Modeling and analyzing vertical interconnections

Continual interest in miniaturization is driving electronic packaging toward three-dimensional (3-D) structures and system integration. Utilization of a third dimension allows designers much more freedom, but at the same time it leads to an increase in the complexity of signal routing. High-density of components and interconnection increases the need for electromagnetic (EM) modeling. This paper focuses on EM modeling and the analysis of vertical interconnection in a stacked 3-D package. Solder-plated polymer balls are used in vertical interconnection between interposers and laser-drilled vias through the interposers. High-frequency responses of the vertical interconnections were studied with 3-D full-wave software. Based on the EM analysis, we propose equivalent circuit models for vertical connections, which were verified with measurements. In addition, an impedance-matching technique in vertical interconnection is discussed.     

Initial results for automated computational modeling ofpatient-specific electromagnetic hyperthermia

Developments in finite-difference time-domain (FD-TD) computational modeling of Maxwell's equations, super-computer technology, and computed tomography (CT) imagery open the possibility of accurate numerical simulation of electromagnetic (EM) wave interactions with specific, complex, biological tissue structures. One application of this technology is in the area of treatment planning for EM hyperthermia. In this paper, we report the first highly automated CT image segmentation and interpolation scheme applied to model patient-specific EM hyperthermia. This novel system is based on sophisticated tools from the artificial intelligence, computer vision, and computer graphics disciplines. It permits CT-based patient-specific hyperthermia models to be constructed without tedious manual contouring on digitizing pads or CRT screens. The system permits in principle near real-time assistance in hyperthermia treatment planning. We apply this system to interpret actual patient CT data, reconstructing a 3-D model of the human thigh from a collection of 29 serial CT images at 10 mm intervals. Then, using FD-TD, we obtain 2-D and 3-D models of EM hyperthermia of this thigh due to a waveguide applicator. We find that different results are obtained from the 2-D and 3-D models, and conclude that full 3-D tissue models are required for future clinical usage.     

Unexpected physical phenomena indicated by FDTD modeling of theSigma-60 deep hyperthermia applicator

We investigate the numerical convergence properties of two-dimensional (2-D) and three-dimensional (3-D) finite-difference time-domain (FDTD) models of the BSD-2000 Sigma-60 annular phased array used for deep hyperthermia. The FDTD modeling data indicate unexpected physical phenomena for the case of Sigma-60 excitation of an elliptical tissue phantom embedded in a circular water bolus. These phenomena include: (1) high-Q energy storage; (2) electromagnetic (EM) mode flipping within the water bolus/phantom; and (3) whispering-gallery transmission of energy to the opposite side of the phantom relative to the exciting dipole pair. We conclude that these phenomena substantially impact the FDTD numerical modeling of this system, and further conclude that the whispering-gallery effect can impact clinical applications of the Sigma-60     

Calibration case study of natural source electromagnetic array datarecorded over a well in Oregon

Experimental results are described for a data acquisition method originally developed by F.X. Bostick (1986) that measures the electric field continuously along a profile. A three step sequence is used in the automated interpretation of electromagnetic (EM) array data. Following some preliminary steps in which an initial model is constructed, each interpretive refinement of the model consists of (1) forward computation of the array response and the numerically evaluated Jacobian, or matrix of first partial derivatives of the response with respect to model parameters; (2) data processing for static removal making use of the relatively short spatial wavelength behavior of the static effect in an analogous fashion to Bostick's method and tuning the data to the desired exploration objective; and (3) a linear correction is made to the model parameters. This three-step sequence is repeated, possibly varying the model definition or processing as interpretive judgement dictates, until the quality of fit of synthetic and field data is less than the typical data uncertainty. These data can be processed to remove shallow effects while maintaining the deep penetration characteristics of the natural electromagnetic (EM) field. Processing and modeling techniques for such data are demonstrated on both synthetic and field data. Very good agreement with actual borehole data is demonstrated     

