John Mould

Silicon substrate ringing in microfabricated ultrasonic transducers

Experimental and theoretical evidence of silicon substrate ringing in microfabricated ultrasonic transducers is presented. This ringing is clearly observed in immersion transducers with a 650 /spl mu/m thick substrate at 7 MHz and harmonics. An analytical model of the ringing is introduced, and simulations based on the model are shown to agree with experimental observation. Experimental results are further compared to simulations carried out in time-domain, large-scale PZFlex models and qualitative agreement is demonstrated. The insights gained from the simulations and experiments are used to design and fabricate a device whose ringing mode is eliminated with a backing layer.

A study of second harmonic generation by focused medical transducer pulses

Second harmonic imaging systems transmit relatively low frequency pulses, e.g., 2.5 MHz, and image the frequency-doubled second harmonic generated by acoustic nonlinearity. Imaging the second rather than the first harmonic eliminates significant wavefront aberration and attenuation on the forward path, narrows the beam, and suppresses sidelobes. This technique is used successfully in commercial medical imaging systems and may become dominant in the near future. However, system optimization requires a better understanding of second harmonic generation by focused ultrasound pulses in tissue. Data and simulations are presented quantifying aberration and second harmonic generation by two-dimensional ultrasound beams in realistic tissue models. A pseudo-spectral solver is used to achieve very high accuracy over long paths through lossy, nonlinear abdominal wall and liver.

Pseudospectral methods for large-scale bioacoustic models

Large-scale simulations of ultrasonic waves in heterogeneous tissue models are useful in biomedical R&D for imaging and therapeutics. The scale of bioacoustic models is hundreds of wavelengths. Typical 2D wave solvers are not practical at this scale, and 3D is out of the question, because of numerical errors and/or computer limits. To achieve much higher performance we use the periodic pseudospectral (PS) method, where spatial derivatives are calculated from FFTs over Cartesian grids. With a 4th order explicit time integrator, the PS method yields the necessary accuracy and efficiency. However, the domain must be periodic. We show how to circumvent this intrinsic limitation with Berengers perfectly matched layer (PML) on the boundaries. High accuracy, computational efficiency, and parallelism are demonstrated and a large-scale bioacoustic model is calculated. Generalizations of the method are described, including attenuation and nonlinearity.

Time-domain models of MUT array cross-talk in silicon substrates

Micromachined ultrasonic transducer (MUT) arrays are topical because, among other opportunities, they may supplant piezoelectric arrays in ultrasound medical imaging. However, imaging system companies need to explore performance and design issues thoroughly before making a serious commitment to these silicon-based electrostatic devices. To this end, a fully nonlinear, 3D MUT virtual prototyping capability was recently added to PZFlex. It is described here and applied to medical-type arrays. Simple representations of MUT plate vibration, including acoustic loading and radiation, are presented. Array cross-talk through the surface structure and silicon substrate is quantified using large-scale models. Additionally, an intuitive 1D electromechanical MUT model is developed for modeling and design guidance.

Laser alignment modeling using rigorous numerical simulations

This paper describes a three-dimensional computer modeling technique for alignment system simulation, and some example calculations. The technique has been developed to address issues of alignment and overlay accuracy for future generation VLSI technology. The analytical basis is a general finite element electromagnetic wave propagation code, EMFlex, that rigorously simulates light scattering from the 3-D alignment mark. Using the Nikon Laser Step Alignment (LSA) system as a model instrument, the overlay error and signal shape are simulated. Examples of an idealized asymmetric metal mark are studied. Preliminary results suggest that the rigorous simulations are substantially different from the one-dimensional Fresnel approximations that have been used previously.

