Full-wave Solution Research Articles

Modeling of dual frequency capacitively coupled plasma sources utilizing a full-wave Maxwell solver: I. Scaling with high frequency

Dual frequency capacitively coupled plasma (DF-CCP) tools for etching and deposition for microelectronics fabrication typically use a high frequency (HF, tens to hundreds of MHz) to sustain the plasma and a low frequency (LF, a few to 10 MHz) for ion acceleration into the wafer. With an increase in both the HF and wafer size, electromagnetic wave effects (i.e. propagation, constructive and destructive interference) can affect the spatial distribution of power deposition and reactive fluxes to the wafer. In this paper, results from a two-dimensional computational investigation of a DF-CCP reactor, incorporating a full-wave solution of Maxwell's equations, are discussed. As in single frequency CCPs, the electron density transitions from edge high to center high with increasing HF. This transition is analyzed by correlating the spatial variation of the phase, magnitude and wavelength of the HF electric field to the spatial variation of the electron energy distributions and ionization sources. This transition is sensitive to the gas mixture, particularly those containing electronegative gases due to the accompany change in conductivity. The consequences of these wave effects on the ion energy distributions incident onto the wafer are also discussed.

Graded index photonic hole: Analytical and rigorous full wave solution

We present a rigorous full wave approach to the omnidirectional photonic hole (PH), an optical system inspired by celestial phenomena and characterized by a radially graded refractive index $n(r)\ensuremath{\sim}1/{r}^{\ensuremath{\alpha}/2}$. It is analytically demonstrated that light capture is effective for $\ensuremath{\alpha}\ensuremath{\ge}{\ensuremath{\alpha}}_{c}=2$. Our analyses are corroborated by precise numerical simulations of steady-state and time-evolution behaviors. The simulations indicate that the optical energy entering the PH system can be kept in captivity for a time duration ${t}_{d}$ scaling as ${t}_{d}\ensuremath{\sim}1/({\ensuremath{\alpha}}_{c}\ensuremath{-}\ensuremath{\alpha})$ when $\ensuremath{\alpha}$ approaches ${\ensuremath{\alpha}}_{c}$. A crucial difference in the time evolution of fields is shown between the cases with $\ensuremath{\alpha}$ close to and equal to ${\ensuremath{\alpha}}_{c}$.

Full Wave Solution for Intel CPU With a Heat Sink for EMC Investigations

A CPU with a heat sink (e.g. Intel Pentium 4 and Intel Pentium dual core) is a challenging problem for EMC analysis. A Very Large Scale Integrated (VLSI) device was modelled using the Finite Element Method (FEM) frequency domain solver to obtain a 3D full wave solution. The electromagnetic (EM) radiation emitted from these high power microelectronic circuits connected to a heat sink was found to have resonant frequencies around 2.4 GHz and 5 GHz with reflection coefficients less than -19 dB and -8 dB respectively. These resonant frequencies are very close to the operating frequency of both IEEE and Bluetooth wireless communication systems. This paper proposes a new benchmark model based on a dual core CPU and dual-source model.

Subspace projection filters for imaging in random media

We consider the problem of selective imaging extended reflectors in cluttered media. We propose a random travel time model for simulating the array response matrix in clutter and we compare it with the full wave solution. Our simplified model captures very well the full wave random medium behavior as this is illustrated by our numerical results. The algorithm for selective array imaging uses coherent interferometry on a filtered version of the data. The filter, which is based on the singular value decomposition of the response matrix, enhances the signal reflected by the edges of the reflector. We illustrate the performance of the imaging algorithm with numerical simulations in the regime of ultrasonic non-destructive testing in concrete.

Interpreting Stationary Wave Nonlinearity in Barotropic Dynamics

Abstract Stationary wave nonlinearity describes the self-interaction of stationary waves and is important in maintaining the zonally asymmetric atmospheric general circulation. However, the dynamics of stationary wave nonlinearity, which is often calculated explicitly in stationary wave models, is not well understood. Stationary wave nonlinearity is examined here in the simplified setting of the response to localized topographic forcing in quasigeostrophic barotropic dynamics in the presence and absence of transient eddies. It is shown that stationary wave nonlinearity accounts for most of the difference between the linear and full nonlinear response, particularly if the adjustment of the zonal-mean flow to the stationary waves is taken into account. The separate impact of transient eddy forcing is also quantified. Wave activity analysis shows that stationary wave nonlinearity in this setting is associated with Rossby wave critical layer reflection. A nonlinear stationary wave model, similar to those used in baroclinic stationary wave model studies, is also tested and is shown to capture the basic features of the full nonlinear stationary wave solution.

