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In this article, the benchmark drift of micromachined thermal wind sensor due to the packaging asymmetry has been analyzed and compensated. For the ideal wind sensors with symmetric packaging, the benchmark does not vary with speed and direction. However, for the real sensors, especially for handmade ones, packaging asymmetry problems are usually inevitable. Consequently, benchmark drifts with wind because of different thermal distribution in each direction, which was verified by the proposed lumped parameters model. The real sensors were tested in a wind tunnel and results showed the benchmark drift as well. The contribution of this work lies in the establishment of the equation of benchmark dependent on wind speed, which can predict benchmark value under different wind speeds by calibration at zero wind speed. This compensation method is extremely simple and convenient for industrial production. After compensation, the relative wind speed errors are reduced from 46 to 8% up to 30 m/s, and the wind direction errors are reduced from 30° to 7° over the full range of 360°.

The concern about process deviations rises because that the performance uncertainty they cause are strengthened with the miniaturization and complication of Microelectromechanical System (MEMS) devices. To predict the statistic behavior of devices, Monte Carlo method is widely used, but it is limited by the low efficiency. The recently emerged generalized polynomial chaos expansion method, though highly efficient, cannot solve uncertainty quantification problems with correlated deviations, which is common in MEMS applications. In this paper, a Gaussian mixture model (GMM) and Nataf transformation based polynomial chaos method is proposed. The distribution of correlated process deviations is estimated using GMM, and modified Nataf transformation is applied to convert the correlated random vectors of GMM into mutually independent ones. Then polynomial chaos expansion and stochastic collection can be implemented. The effectiveness of our proposed method is demonstrated by the simulation results of V-beam thermal actuator, and its computation speed is faster compared with the Monte Carlo technique without loss of accuracy. This method can be served as an efficient analysis technique for MEMS devices which are sensitive to correlated process deviations.

For the development of micro-electro-mechanical system (MEMS) technology during the past several years, MEMS design has requirements of high precision, high efficiency, iterative design, joint design of structure and circuit and so on. With the improvement of thermal wind sensor performance requirements and the complexity of the application environment, it is becoming increasingly difficult to ignore the impact of environmental factors. However, there is no system-level model considering the influence of environmental factors adequately in macro model. To solve these problems, a 2D thermal wind sensor macro model considering environmental factors is proposed. In order to build a macro model which can reflect the output of sensors in different environments, this paper, starting from the basic law of heat transfer, proposes an accurate macro model of the thermal wind sensor. The model proposed in this study accurately considers the influence of thermal and transport properties in different environments, and can be simulated together with the interface circuits in Cadence software. The results indicate that the variation of temperature and atmospheric pressure in the natural range can affect the sensor output by more than 15%, and the influence of relative humidity should not be ignored when the temperature is higher than 70 °C. Furthermore, the flow direction over the sensor can be further studied according to the 2D equivalent circuit model. The simulation results agree well with the experimental results, and the results can provide a valuable reference for the research and practical application of thermal wind sensors.

Due to the increasing complexity of microelectromechanical system (MEMS) devices, the accuracy and precision of two-dimensional microstructures of SU-8 negative thick photoresist have drawn more attention with the rapid development of UV lithography technology. This paper presents a high-precision lithography simulation model for thick SU-8 photoresist based on waveguide method to calculate light intensity in the photoresist and predict the profiles of developed SU-8 structures in two dimension. This method is based on rigorous electromagnetic field theory. The parameters that have significant influence on profile quality were studied. Using this model, the light intensity distribution was calculated, and the final resist morphology corresponding to the simulation results was examined. A series of simulations and experiments were conducted to verify the validity of the model. The simulation results were found to be in good agreement with the experimental results, and the simulation system demonstrated high accuracy and efficiency, with complex cases being efficiently handled.

In this paper, the simple, rejection-based kinetic Monte Carlo simulation method is applied for the approximate simulation of the etch rates and three-dimensional etch structures during anisotropic wet etching of sapphire. Based on the analysis of the composition of the atomic structure of sapphire, a model of the simplified atomic structure of sapphire is proposed, which reduces the difficulty of classifying types of surface atoms on the different crystallographic planes. This enables adopting a previously proposed six-index classification method (to differentiate effectively between the various surface atoms of sapphire) and a previously proposed removal probability function (RPF) (to link the removal probability of the surface atom with the configuration of its neighbors). By reducing errors between simulated rates and experimental rates of 11 typical crystallographic planes in the and crystallographic zones continuously with an evolutionary algorithm, reasonable values of nine energy parameters of the RPF are obtained. The simulated results describe approximately the experimental counterparts.

