Convection behavior analysis of CMOS MEMS thermal accelerometers using FEM and Hardee’s model

This paper presents convection behavior investigation of CMOS MEMS convective accelerometers using both analytical and FEM techniques. In a first part, a newly developed accelerometer 3D model is used in FEM simulations to model convection behavior as a function of design geometry and temperature. Using various sizes of two different cover shapes, sensitivity reading and its maximum position in cavity are found to be largely affected by both cover size and shape. In addition, a sensor with cavity width of 600 μm produces sensitivity saturation starting at a cavity depth of 200 μm, for both cover shapes. Using FEM data and curve fitting, differential temperature is claimed to be linearly linked to the effective heater temperature to the power of 1.7. Using the same cavity design and from computed heating efficiency values, we found that a 60 μm width heater offers the best efficiency. This cavity and heater designs give an optimal detector position of 120 μm from heater center along the sensitive axis. Moreover, dual axis accelerometers are found to be more power efficient than single axis ones. In the second part, we present Hardee’s spherical model and investigate its possible application on convective accelerometers. It is shown that inner and outer isotherms deformation, caused by accelerometer design and convection process, should be modeled by including sensor geometry parameters in the derived governing equations. Moreover, Hardee’s biasing temperature relation has to be revised if it is to be used for convective accelerometers.     

The finite-element method with domain decomposition for electromagnetic bistatic scattering from the comprehensive model of a ship on and a target above a large-scale rough sea surface

The domain decomposition method (DDM) and finite-element method (FEM) are developed for numerical solution of bistatic scattering from the composite model of a ship on and a target above a two-dimensional (2-D) randomly rough sea surface under an electromagnetic (EM) wave incidence at low grazing angle. The coupling boundary conditions on the interface between two adjacent subdomains are derived when the conformal perfectly matched layer is used as the truncation boundary of the FEM, and the final coupling matrices are obtained by using the inward-looking approach. Because the computational domain with several millions of unknowns can be solved on a personal computer, our FEM-DDM method is powerful for scattering simulation of a very large-scale rough surface with targets presence. In addition to reduction of the memory storage, the superiority of this method in computing time over the conventional FEM is also demonstrated. Our codes are examined by the FEM without DDM, the forward-backward method (FBM), and generalized FBM for some simple cases. Numerical simulations of bistatic scattering from a comprehensive model of a ship on and a target above the 2-D randomly rough perfectly conducting sea surface in large electric scale are obtained, and its functional dependence on many physical parameters of the targets and oceanic status are discussed.     

Effects of precipitation and cloud ice on brightness temperaturesin AMSU moisture channels

Extinction by ice and rain at the AMSU frequencies used in water vapor profile retrievals is investigated with DMSP observations and brightness temperature simulations of a convective storm system. The simulations are based on mesoscale forecast model output of atmospheric, cloud, and rain profiles from which the absorption and scattering due to both liquid and frozen hydrometeors are calculated. Comparison with satellite observations indicates discrepancies of more than 90% (up to 60 K), of which only about 20% results from ignoring scattering by model-prescribed ice. The major source of error is the inability of the forecast model to produce the spatially localized high ice concentrations which cause the low microwave brightness temperatures. A criterion based on the difference between measured brightness temperatures at 183.31±3 and 183.31±1 GHz is suggested to screen out convective events before water vapor retrieval. Application to the case study examined improved agreement between simulated and observed brightness temperatures by up to a factor of two     

Development of Warpage Measurement System to Simulate Convective Solder Reflow Process