On full-wave solution for VLF waves in the near-Earth space

A VLF wave that propagates in the Earth's plasmasphere in the whistler mode must be converted into free space mode in order to be observed on the ground. This conversion takes place in collisional and highly inhomogeneous ionospheric plasma, which makes the description of the process not easy. Since an understanding of this process is vital for the analysis of VLF data, it has been in the focus of research since the beginning of whistler studies. A general approach to this problem, which is based on Maxwell's equations in magnetized plasma, is well developed and commonly accepted. However, its direct implementation meets serious difficulties which reveal themselves in numerical swamping. The intrinsic reason behind this is the existence of evanescent mode in the whistler frequency band. This leads to exponential growth of numerical solutions to the general set of equations. Various methods that have been developed to suppress this instability shift a solution of the physical problem to the field of simulation skill, so that the essential part of solution remains largely hidden. In this work we develop a new approach to the problem in which the evanescent mode is analytically excluded from consideration, making numerical calculations plain and straightforward. Using this approach, we find the field of whistler mode wave incident on the ionosphere from above in the whole span of altitudes, and calculate the reflection coefficient as a function of frequency for a number of incidence angles. We explain a quasiperiodic behaviour of the reflection coefficient by resonance absorption of the waves in the lower ionosphere.

Finite-element modeling of depth and range dependent acoustic propagation in oceanic waveguides

Finite-element models (FEMs) of ocean acoustic waveguides are capable of predicting the full wave solution including the effect of inhomogeneities and interfaces. However the method appears computationally feasible at present only for low to intermediate frequencies. The FEM discussed in this paper treats the radiation boundary condition involving multiple propagating modes using a penalty function approach. The effect of a point source has been represented as a pressure boundary condition on a small boundary surrounding the source. The FEM has been validated with a few examples of ideal waveguides. The FE results for a range and depth dependent parallel waveguide--an ASA benchmark problem [F. B. Jensen and C. M. Ferla, J. Acoust. Soc. Am. 87, 1499-1520 (1990)]--compare well with published results.

On Simplified Fast Modal Analysis for Through Silicon Vias in Layered Media Based Upon Full-Wave Solutions

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Based on equivalent magnetic frill array model and Galerkin's procedure, we present a simplified full-wave algorithm to characterize the propagation behavior and signal integrity of massive number of through silicon vias (TSV) for the 3-D system-in-package (SIP) and system-on-chip (SOC) applications. The proposed method employs the Fourier transform and takes advantage of circular cylindrical shapes with Bessel's functions and the addition theorem to solve the Helmholtz equations without resorting numerical discretization. As a result, it provides closed form solutions with high precision. Since the algorithm does not rely on numerically generated meshes, it gains one to two orders of magnitude in speed, compared to popular commercial software packages. Numerical examples demonstrate that the new method provides good agreement with the HFSS results. As the number of vias increases the new method gains more in both speed and accuracy. </para>

Characteristics of VLF atmospherics near the resonance frequency of the Earth-ionosphere waveguide 1.6–2.3 kHz by observations in the auroral region

Abstract. Recordings of ELF-VLF waves with the right-hand (RH) and the left-hand (LH) circular polarization were made in Northern Finland. Analysis showed a difference between the RH and LH polarized waves. A pronounced maximum of the wave amplitude was observed at the first critical frequency of the Earth-ionosphere waveguide (the first transverse resonance) around 1.6–2.3 kHz. The wave had the circular LH polarization at this maximum. To interpret observations, we computed the characteristics of the waveguide modes by using the full wave solution in the night model of the ionosphere. Computations show that the spectral maximum at the first transverse resonance frequency arises from a small absorption of the LH polarized radio wave in the magnetized ionosphere plasma, forming the upper boundary of the Earth-ionosphere waveguide.

Scattering of Electromagnetic Waves From a Rectangular Plate Using an Enhanced Stationary Phase Method Approximation

A time-efficient high frequency analytical model for the calculation of the scattered field from a perfect electric conductor (PEC) plate is presented here, which is based on the physical optics (PO) approximation and the stationary phase method (SPM). Using the SPM analysis for the three-dimensional (3D) scattering problem under consideration, the scattered electric field is calculated analytically. It follows that the analytical formula proposed here yields an accurate and fast algorithm for the calculation of the scattered electromagnetic (EM) field, which can be used trustfully in a variety of radio propagation problems. The accuracy of the proposed analytical method is checked through a straightforward numerical integration over the PO currents, as well as through finite element boundary integral full-wave exact solution. Comparison results are given in the far field, Fresnel zone and the near field area.