Three-dimensional magnetotelluric modelling and inversion

An outline is presented of the nature of the problem of making quantitative use of magnetotelluric data for geophysical exploration. The authors discuss their view and experiences in dealing with the modeling and interpretation problems. The key step is considered to be the modeling step, which is that of predicting the response of a given distribution of electrical properties within the Earth to the electromagnetic excitation. Decisions about modeling methods also consider the interpretation process that will be used. The electromagnetic problem is three-dimensional which makes it necessary to use numerical methods. Difference equations are used and the authors investigate spacing requirements and two approaches to solving the system of equations: a relaxation method and a direct solution method. The relaxation method is found to be much faster, but it is very difficult to eliminate all the errors in the resulting solution. The interpretation problem is approached using a scheme that minimizes the joint probability of fitting the observed data and adhering to an a priori conductivity model. A relaxation procedure is used to solve this problem and the behavior of the procedure is examined associated with the application of magnetotellurics to exploration problems. Some of the problems in signal resolution that arise when interpreting the data are noted     

A rigorous coupled-wave analysis and crossed-diffraction gratinganalysis of radiation and scattering from three-dimensionalinhomogeneous objects

A rigorous coupled-wave analysis (RCWA) algorithm useful for studying the radiation and scattering from three-dimensional (3-D) inhomogeneous objects is developed. A spherical electromagnetic (EM) state variable (SV) form of Maxwell's equations is presented. The RCWA method is used to numerically study EM dipole radiation within and exterior to an inhomogeneous spherical shell     

Scattering of an Electromagnetic Pulse by a Moving Wedge

The paper is concerned with the analysis of 2-D scattering of an electromagnetic (EM) pulse by a perfectly conducting wedge moving with a relativistic velocity in a free space. The incident signal is described by a Dirac delta function. Analytical solution to this scattering problem is found, and its physical interpretation is given. The field representation, valid for all scatterer velocities, is then simplified to the case of moderate and low velocities, appropriate for practical applications.     

Nonrigid 2-D/3-D registration for patient specific bronchoscopy simulation with statistical shape modeling: phantom validation

This paper presents a nonrigid registration two-dimensional/three-dimensional (2-D/3-D) framework and its phantom validation for subject-specific bronchoscope simulation. The method exploits the recent development of five degrees-of-freedom miniaturized catheter tip electromagnetic trackers such that the position and orientation of the bronchoscope can be accurately determined. This allows the effective recovery of unknown camera rotation and airway deformation, which is modelled by an active shape model (ASM). ASM captures the intrinsic variability of the tracheo-bronchial tree during breathing and it is specific to the class of motion it represents. The method reduces the number of parameters that control the deformation, and thus greatly simplifies the optimisation procedure. Subsequently, pq-based registration is performed to recover both the camera pose and parameters of the ASM. Detailed assessment of the algorithm is performed on a deformable airway phantom, with the ground truth data being provided by an additional six degrees-of-freedom electromagnetic (EM) tracker to monitor the level of simulated respiratory motion.     

A moment method solution for the shielding properties of three-dimensional objects above a lossy half space

In this paper, a moment method (MM) solution for analyzing the electromagnetic (EM) shielding properties of three-dimensional (3-D) lossy dielectric and magnetic objects over a lossy half space is presented. An MM, based on a volume formulation and a special Green's function in the spectral domain, is developed. Plane waves with TMz and TEz polarizations incident upon 3-D lossy material structures are demonstrated for the shielding effects of those bodies in the presence of a lossy ground. Some of the results are compared with those evaluated by applying the finite difference time domain method, and good agreements are obtained. The MM solution can be used to study the shielding problems for 3-D objects located above a lossy ground.     