In this paper, a warpage measurement system to simulate forced convective reflow is discussed. A warpage measurement system that can simulate convective reflow enables the real-time monitoring of printed wiring boards (PWBs), PWB assemblies (PWBAs), and chip package warpage during the reflow process. This paper will describe the two major parts of the warpage measurement system: the optical measurement part which utilizes the projection Moire method and advanced image processing, as well as the laboratory oven which is used to simulate forced convective reflow. This is the first system that allows PWB/PWBA/chip package warpage to be measured during a simulated convective reflow process. Also, this is the first system that employs automatic image segmentation to separately extract the warpage of the PWB and electronic components from the same measurement. The results will show that when compared to infrared heating which was previously used in this research area, convective heating minimizes thermal gradients on the PWB/PWBA sample. Thermal gradients on the PWB/PWBA sample have the inadvertent effect of inducing warpage into the sample and will interfere with the warpage measurement result. In the first design iteration presented in this paper, the system can simulate low ramp rate industrial convective reflow profiles and simultaneously measure the warpage of PWBAs. A computational fluid dynamics (CFD) model of the system was developed to determine how to increase the system's heating rate. The CFD model was used to perform a design of simulations (DOS) and regression analysis. The validated regression results will be used to predict oven design parameters to enable the next iteration of the convective system to simulate high ramp rate convective reflow profiles. This paper will show that the presented system is a powerful tool for measuring the warpage of PWBs, PWBAs, and chip packages.     

Numerical analysis of the effects of the magnetic self-field on the transport properties of a multilayer HTS cable

In this paper, the effects of the magnetic self-field on the transport properties of a multilayer high-T/sub c/ superconducting (HTS) cable are investigated by means of two-dimensional finite-element method (FEM) simulations. Analyzed is a three-layer HTS cable, but the developed methods can be used for a different number of layers. The superconductor is described by the nonlinear power-law relation E=E/sub c/(J/J/sub c/)/sup n/, where the parameters J/sub c/ and n depend on the magnetic field experienced by the material. This dependence decreases the global transport capacity of the superconductor, enhancing its AC losses. It is shown that, especially at high transport currents, the AC losses are considerably higher than in the case where the dependence on the magnetic field is neglected. A simple electrical model, considering the cable from macroscopic point of view, has been proposed for finding the optimal winding pitches, leading to a uniform current repartition. The use of this electrical model allows to overcome the difficulties of direct three-dimensional FEM computations. In addition, the rapidity of solutions by the electric model gives the possibility of testing quickly many geometrical configurations in order to find the ones leading to an even current repartition. This optimization process would not be possible with detailed FEM simulations.     

Extraction of Virtual Scattering Centers of Vehicles by Ray-Tracing Simulations

Radar images of complex targets can be understood as a superposition of the reflected signals from a high number of scattering centers. To model complex targets for radar simulations, the plurality of scattering centers should be reduced to few significant scattering centers in order to minimize computational effort. The scope of this work is to present a technique to generate a significantly simplified RCS model of the vehicle with a limited number of virtual scattering centers, each with its own scattering characteristic, and how to group these scattering centers in a cluster database. The work is based on ray-tracing simulations of complex vehicle models. The ray-tracing simulations have been validated by measurements. The scattering centers may not be physically existing strong scattering centers, but virtual scattering centers representing a certain scattering behavior. In this paper, a technique for extracting such virtual scattering centers from a complex 3D-vehicle-model is presented. It is based on ray-tracing simulations of such models. As an example, the design model of a Ford Focus is used.      

Compact modeling of vertical hall-effect devices: electrical behavior

This paper presents the development of a design-oriented compact model of vertical Hall-effect sensors integrated in CMOS technologies. Such a model makes easier the design of integrated Hall systems, permitting designers to co-simulate the Hall sensing element with the biasing and processing electronics thanks to a single electrical simulator. Here focus is put on the electrical behavior, i.e. the resistive behavior of a 5-contact vertical Hall device. The model is based both on theoretical considerations and on FEM numerical simulations performed with COMSOL^®. The result is a new predictive compact model, written in Verilog-A, with 7 input terminals and 14 parameters, mainly sensor geometrical and technological parameters. These parameters can be easily extracted from measurements carried out on a single sensor. The compact model has been validated by FEM simulations, as well as by comparing its response with experimental results obtained from a vertical Hall device fabricated in a CMOS 0.35 μm technology. The root mean square error of the model with respect to experimental results obtained on a wide range of typical sensor biasing conditions is below 2 %. Such a resistive model opens the way to an efficient, complete compact model of the vertical Hall device, i.e. including the Hall-effect as well as all the second-order galvanomagnetic effects.     