NON UNIFORM GRATING COUPLERS FOR COUPLING OF GAUSSIAN BEAMS TO COMPACT WAVEGUIDES

Coupling to compact waveguides can have improved efficiency with use of a grating with non uniform teeth. A combined numerical and mathematical technique for designing this coupler and Finite Element Method results is presented. This paper is a preprint of the final paper which was published in the Integrated Photonics Research Technical Digest, Optical Society of America, 1994 * Currently at Integrated Photonic Systems, Inc. P.O. Box 717, Clarksburg, NJ 08510, (609) 259-1654, e-mail: lcw@intphsys.com NON UNIFORM GRATING COUPLERS FOR COUPLING OF GAUSSIAN BEAMS TO COMPACT WAVEGUIDES Lawrence C. West, Charles Roberts, and Jason Dunkel AT&T Bell Laboratories, Room 4G518, Holmdel, NJ 07733 (908) 949-8715 and Gregory Wojcik, John Mould, Jr., Weidlinger Associates, 4410 El Camino Real, Los Altos, CA 94022 (415) 949-3010 INTRODUCTION: The beams that emit from lasers are typically have a Gaussian spatial profile. Yet the field profile that emits from a uniform grating is one of a decaying exponential[1]. This fundamental mismatch prevents high efficiency (> 90%) coupling of light into compact waveguides. This limitation has been supported by the difficulty of making high precision waveguide gratings in the near infrared on semiconductor surfaces, especially when non-uniform. However, improved lithography techniques and use of practical devices in the mid-IR overcome these limitations. We discuss a method for understanding and designing grating couplers that may emit beam profiles other than a decaying exponential. Special attention is given to the Gaussian beam profile because of its importance to the laser community and it’s minimum diffraction spread. The basic technique is to vary the tooth width along the grating coupler so as to project the desired beam image. THE DESIGN METHOD: We use a numerical Finite Element Method[2] to measure the complex amplitude reflection, transmission, and scattered power coefficients for a single mode waveguide for various tooth depths, widths, and geometries. A single mode is injected into a waveguide and scattered off a single tooth within the waveguide. The resultant complex reflection and transmission coefficients into the single mode are measured. The energy difference of these and the original beam is assumed to be the scattered power. A table of these coefficients versus tooth parameters is created. For fabrication simplicity, we typically constrain ourselves to a constant depth tooth so the grating can be fabricated with a single mask and single etch. But actual lithography results, such as a change in etch hole profile for smaller teeth, can and should be taken into account by a substitution of those teeth with their respective coefficients. Figure 1: Geometry of scattering problem solved per tooth. The grating itself will be made of an ensemble of the individual teeth. The tooth spacing will remain roughly constant (this is not a chirped grating) but the tooth size will change. The spacing between teeth can be adjusted to correct for phase changes under the teeth so as to maintain a flat phase profile in the scattered beam, but this is a small percentage of the overall spacing. These Input Reflection Transmission Scattered Power GaAs Substrate Ge Waveguide tooth 0.6 m 1.75 m n = 4.0 n = 3.27 = 10.0 m 0 w reflection and transmission coefficients are calculated by subtracting the original mode as if there were no tooth and taking the remainder as a change in transmission or reflection caused by the tooth. Shown here is a chart of the coefficients for the tooth of Figure 1 with a 0.477 mm deep tooth. Of particular interest is the scattered power versus tooth width. Since the period of the grating is 3.0 micrometers to match the phase period of the waveguide mode, the maximum tooth size is 3.0 micrometers, at which point the waveguide is a smaller unconfined material. The scattered power is almost linear in tooth width with a proportionality of α. The reflection coefficient is almost a constant. We use these assumptions to derive a simple analytic form for the scattered light. A simple first order derivation of the desired tooth width can be found by assuming the grating is efficient, so that the power remaining in the grating is that which has not been scattered yet. Since the desired scattered power is proportional to the product of remaining power in the guide and the tooth width with constant α, we have the n’th tooth has a size of w p e e dz n z z z z z zc = ∫ α 2 0 2

Dielectric and mechanical absorption mechanisms for time and frequency domain transducer modeling

In all practical transduction systems-such as biomedical imaging arrays, underwater sonar systems or piezoelectric actuators and transformers, electromechanical losses impact overall system performance. Adverse effects of these losses include heat generation, sub-optimal electrical matching, and reduced operational efficiency. Consequently, it is imperative to fully understand the implications of loss mechanisms and incorporate them properly in numerical and analytical models. In this paper, time-domain electromechanical absorption mechanisms are studied in terms of their physical mechanisms and frequency-domain counterparts. We examine the mechanical and dielectric losses of some common piezoelectric materials and discuss some of the issues that arise in attempting to measure and model them.

