Search

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.

A novel test structure to characterize the fracture strength of MEMS (Micro-electro-Mechanical Systems) thin films is presented. The test structure is comprised of a micro fabricated chevron-shaped thermal actuator and test specimen. The test structure is capable of producing large displacement and stress while keeping a relatively low temperature gradient across the test specimen. A voltage is applied across the beams of the chevron-shaped actuator, producing thermal expansion force to fracture the test specimen. Actuator deflection is computed based on elastic analysis of structures. To verify the test structure, simulations have been implemented using COMSOL Multiphysics. A 620 μm long, 410 μm wide, 10 μm thick test structure produced stress of 7.1 GPa while the applied voltage is 5 V. The results indicate that the test structure is suitable for in-situ measurement of the fracture strength of MEMS thin films. Keywords: MEMS thin films, Fracture strength, Chevron-shaped thermal actuator

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 formation and evolution of etch profiles with different mask shapes and sizes on C-plane wafers of sapphire are analyzed based on undercutting rate distributions of characteristic planes. The effect of concentrations of etchants on etch profiles is further analyzed. Firstly, etch rate distributions under different experimental conditions (236 °C, H2SO4:H3PO4 = 3:1 and 6:1) are obtained by wet etching experiments of sapphire hemispheres. Undercutting rate distributions of characteristic planes on C-plane wafers under different experimental conditions are obtained by the maximum positive curvature (MPC) recognition method. Then, the effect of different mask shapes and sizes on the formation and evolution of etch profiles of complex cavities and islands on C-plane wafers are analyzed based on the undercutting rate distribution under the experimental condition (236 °C, H2SO4:H3PO4 = 3:1). Finally, characteristic differences of etch profiles on C-plane wafers at different concentrations are explained based on undercutting rate distributions of characteristic planes at the corresponding concentrations (236 °C, H2SO4:H3PO4 = 3:1 and 6:1). These provide a basis for the study of the anisotropic wet etching mechanism of sapphire.

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%.

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.

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 simple method for in situ determination of the coefficient of thermal expansion (CTE) of polysilicon thin films by using micro-rotating structures is presented. The structures are heated electrically and deflect due to the thermal expansion. An analytical expression is derived to relate the CTE of the polysilicon thin film with the lateral displacement, geometrical parameters and the average temperature of the test structure. The lateral displacement is designed to be a constant value (2 μm), while the average temperature of the test structure can be obtained from the measurement of resistance of the test structure. Instead of an optical or visual readout, electrical input and electrical readout are utilized. In the experiments, a current–voltage measurement system only is required and all measurements can be carried out in atmosphere. Finite element analysis and experimental results with surface micromachined polysilicon thin films are used to demonstrate the effectiveness of the proposed method. The average value of the obtained CTE is (2.76 ± 0.09) × 10− 6 K− 1 with temperature ranging from 450 K to 500 K.

A three-dimensional (3D) simulation system is developed for the moving mask UV lithography of thick photoresist. The exposure simulation model is obtained with consideration of the mask moving function, the refraction and energy loss of the UV light at the surface of photoresist, and the reflection at the photoresist/substrate interface. The development model is calculated by the fast marching method. In addition, the energy deposition distributions and the three-dimensional development profiles are presented under different conditions to study the effect of various parameters and to verify the accuracy by experiment. The results will be useful to understand the effects and to control the exposure conditions in the design process of moving mask UV lithography for thick-photoresist in the future.

In this paper, a direct and simple method to characterize the elastic modulus of individual layers for composite films byin situmeasuring of MEMS test structures is presented. The structure is composed of a set of microactuators which contains a rigid plate with two supporting composite beams. A model is developed to describe analytically the relationship between the force and the deflection of microactuators by electrostatic measurements, and the elastic modulus of multi-layered beams with different widths are evaluated. FEM simulations are implemented to validate the accuracy of the relationship between the on-load voltage and the capacitance between the microactuator and the electrode on the substrate. Test structures are fabricated using CMOS-MEMS process and experiments are to be carried out soon.

Piezoresistive sensor was one of the earliest silicon MEMS devices, which based on the theory of piezoresistive. In order to build the piezoresistive IP library for the MEMS foundry, we improved the structures of the piezoresistive based on the achievement of Liwei Lin1, and new analytic model and design software for square shape membrance has been developed. The ability to calculate sensitivity and linearity of MEMS piezoresistive sensor using the new model have been demonstrated. As results, output voltage, sensitivity and linearity characteristics of MEMS sensor are presented in this paper.

A new structure of gap adjustable MEMS resonator has been proposed, and an analytical model of the gap adjustable structure has been developed. This model is a 2D vibration system. An opposite type MATA was used to push the fixed finger structure to move, as a result, the gap between the fingers changed. Simulation results show that the displacement of the mechanical oscillator increased when the MATA provided a step force, and the vibration amplitude was modulated when the force was in a cyclical form. In order to improve the stability of the structure, the folded beams were changed into clamped beams. An FEA simulation told us that when the gap changed, the vibration amplitude increased.

Fast marching method is an accurate, extremely fast numerical technique in analyzing and computing moving fronts which can develop sharp corners and change topology. We successfully accomplish this method in two dimensions and the two-dimensional lithography process simulation of SU 8 photoresists has been implemented. The obtained results indicate that the fast marching method can actually accelerate the simulation and be used as an effective method for thick photoresist lithography process simulations.

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.

This paper presents the models for the ultraviolet (UV) lithography of thick photoresists such as thick SU-8. Simulations for various lithography conditions have been conducted using these models based on the improved dynamical cellular automata method. Some experiments on SU-8 2075 layers under UV source with 365nm wavelength have been implemented to verify the simulation results. The results confirm the validity of the proposed models.

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.

A 3-D Monte Carlo simulator was used to model the profile evolution of silicon during plasma etching. The profile simulation is based on the kinetics model developed from beam studies. The profile evolution of patterned samples etched in an inductively coupled plasma etcher was simulated. The mechanisms of microtrenching and sidewall bowing forming were discussed. Nondirectional ions were primarily responsible for the sidewall bowing; while ions reflected form bowed feature sidewalls were primarily responsible for the microtrenching. The profile evolutions under different processing conditions were simulated, including different neutral-to-ion ration, different energy and different ion angular distribution.

In this paper, we present the model of electron beam lithography. This model includes elastic cross section, inelastic cross section, energy-loss rate model and etch rate model. For elastic cross section, Rutherford cross section and Browning's Mott cross section are adopted. For inelastic cross section, Moller cross section and Gryzinsky cross section are used. To calculate energy-loss rate, we use different forms of Bethe formulas. The etch rate model is used to calculate the etch rate. The simulation is implemented with Monte Carlo method for PMMA resist. Various development profiles are obtained through the simulation.

The complex scattering process of the high-energy electron beams in resist is simulated by Monte Carlo method. The energy deposition distributions are presented under different exposure conditions. The three-dimensional (3-D) development profiles are obtained with the developing threshold model. It is found that, in the high energy range, higher electron beam energy, thinner resist, appropriate dose and lower substrate's atom number will cause lower proximity effect. Based on the simulations, we can explain the proximity effect and the dose control on proximity effect correction via the three-dimensional development profiles. The results will be useful to optimize the exposure conditions in electron beam lithography, and to provide more accurate data for proximity effect correction.