Novel thermal model of microchannel cooling system designed for fast simulation of liquid-cooled ICs

The research and design of liquid-cooled integrated circuits (IC) relies heavily on accurate simulation. Ideally, finite-element-method (FEM) based tools should be used for this purpose. However, in most cases a fully coupled thermo-fluidic simulation of complex ICs is very long, mostly due to the fact that the simulation of fluid dynamics is very time consuming. Therefore, in this paper we propose a novel model for thermal simulation of ICs cooled by integrated microchannels which significantly reduces the simulation time. The new approach is based on removing the fluid from the model and treating the solid-liquid boundary as a convective boundary, described by the convection equation. It is shown that the proposed model offers very good accuracy in steady-state, with errors below 3 °C in every chip point. In transient domain the results are equally good, with the maximum error around 3.3 °C (6% relative error). Moreover, the simulation times have been reduced by about two orders of magnitude with respect to fully coupled FEM simulation. However, the proposed model has also important limitations: currently ICs with only one layer of straight microchannels are supported and the model requires recalculation if some chip parameters are changed.     

圆形槽波导到矩形波导结的有限元分析

设计基于圆形槽波导的元件经常会用到圆形槽波导到矩形波导结.应用有限元法(FEM)分析了N端口波导结.采用完全匹配层(PML)将槽波导的开放边界截断为有限区域,然后对圆形槽波导到矩形波导结的散射特性进行了数值计算,得出的散射参量为圆形槽波导振荡器输出结构的优化设计提供了依据.     

Assessment of Complex Radiated EMC Problems Involving Slotted Enclosures Using a 2-D Generalized Circuital Approach

A 2D version of the generalized circuital analysis (GCA) has been used along with the finite element method (FEM) to estimate both the radiated perturbation produced by an arbitrary current distribution (represented by a set of linear current sources) covered by a slotted enclosure, and the field coupled to a slotted screen due to a radiated perturbation. The effect of a given enclosure is modeled by means of a scattering matrix (which depends only on its geometry) obtained by the FEM. On the other hand, any arbitrary perturbating field can be expanded in a series of cylindrical harmonics, and then, the total field is computed everywhere using the scattering matrices. This method has the advantage over conventional FEM approaches that FEM is applied only once, and then a wide range of electromagnetic compatibility (EMC) problems can be solved with almost no extra computational effort. Two-dimensional models of relevant EMC problems involving both emission and immunity have been studied in order to extract useful information for actual 3D systems. In spite of the 2D approach, very interesting conclusions can be derived from the examples presented in this paper (like the effect of slot resonances in the field distribution within slotted enclosures or the coupling between two connected cavities).     

A nonlinear macromodel for current-feedback operational amplifiers

This paper proposes a macromodel to emulate the nonlinear behavior of current-feedback operational amplifiers (CFOAs) at low-frequency. The main difference between this macromodel and those reported previously in the literature is that herein, real physical active device performance parameters along with parasitic elements associated to the input–output terminals of the amplifier are considered. To validate the deduced behavioral model, a saturated nonlinear function series (SNFS) based on CFOAs is built and numerical simulations are generated. In this point, the modeling problem is cast in terms of an augmented set of equations but that, unlike a piece-wise linear (PWL) approach, the dynamic behavior of each CFOA is considered. Afterwards, the SNFS is experimentally tested by using commercially available active devices, confirming good agreement among theoretical simulations and experimental tests at two operating frequencies and showing a better accuracy compared with a PWL approach and a linear model for CFOAs. Because the derived nonlinear macromodel for CFOAs is used for generating the behavioral model of the SNFS, one concludes that the latter is also both accurate and efficient with respect to traditional techniques, such as PWL approaches.     