In this paper, we propose a thermal wind speed sensor Verilog-A model with thermal-fluid-electric hybrid characteristics. Because the structure of the thermal wind sensor and the interface circuit chip are designed separately, which cannot effectively carry out MEMS-IC (integrated circuit) co-simulation, the overall performance of the sensor and interface circuit chip is prone to large deviation. At the same time, the separation of MEMS structure and IC design process leads to long product development cycle and high cost. This paper proposes an improved simulation model by analyzing the behavior characteristics of the thermal wind speed sensor. The simulation model consists of 11 thermistors, 3 capacitors, a voltage-controlled voltage source, and a voltage-controlled current source. The Taylor series expansion of the differential equation of heat conduction is carried out, and then the thermistor and capacitor networks are established according to the corresponding relationship between the thermal parameters and the electrical parameters, including the thermal conduction unit, the convection unit and the heat capacity in the chip. The model fully considers the effects of various physical effects and parasitic effects, and is implemented using the hardware description language Verilog-A. The sensor and interface circuit can be simulated simultaneously to optimize the circuit design. It is beneficial to the integration of sensors and interface circuit, reducing the number of tape-outs, increasing the success rate, and reducing costs. The consistency between the simulation results and the experimental curves verified the correctness of the macro model. The behavior characteristics of constant power (CP) and constant temperature heating were described. In CP mode, the output voltage error is less than ± 6.5%, the chip temperature error is less than 4.0%. The presented modeling approach can be the basis for the development of complete MEMS-IC design technology library of thermal wind speed sensor, aiming at optimum designs of integrated thermal wind speed sensor.

This paper presents a piezoresistive barometric pressure sensor fabricated by using a Silicon-on-Nothing (SON) technology. Array of silicon trenches were annealed in hydrogen environment to form continuing crystalline silicon membrane over a vacuum cavity. Epitaxial growth on the silicon membrane is then completed for the desired thickness. All processes are CMOS compatible and performed on the front side of the silicon wafer. The piezoresistive barometric pressure sensor has been demonstrated with pressure hysteresis as low as 0.007%.

Thick SU-8 photoresist has been a popular photoresist material to fabricate various mechanical, biological, and chemical devices for many years. The accuracy and precision of the ultraviolet (UV) lithography process of thick SU-8 depend on key parameters in the set-up, the material properties of the SU-8 resist, and the thickness of the resist structure. As feature sizes get smaller and pattern complexity increases, accurate control and efficient optimization of the lithography process are significantly expected. Numerical simulations can be employed to improve understanding and process design of the SU-8 lithography, thereby allowing rapid related product and process development. A typical comprehensive lithography of UV lithography of thick SU-8 includes aerial image simulation, exposure simulation, post-exposure bake (PEB) simulation, and development simulation, and this article presents an overview of the essential aspects in the comprehensive simulation. At first, models for the lithography process of the SU-8 are discussed. Then, main algorithms for etching surface evolvement, including the string, ray tracing, cellular automaton, and fast marching algorithms, are introduced and compared with each other in terms of performance. After that, some simulation results of the UV lithography process of the SU-8 are presented, demonstrating the promising potential and efficiency of the simulation technology. Finally, a prospect is discussed for some open questions in three-dimensional (3D) comprehensive simulation of the UV lithography of the SU-8.

A three-dimensional topography simulation of deep reactive ion etching (DRIE) is developed based on the narrow band level set method for surface evolution and Monte Carlo method for flux distribution. The advanced level set method is implemented to simulate the time-related movements of etched surface. In the meanwhile, accelerated by ray tracing algorithm, the Monte Carlo method incorporates all dominant physical and chemical mechanisms such as ion-enhanced etching, ballistic transport, ion scattering, and sidewall passivation. The modified models of charged particles and neutral particles are epitomized to determine the contributions of etching rate. The effects such as scalloping effect and lag effect are investigated in simulations and experiments. Besides, the quantitative analyses are conducted to measure the simulation error. Finally, this simulator will be served as an accurate prediction tool for some MEMS fabrications.