ERROR ANALYSIS OF A TWO-LAYER METHOD FOR THE ELECTROMAGNETIC CHARACTERIZATION OF CONDUCTOR-BACKED ABSORBING MATERIAL USING AN OPEN-ENDED WAVEGUIDE PROBE

A two-layer nondestructive method for characterizing the electric and magnetic properties of lossy conductor-backed magnetic materials using a ∞anged rectangular-waveguide probe is examined. The two re∞ection measurements necessary to determine both permittivity and permeability are made by flrst applying the probe to the material under test and then applying the probe to a known-material layer placed on top of the material under test. The theoretical re∞ection coe-cient is obtained using a rigorous full-wave solution, and an extrapolation scheme is used to minimize the error due to truncating the modal expansion of the waveguide flelds. An error analysis is performed to compare the performance of the technique to the two-thickness method, which utilizes two difierent thicknesses of the material under test. The properties of the known material layer that result in the least error due to network analyzer uncertainty are determined. The sensitivity of the two-layer method is also explored and discussed.

Computational Environment for Simulating Lightning Strokes in a Power Substation by Finite-Difference Time-Domain Method

A computational environment was developed for simulating transient electromagnetic phenomena involving complex structures. The system is based on the finite-difference time-domain method and includes tools such as a graphical user interface, a 3-D structure visualization module, thin-wire formulation, dielectrics and metallic blocks, perfectly matched layers, voltage and current sources, creation of field distribution images, voltage and current calculations, among others, all of them associated with automatic domain division for parallel (distributed) processing. In this paper, this system is used for obtaining full-wave solutions, for the first time, of lightning surge interactions with the structural part of a power substation. Parameters such as transitory step and touch voltages and potential distribution on ground surface are calculated for 1 kA peak for the injected surge current.

Analyzing absorption and scattering spectra of micro-scale structures with spectroscopic optical coherence tomography

We demonstrate the feasibility of characterizing the absorption and scattering spectra of micron-scale structures in a turbid medium using a spectroscopic optical coherence tomography (SOCT) system with a bandwidth of 430-650 nm. SOCT measurements are taken from phantoms composed of fluorescent microspheres. The absorption and scattering spectra are recovered with proper selections of spatial window width in the post processing step. Furthermore, we present an analysis using numerical OCT simulation based on full-wave solutions of the Maxwell's Equation to elucidate the origination of the multiple peaks in the OCT image for a single microsphere. Finally, we demonstrate the possibility of identifying contrast agents concentrated in micron-sized scale in an SOCT image. Two different types of microspheres in gel phantom are discriminated based on their distinguished absorbent feature.

Comparison of the Monte Carlo ion cyclotron heating model with the full-wave linear absorption model

To fully account for the wave-particle interaction physics in ion cyclotron resonant frequency (ICRF) heating experiment, finite orbit effects and non-Maxwellian distribution have to be self-consistently coupled with full-wave solutions. For this purpose, the five-dimensional Monte Carlo code ORBIT-RF [M. Choi et al., Phys. Plasmas 12, 1 (2005)] is being coupled with the two-dimensional full-wave code AORSA [E. F. Jaeger et al., Phys. Plasmas 13, 056101 (2006)] to iteratively evolve the ion distribution in four-dimensional spatial velocity space that is used to update the dielectric tensor in AORSA for evaluating the full-wave fields. In this paper, it is demonstrated that using the full-wave fields from a Maxwellian dielectric tensor in AORSA and confining the resonant ions to their initial orbits in ORBIT-RF, ORBIT-RF largely reproduces the AORSA linear wave absorption profiles for fundamental and higher harmonic ICRF heating. An exception is an observed inward shift in the ORBIT-RF absorption peak for high harmonics near the magnetic axis compared with that of AORSA, which can be attributed to a finite orbit width effect. The success of this verification supports the validity of the Monte Carlo wave-particle interaction model and the readiness of the iterative coupling between ORBIT-RF and AORSA for an improved modeling of ICRF heating experiments.

Special Issue on Remote Sensing of Building Interior

The 15 papers in this special issue focus on remote sensing of building interior and can be categorized into: 1) system design and instrumentation; 2) advanced imaging techniques for elimination of glint from large flat wall structures; 3) radar polarimetry; 4) passive microwave radiometry; 5) advanced forward models based on high-frequency methods as well as full-wave solutions based on finite-difference time-domain technique for large-scale problems; and 6) detection and identification techniques of behind the wall stationary and moving concealed and unconcealed targets.