Sensitivity and power modeling of CMOS mems single axis convective accelerometers

In this paper, we present 3D finite element modeling and simulation of a CMOS MEMS single axis convective accelerometer. We describe the sensor architecture and present a sensor geometry model to be used in 3D FEM simulations. Differences between 3D and previously published 2D simulations are discussed. This work investigates 3D effects which give the opportunity to better predict not only sensor sensitivity but also power dissipation. Experimental sensitivity values and 3D FEM ones are compared for two different sensor geometries and two different heater temperatures. For a prototype having a heater-cavity border distance of 340 µm and a heater length of 230 µm, maximum sensitivity point is obtained for detectors localized at a distance of 125 µm from heater center. This distance should be moved to 90 µm if a 50 µm heater length is used. So, detectors should be placed closer to the heater than the usually used mid distance. Moreover, optimal detectors location shifts closer to the heater as heater length shrinks. We also show that if heater length is reduced by 80% (from 230 to 50 µm), then both electrical power and sensitivity decrease by 63% and 55%, respectively. So, best efficiency is obtained for shorter heaters. In addition, detector's length decrease is found to have a significant effect on sensitivity, with an increase of 58% and 87% using heater lengths of 230 µm and 50 µm, respectively. Here, detector's length decreased from the total side bridge length to a fraction of this length equals to 2.5%. Optimal length is obtained when detectors are implemented on the same side bridge fraction as that used to implement the heater on the central bridge.     

Doppler Spectra From a Two-Dimensional Ocean Surface at L-Band

An approximate time-harmonic three-dimensional electromagnetic boundary-integral method, the small-slope integral equation, is combined with a series expansion of the Creamer surface representation at second order with respect to the height, denoted by Creamer (2). The resulting model provides at low numerical cost simulations of the nonlinear ocean surface Doppler spectrum at L-band. As a result of approximations, the model is designed for a low-wind speed, typically up to 5 m/s. It is shown that applying directly a second-order model such as Creamer (2) to a semiempirical sea surface spectrum induces an unrealistic magnification of small-scale roughness that is involved in the scattering process at microwave frequencies. This paper thus proposes an undressed version of the Pierson–Moskowitz spectrum that corrects this artifact. Full-polarized Doppler simulations at L-band and 70$^circ$incidence are presented. Effects of the surface nonlinearities are outlined, and the simulated Doppler spectra show correct variations with respect to wind speed and direction.     

考虑散射效应的改进的互连线统计时序分析

考虑纳米尺度互连线的散射效应,提出了一种改进的时序分析方法.首先,考虑互连线宽度和厚度的影响,提出了一个简单的散射效应的解析模型.然后,利用这个模型和SS2M得到了过渡时间的统计表达式.实验结果表明,当考虑散射效应后,互连线的延时和过渡时间将进一步增加.同时,提出的统计SS2M模型与SPICE蒙特卡罗分析结果比较,均值的平均误差在4.16%以内,而方差的平均误差在3.06%以内.     

Improved Statistical Interconnect Timing Analysis Considering Scattering Effect

考虑纳米尺度互连线的散射效应,提出了一种改进的时序分析方法.首先,考虑互连线宽度和厚度的影响,提出了一个简单的散射效应的解析模型.然后,利用这个模型和SS2M得到了过渡时间的统计表达式.实验结果表明,当考虑散射效应后,互连线的延时和过渡时间将进一步增加.同时,提出的统计SS2M模型与SPICE蒙特卡罗分析结果比较,均值的平均误差在4.16%以内,而方差的平均误差在3.06%以内.     

