenomena in the Bosch process, such as the formation and adjustment of sidewall scallops, the lag and pattern transfer effects and the profile control of trench etching. The simulation results are in good agreement with experimental results and the proposed simulation system demonstrates to be high accurate and efficient.