Estimating one-dimensional models from frequency-domainelectromagnetic data using modular neural networks

An artificial neural network interpretation system is being used to interpret data from a frequency-domain electromagnetic (EM) geophysical system in near real time. The interpretation system integrates 45 separate networks in a data visualization shell. The networks produce interpretations at three different transmitter-receiver (Tx-Rx) separations for half-space and layered-Earth interpretations. Modular neural networks (MNNs) were found to be the only paradigm that could successfully perform the layered-Earth interpretations. An MNN with 16 inputs, five local experts, each with seven hidden processing elements, and three outputs was trained on 4795 patterns for 200 epochs. For two-layer models with a resistivity contrast greater than 2:1, resistivity estimates had greater than 96% accuracy for the first-layer resistivity, greater than 98% for the second-layer resistivity, and greater than 96% for the thickness of the first layer. If the contrast is less than 2:1, the resistivity accuracies are unaffected but thickness estimates for layers less than 2 m are unreliable. A Tx-Rx separation of 16 m with maximum depth of penetration of 8 m was assumed for the example cited     

A spectral Lanczos decomposition method for solving 3-Dlow-frequency electromagnetic diffusion by the finite-elementmethod

A very efficient three-dimensional (3-D) solver for the diffusion of the electromagnetic fields in an inhomogeneous medium is described. The proposed method employs either the node-based or the edge-based finite-element method (FEM) to discretize Maxwell's equations. The resultant matrix equation is solved by the spectral Lanczos decomposition method (SLDM), which is based on the Krylov subspace (Lanczos) approximation of the solution in the frequency domain. By analyzing some practical geophysical problems, it is shown that the SLDM is extremely fast and, furthermore, the electromagnetic fields at many frequencies can be evaluated by performing the SLDM iteration only at the lowest frequency     

基于MoM-PO的各向异性阻抗面电磁散射研究

该文基于阻抗边界条件(IBC),采用矩量法-物理光学(MoM-PO)混合算法,研究了3维各向异性阻抗面的电磁散射特性。根据表面等效原理,将空间散射场等效为MoM区和PO区电磁流的辐射场,感应电磁流以3维RWG (Rao-Wilton-Glisson)矢量基函数展开。以表面阻抗并矢表征电磁参数,给出典型各向异性阻抗面目标的电磁仿真算例,结果与Mie级数等精确解吻合良好,显示了该方法的有效性。     

Full-wave simulation of electromagnetic coupling effects in RF and mixed-signal ICs using a time-domain finite-element method

This paper describes the computer simulation and modeling of distributed electromagnetic coupling effects in analog and mixed-signal integrated circuits. Distributed electromagnetic coupling effects include magnetic coupling of adjacent interconnects and/or planar spiral inductors, substrate coupling due to stray electric currents in a conductive substrate, and full-wave electromagnetic radiation. These coupling mechanisms are inclusively simulated by solving the full-wave Maxwell's equations using a three-dimensional (3-D) time-domain finite-element method. This simulation approach is quite general and can be used for circuit layouts that include isolation wells, guard rings, and 3-D metallic structures. A state-variable behavioral modeling procedure is used to construct simple linear models that mimic the distributed electromagnetic effects. These state-variable models can easily be incorporated into a VHDL-AMS simulation providing a means to include distributed electromagnetic effects into a circuit simulation.     

Extraction of network parameters in the electromagnetic analysis ofplanar structures using the method of moments

Integration of electromagnetic (EM) and circuit analyses for the modeling of spatially distributed microwave and millimeter-wave circuits requires the establishment of ports that are defined in both the circuit and EM realms. Four EM techniques are developed here and contrasted for the extraction of the port network parameters at circuit compatible ports. A full-wave method of-moments EM analysis directly yielding network parameters of a slot-stripline-slot structure is formulated     

Coupled Field Inside Shielding Enclosure With an Aperture Due to Nearby Lightning

Due to a nearby lightning return stroke, the coupled electromagnetic (EM) fields inside a rectangular shielding enclosure, on the finitely conducting ground, with an aperture in one wall are calculated numerically by using the finite-difference time-domain (FDTD) method. First, the near fields generated by the return stroke are obtained in two-dimensional (2-D) cylindrical coordinates by the FDTD method. Then, the coupled fields inside a rectangular shielding enclosure are calculated in three-dimensional (3-D) rectangular coordinates through the total field-scattered field connecting boundary, with the sources obtained by coordinates transformations of the return stroke near fields     