A microstructure beam is one of the fundamental elements in MEMS devices like cantilever sensors, RF/optical switches, varactors, resonators, etc. It is still difficult to precisely predict the performance of MEMS beams with the current available simulators due to the inevitable process deviations. Feasible numerical methods are required and can be used to improve the yield and profits of the MEMS devices. In this work, process deviations are considered to be stochastic variables, and a newly-developed numerical method, i.e., generalized polynomial chaos (GPC), is applied for the simulation of the MEMS beam. The doubly-clamped polybeam has been utilized to verify the accuracy of GPC, compared with our Monte Carlo (MC) approaches. Performance predictions have been made on the residual stress by achieving its distributions in GaAs Monolithic Microwave Integrated Circuit (MMIC)-based MEMS beams. The results show that errors are within 1% for the results of GPC approximations compared with the MC simulations. Appropriate choices of the 4-order GPC expansions with orthogonal terms have also succeeded in reducing the MC simulation labor. The mean value of the residual stress, concluded from experimental tests, shares an error about 1.1% with that of the 4-order GPC method. It takes a probability around 54.3% for the 4-order GPC approximation to attain the mean test value of the residual stress. The corresponding yield occupies over 90 percent around the mean within the twofold standard deviations.

A deep reactive ion etching (DRIE) process (Bosch process) is used extensively in the fabrication of microelectromechanical systems (MEMS). Modeling and simulation studies have helped improve our understanding and process design. The Bosch process consists of multiple cycles of alternating etching and deposition steps. Based on a narrow band level set method, by integrating etching simulation and deposition simulation modules, a simulation system is proposed for three-dimensional (3-D) simulation of the Bosch process with arbitrarily complex mask shapes. To verify the simulation system, a series of simulations and experiments have been performed. The simulation results are in good agreement with the experiments. The method may be used to optimize the practical Bosch process and to design and control the profile of high-aspect ratio microstructures.

Display Omitted A comprehensive aerial image model is developed for 3D UV lithography of SU-8.Efficient approaches for large scale 3D simulations of SU-8 lithography are presented.A 3D hash fast marching method is developed to calculate the final development profiles. Three-dimensional (3D) simulations are useful to optimize the lithography process of thick photoresists, however, less efficient models and etching surface advancement algorithms limits current application of various simulation tools. This paper presents a comprehensive aerial image model based on Fresnel diffraction to simulate the 3D inclined/vertical UV light intensity distribution into the SU-8 with the diffraction, refraction, absorbance and reflection during light transmission efficiently considered simultaneously. The aerial image model are solved by using adaptable element size in x, y and z direction to speed up the calculation. The improved two-dimensional (2D) Dill exposure model, the post exposure bake (PEB) model and the Enhanced Notch model are also extended to three dimensions. Furthermore, a 3D hash fast marching method is developed to calculate the final development profiles with less required memory elements. Thus various large scale 3D simulations of thick SU-8 lithography process can be well implemented, and the simulated development profiles have been verified by experimental results.

A 2-D simulation system based on a 2-D dynamic cellular automata method, integrating aerial image simulation, exposure simulation, post-exposure bake simulation, and development simulation modules is presented for inclined ultraviolet (UV) lithography processes of thick photoresists such as SU-8 photoresists. To verify the simulation system, a series of experiments have been performed for SU-8 2000 series photoresists under UV source with 365 nm (2.6 mW/cm2) radiation. The simulation results demonstrate to be in agreement with the experimental results. This is useful to optimize the inclined UV lithography processes of SU-8 photoresists, and to accurately design and control the dimensions of some SU-8 microstructures.

The two-dimensional (2D) dynamic cellular automata (CA) method for photoresist etching simulation has been successfully improved by using novel update rules and a novel compensation value calculation method. The improved 2D dynamic CA method demonstrates to be more efficient and accurate. The deep ultraviolet (UV) lithography processes of SU-8 photoresists have been successfully simulated using aerial image simulation, exposure simulation, post-exposure bake simulation and development simulation models, based on the improved CA method. Simulation results demonstrate good agreement with the experimental results. This is useful to optimize the UV lithography process of SU-8 photoresists and improve the efficiency of the design of some micro-electro-mechanical systems devices.