Near-field optical power transmission of dipole nano-antennas

Nano-antennas in functional plasmonic applications require high near-field optical power transmission. In this study, a model is developed to compute the near-field optical power transmission in the vicinity of a nano-antenna. To increase the near-field optical power transmission from a nano-antenna, a tightly focused beam of light is utilized to illuminate a metallic nano-antenna. The modeling and simulation of these structures is performed using 3-D finite element method based full-wave solutions of Maxwell’s equations. Using the optical power transmission model, the interaction of a focused beam of light with plasmonic nano-antennas is investigated. In addition, the tightly focused beam of light is passed through a band-pass filter to identify the effect of various regions of the angular spectrum to the near-field radiation of a dipole nano-antenna. An extensive parametric study is performed to quantify the effects of various parameters on the transmission efficiency of dipole nano-antennas, including length, thickness, width, and the composition of the antenna, as well as the wavelength and half-beam angle of incident light. An optimal dipole nano-antenna geometry is identified based on the parameter studies in this work. In addition, the results of this study show the interaction of the optimized dipole nano-antenna with a magnetic recording medium when it is illuminated with a focused beam of light.

Physical optics modeling of 2D dielectric lenses

We propose an advanced physical optics formulation for the accurate modeling of dielectric lenses used in quasi-optical systems of millimeter, submillimeter, and infrared wave applications. For comparison, we obtain an exact full-wave solution of a two-dimensional lens problem and use it as a benchmark for testing and validation of asymptotic models being considered.

Analytical closed-form solutions for different configurations of parallel-coupled microstrip lines

Closed-form solutions are presented for the even- and odd-mode impedances of the parallel-coupled microstrip lines with different configurations. The first set of equations is for the conventional-coupled microstrip lines. The second set is for the parallel-coupled microstrip lines with a slotted ground plane and the third set is for the parallel-coupled microstrip lines with a slotted ground plane and a floating-potential conductor added to cover most of the slot in the ground plane. The solution is achieved using the conformal mapping technique, which also considers the effect of any fringe capacitor that has an impact on the impedance of the coupled lines. To validate the accuracy of the presented equations, a comparison is made with the available empirical solution (only for the conventional-coupled microstrip lines), a numerical solution (using Galerkin&apos;s technique) and the full-wave electromagnetic solution using the software HFSS. The result of the comparison indicates the high accuracy of the presented equations over a wide range of design parameters. The difference between the calculated values using the derived equations and those from the full-wave electromagnetic analysis is &lt;5% for most of the cases. To validate the derived equations experimentally, they are used to design a 3 dB coupler. The result of measurements on the manufactured coupler confirms the accuracy of the presented equations.

A Unified Finite-Element Solution From Zero Frequency to Microwave Frequencies for Full-Wave Modeling of Large-Scale Three-Dimensional On-Chip Interconnect Structures

It has been observed that a full-wave finite-element-based solution breaks down at low frequencies. This hinders its application to on-chip problems in which broadband modeling from direct current to microwave frequencies is required. Although a static formulation and a full-wave formulation can be stitched together to solve this problem, it is cumbersome to implement both static and full-wave solvers and make transitions between these two when necessary. In this work, a unified finite-element solution from zero frequency to microwave frequencies is developed for full-wave modeling of large-scale three-dimensional on-chip interconnect structures. In this solution, a single full-wave formulation is used. No switching to a static formulation is needed at low frequencies. This is achieved by first identifying the reason why a full-wave eigenvalue-based solution breaks down at low frequencies, and then developing an approach to eliminate the reason. The low frequency breakdown problem was found to be attributed to the discrepant frequency dependence of the real part and the imaginary part of the eigenvalues, which leads to an ill-conditioned eigenvalue system at low frequencies. The discrepant frequency dependence of the real part and the imaginary part is further attributed to the different scaling of the transverse and longitudinal fields with respect to frequency in a transmission-line type structure. By extracting transverse and longitudinal fields separately in the framework of a full-wave formulation, we avoid the numerical difficulty of solving an ill-conditioned eigen-system at low frequencies. The validity of the proposed approach is demonstrated by numerical and experimental results.

PEEC Formulation Based on Dyadic Green's Functions for Layered Media in the Time and Frequency Domains

This paper presents a novel time- and frequency-domain concept of modeling with the partial element equivalent circuit (PEEC) method, which applies the mixed potential integral equation (MPIE) with dyadic Green's functions for layered media (DGFLM-PEEC). On the one hand, it represents an exact full-wave semianalytical solution for an arbitrary configuration of traces and via holes in multilayered printed circuit boards. On the other hand, the DGFLM-PEEC model is represented in a circuit form, and thus, may be included in general-purpose circuit simulators. The paper derives a general DGFLM-PEEC formulation, which may be applied to all types of the MPIE with dyadic Green's functions. Using this concept, a particular type of layered media, namely a lossy dielectric between two grounds (stripline region), is thoroughly investigated and used to set up a particular DGFLM-PEEC model. The closed-form expressions for partial inductances and potential coefficients have been derived for this case. The time- and frequency-domain DGFLM-PEEC models for the stripline region have been validated using the measurements and the simulation by the method of moments.