Nonlinear pulse calculations and data in water and a tissue mimic

Nonlinear propagation is recognized as an important aspect of ultrasonic medical imaging. In particular, rigorous estimates of tissue bioeffects must include it. Regulatory standards rely on measurements in water to estimate effects in lossy tissue, but nonlinearity confuses the relationship. To help clarify the connection the authors complement laboratory hydrophone data with computer simulations of acoustic pulses in water and a tofu tissue mimic. A 2.25 MHz focused disk transducer is used instead of a rectangular medical array to facilitate modeling with a 2D pseudospectral solver that includes causal attenuation, inhomogeneity, multiple reflections, nonlinearity, and shock smoothing. Pressure scans near the transducer characterize the source and drive the wave solver. Measured and calculated nonlinear acoustic fields are compared over a 6 cm range in water and behind tofu cylinders. In the absence of high drive data the authors rely on nonlinear simulations to contrast water and tofu results, in anticipation of derating studies.

Some image modeling issues for I-line, 5X phase-shifting masks

The current image-theoretical basis for phase shifting masks (PSMs) relies on the scalar and Kirchhoff approximations, which neglect vector wave and edge diffraction effects around the mask. In this paper we use EMFlex finite element modeling to quantify vector diffraction effects, and show a method for modeling broadband illumination using the codes transient (optical pulse) capability and the Fourier transform in time. Simulations indicate that: the Kirchhoff approximation applied to etched quartz PSMs can lead to unacceptable errors due to a dark boundary layer on the quartz sidewall; diffraction produces relatively strong vector wave fields near feature edges but their contribution to the lithographic image is negligible; and the paraxial partial coherence approximation is generally valid for 4x or 5x projection systems. We discuss examples illustrating needs for better PSM metrology and phase measurements.

Anatomy of a Disaster: A Structural Investigation of the World Trade Center Collapses

The purpose of this study is to analyze the damage to the structure of each of the WTC Twin Towers due to the high speed impacts of the Boeing 767 airplanes and subsequent fires such as to elucidate why the Twin Towers stood for as long as they did, and why they ultimately collapsed. The Boeing 767 airplane attacks on WTC 1 and WTC 2 caused immediate and significant structural damage to the towers: In each case, exterior columns were severed and the floor system at the point of impact was damaged. The airplanes broke up during the impact and the resulting projectiles and fragments proceeded to inflict further damage to the core. Much of the impact damage to the exterior walls of the towers was evident. However, damage to the interior was not visible and cannot be quantified on the basis of the physical evidence. Dynamic nonlinear explicit finite element FLEX simulations coupled with independently validated airplane crash models were leveraged to understand and assess the structural states of damage to the tower interiors that could not be observed; this includes the degradation or loss of the load carrying capacity of columns and floor assemblies as well as the stripping of fireproofing from structural members. The impact damage to the structure was substantial but so were the reserve capacity and redundancy of the structure. Iterative analyses of the load redistribution in the impact damaged towers clearly indicate that the that the outer tube structure was very effective in developing Vierendeel action around the severed exterior columns and that the outrigger hat truss provided a substantial redundant load path away from the damaged core columns. Although not specifically designed for this purpose, the hat trusses served to delay the eventual collapse of the towers. These analyses also indicate that the damage to the corner of the core in WTC 2 left it in a state more vulnerable to subsequent thermal loads compared to WTC 1. This eccentric damage, more than the height of the airplane impact, resulted in a shorter time to collapse for WTC 2, considering that the fire environments in both towers were not meaningfully different. Further degradation or loss of the load carrying capacity of columns stripped of fireproofing by direct debris impact and heated by fire is shown to be the cause of each collapse. The examination of smoke flow from each building indicates that there were no floor collapses subsequent to the initial impact throughout the fire [1] and our 1 Chief Technology Officer, Weidlinger Associates Inc., 375 Hudson Street, New York, NY 10014. Phone: 212.367.3000. Email: abboud@wai.com. 2 Chairman, Weidlinger Associates Inc., 375 Hudson Street, New York, NY 10014. Phone: 212.367.3000. Email: levy@wai.com. 3 Weidlinger Associates, Inc., 4410 El Camino Real, Los Altos, CA 94022. Phone: 650.949.3010 4 Weidlinger Associates, Inc, 2525 Michigan Avenue, Santa Monica, CA 90404. Phone: 310.998.9154