This paper presents a novel 3D continuous cellular automaton (CA) model with high index planes such as (2 1 1), (3 1 1), (3 3 1) and (4 1 1) efficiently incorporated. A dynamic algorithm has also been developed to speed up the simulation process and reduce the memory usage. A 3D silicon anisotropic etching simulator, SEAES, has been implemented based on the 3D continuous CA model and the dynamic algorithm. The simulation results by SEAES have been found to be in good agreement with the experimental results, and the arbitrarily complex mask shapes and the merging of 3D etching profiles can be both efficiently and accurately handled. This is identified to be useful for the research of anisotropic etching technologies and the development of micro-electro-mechanical systems (MEMS) design.

A novel three-dimensional (3-D) dynamic cellular automata (CA) model is presented for a photoresist-etching process simulation (photoresist-dissolution simulation and development simulation). In the 3-D dynamic CA model, the Moore neighborhood is adopted, and the boundary cells are only processed by using a boundary cell array, a corresponding linked list of pointers to the boundary cells, and a state flag to indicate the relations between the cells and the etching boundary. A time-compensation method is also introduced to speed up the photoresist-etching simulation. Therefore, the simulation speed is greatly increased compared with that of the static 3-D CA model, and the preferential etch in different directions reported in cell-removal models is significantly reduced. The 3-D dynamic CA model was successfully tested using some well-known etch-rate distribution test functions and has been shown to be stable, accurate, and fast. Exposure simulation, post-exposure bake simulation, and photoresist-etching simulation have been successfully integrated together to further study the effectiveness of the 3-D dynamic CA model. Simulation results show an agreement with available experimental results

This paper presents a two-dimensional (2D) modified cellular automata (CA) algorithm for accurate boundary movement of deposition process simulation. The algorithm incorporates deposition rate calculation methods based on a cell structure. Isotropic and anisotropic deposition processes were successfully simulated by the algorithm, and the simulation profiles show good agreement with available experimental results. The deposition process with defects on the substrate was also implemented using this algorithm. The 2D modified CA algorithm demonstrates accuracy and capability of handling complex boundary and initial conditions. It is useful for the deposition process simulation of microelectromechanical systems and integrated circuits.

A novel two-dimensional (2D) dynamic cellular automata (CA) model is presented for photoresist etching process simulation. The speed of the dynamic CA model increases by over ten times compared with the 2D static CA model. At the same time, the simulation accuracy is also increased in this model. The dynamic CA model has been successfully tested using some well-known etch-rate distribution test functions and is demonstrated to be stable even in areas where the fluctuation in etch rates is very sharp.

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.

In the fabrication of micro-electro-mechanical systems (MEMS) devices, manufacturing process variations are usually involved. For these devices sensitive to process variations such as doubly-clamped beams, mismatches between designs and final products will exist. As a result, it underlies yield problems and will be determined by design parameter ranges and distribution functions. Topographical changes constitute process variations, such as inclination, over-etching, and undulating sidewalls in the Bosch process. In this paper, analytical models are first developed for MEMS doubly-clamped beams, concerning the mentioned geometrical variations. Then, finite-element (FE) analysis is performed to provide a guidance for model verifications. It is found that results predicted by the models agree with those of FE analysis. Assigning process variations, predictions for performance as well as yield can be made directly from the analytical models, by means of probabilistic analysis. In this paper, the footing effect is found to have a more profound effect on the resonant frequency of doubly-clamped beams during the Bosch process. As the confining process has a variation of 10.0%, the yield will have a reduction of 77.3% consequently. Under these circumstances, the prediction approaches can be utilized to guide the further MEMS device designs.

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.

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.

Three-dimensional oblique microstructures of SU-8 negative thick photoresists have drawn more attention with the rapid development of inclined UV lithography technology. In this paper, a simple model based on the Fresnel diffraction theory is developed to simulate the inclined UV lithography and predict the profiles of developed oblique SU-8 structures by utilizing the paraxial approximation approach. The reflection, refraction, absorption of the SU-8 photoresists and the reflection at the wafer surface are integrally incorporated in the model to improve the accuracy. The parameters, which have significant influence on the profile quality, have been studied in simulation. Simulation results demonstrate good agreement with the experimental results, where the oblique SU-8 structures were fabricated on glass and silicon wafers. To eliminate reflected UV light at the wafer surface, Ti films were sputtered on the glass wafers, followed by wet oxidation, thus employed as an antireflection layer. By contrast, the silicon wafers were used to fabricate the oblique SU-8 structures with reflected induced patterns. This model is useful to optimize the inclined UV lithography process of SU-8 thick photoresists and improve the efficiency of the design of some micro-electro-mechanical system devices.