Petroleum exploration using controlled-source electromagneticmethods

A tutorial overview is presented of controlled-source electromagnetic (CSEM) geophysical methods as they are applied in petroleum exploration. CSEM methods utilize man-made sources to investigate the variation of electrical conductivity in the Earth, typically in the depth range of hundreds of meters to several kilometers. Over the frequency range used in CSEM (typically 0.1 Hz to 10 KHz), displacement currents can usually be ignored so the EM fields are diffusive in nature. The basic theory for CSEM methods and some simple approximate solutions which provide insight into the behavior of quasistatic EM fields are given. An overview of data inversion methods is also given, as well as examples of typical applications. It is argued that CSEM methods offer a number of advantages compared to natural-source electromagnetic (NSEM) methods such as magnetotellurics (MT). These include relative insensitivity to regional effects and small near-surface inhomogeneities which adversely affect MT, and the ability to utilize different source types and orientations to improve resolution. NSEM methods can, however, probe deeper conductivity structures than CSEM methods     

Numerical coupling models for complex systems and results

The paper gives a status of present electromagnetic (EM) coupling modeling capabilities. Starting from topologically designed systems, it shows how formal rules of the EM topology approach can provide guidance for EM coupling analysis or the development of protection against intentional electromagnetic interference (EMI)- related threats, even in the case of a poorly shielded system. After a review of currently available mature numerical techniques, a strategy allowing one to chain different numerical tools (including three-dimensional analysis tools, cable-networks tools, and circuit analysis procedures) is proposed in order to achieve EM coupling assessments on real complex systems. The paper also gives a status on several scientific trends likely to enhance modeling capabilities in the future.     

Simple high frequency solution for interior fields of open-ended parallel plate waveguide

The problem of electromagnetic (EM) plane wave scattering by an open-ended, perfectly-conducting, semi-infinite two-dimensional (2-D) parallel plate waveguide with a thin uniform layer of lossy material on its inner walls is analysed using a high frequency method. The fields coupled into the waveguide from the exterior are found via the uniform geometrical theory of diffraction (UTD) ray method.<>     

Finite-element method modeling of superconductors: from 2-D to 3-D

A three-dimensional (3-D) numerical modeling technique for solving problems involving superconducting materials is presented. The model is implemented in finite-element method software and is based on a recently developed 3-D formulation for general electromagnetic problems with solid conductors. It has been adapted for modeling of superconductors with nonlinear resistivity in 3-D, characterized by a power-law E-J relation. It has first been compared with an existing and verified two-dimensional (2-D) model: Compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Second, the model has been tested for computing the current distribution with typical 3-D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2-D models.     

Susceptibility analysis of wiring in a complex system combining a3-D solver and a transmission-line network simulation

This paper deals with the application of electromagnetic field-to-transmission-line coupling models for large cable systems analysis. It emphasizes the use of Agrawal's (1980) model applied here in a numerical simulation of an electromagnetic susceptibility problem up to 500 MHz. Based on the concepts of EM topology, the proposed methodology consists in calculating the incident fields with a three-dimensional (3-D) computer code and the coupling on cables with a multiconductor transmission-line network computer code. In order to validate the efficiency of this methodology in an industrial context, an experiment has been performed on a prototype wiring installed in a Renault Laguna car, stressed by an EM plane wave. Numerous validation configurations have been carried out. First, the prototype cable network under study has been tested on a ground plane to validate the coupling model but also, to validate the cable-network topology itself. Second, EM fields have been measured onto the structure and inside the structure. Then, they have been compared to 3-D calculations, performed with an FDTD code. Third, comparisons between measurements and calculations of bulk currents and voltages on 50 Ω loads on the wiring have been achieved