Passive cooling of large-area organic light-emitting diodes

The authors investigated passive cooling of large-area organic light-emitting diodes (OLEDs) with special focus on convective cooling. Electro-optical and thermal behaviour of large-area OLED devices are therefore modelled using finite element method (FEM) and computational fluid dynamics (CFD) simulations. Resulting temperature and luminance distributions are compared with measurement data at different driving conditions and test setups. The investigation yields that including laterally resolved convection coefficients from CFD simulations greatly improves model accuracy compared to simpler convection estimations. These findings are important for OLED and their heat spreader design especially for features like flexible, transparent, high-power and or large-area due to their specific limitations for heat spreading and or their high heat spreading requirements.     

Multipoint Galerkin asymptotic waveform evaluation for model orderreduction of frequency domain FEM electromagnetic radiationproblems

In this paper, a model order reduction technique is presented. This technique, known as Galerkin asymptotic waveform evaluation (GAWE), or multipoint Galerkin asymptotic waveform evaluation (MGAWE) if multiple expansion points are considered simultaneously, can be used to reduce matrices describing electromagnetic (EM) phenomena generated through the finite element method (FEM) to a smaller space while still accurately approximating the characteristics of the original responses. The resulting solution procedure of using GAWE or MGAWE, to solve FEM equations allows for wideband frequency simulations with a reduction in total computation time. Numerical simulations using these methods are shown along with traditional methods such as using an LU decomposition at each frequency point of interest and asymptotic waveform evaluation (AWE). Comparisons in accuracy as well as computation time are also given     

Bonding-Induced Strain Effects in InP DFB Components Soldered p-Side-Up on AlN Substrates

Bonding-induced strain is shown to have significant impact on the performance of distributed feedback (DFB) lasers mounted p-side up on AlN carriers using AuSn solder. Degree of polarization (DOP) of photoluminescence was used to estimate top-side longitudinal strain profiles in InP chips soldered to AlN carriers. Asymmetric strain profiles were revealed, the orientation of which are shown to be dependent on bonding tool coplanarity. Solder profiles measured on the same chips by scanning electron microscopy (SEM) were found to be nonuniform. Finite-element method (FEM) simulations were used to confirm that the asymmetric strain profiles resulted from solder nonuniformity caused by the bonding process. The FEM simulations were extended to analyze the effects of various bonding parameters on the top-side longitudinal strain profiles in InP chips, and suggestions are made for minimizing strain variations. The measured strains were included in a DFB laser model, and are shown to cause changes in slope efficiency and threshold current. These changes in slope efficiency and threshold current with bonding compare well with data collected from a large ensemble of DFB laser devices measured before and after the mounting process.      

MLEK crystal growth of (100) indium phosphide

We have used a combined magnetic liquid encapsulated Kyropoulos/Czochralski (MLEK/ MLEC) technique to produce twin-free indium phosphide (InP) crystals. This technique has advantages over the standard LEC method used for commercial production of InP. By stabilizing convective flows with a magnetic field and controlling the angle between solid and liquid, one can grow large diameter twin-free (100) InP crystals; they are shaped with a flat top as is typical for Kyropoulos growth, and then pulled from the magnetically stabilized melt as in Czochralski growth. This shaping method has the benefit of maximizing the number of single crystal wafers which can be sliced from the boule. MLEK InP growth is distinguished from other methods such as LEC and MLEC with respect to solid-liquid interface shape, dislocation density, and impurity distribution. This process has demonstrated that twin-free InP (100) crystals can be consistently grown.     

A composite discrete-continuous approach to model the microwaveemission of vegetation

A new approach to model the microwave emission of vegetation is described in the paper. The modeling is based on the combination of both the discrete approach to simulate single scattering albedo ω and the continuous approach to simulate vegetation scattering effects. This composite model COMPOS is designed first to account for absorption effects in a more accurate way than the continuous approach and secondly to remain relevant for inversion procedures. Sensitivity studies showed that the use of a priori information about the vegetation structure is relevant to simulate ω. So, a reduced number of input parameters can be used in the composite model. Simulations of single scattering albedo ω, of canopy opacity and of wheat emissivity have been compared with several sets of radiometric data. The comparisons show that the composite approach simulations are consistent with the microwave observations