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Evidence for a Multiphase ISM in Early Type Galaxies and Elliptical Galaxies with Strong Radio Continuum

We have observed NGC 1316 (Fornax A) with the ROSAT HRI. In this paper, we present the results of these observations and we complement them with the spectral analysis of the archival PSPC data. The spectral properties suggest the presence of a significant component of thermal X-ray emission (greater than 60%), amounting to approx. 10(exp 9) solar mass of hot ISM. Within 3 feet from the nucleus of NGC 1316, the HRI X-ray surface brightness falls as r(exp -2) following the stellar light. In the inner approx. 30 inch., however, the X-ray surface brightness is significantly elongated, contrary to the distribution of stellar light, which is significantly rounder within 10 inch. This again argues for a non-stellar origin of the X-ray emission. This flattened X-ray feature is suggestive of either the disk-like geometry of a rotating cooling flow and/or the presence of extended, elongated dark matter. By comparing the morphology of the X-ray emission with the distribution of optical dust patches, we find that the X-ray emission is significantly reduced at the locations where the dust patches are more pronounced, indicating that at least some of the X-ray photons are absorbed by the cold ISM. We also compare the distribution of the hot and cold ISM with that of the ionized gas, using recently obtained H(sub alpha) CCD data. We find that the ionized gas is distributed roughly along the dust patches and follows the large scale X-ray distribution at r greater than 1 foot from the nucleus. However, there is no one-to-one correspondence between ionized gas and hot gas. Both morphological relations and kinematics suggest different origins for hot and cold ISM. The radio jets in projection appear to pass perpendicularly through the central X-ray ellipsoid. Comparison of thermal and radio pressures suggests that the radio jets are confined by the surrounding hot gaseous medium.

Kim, Dong Woo↗

High-Velocity Ly(Alpha) Emission from SMR 1987A

The high-velocity Ly(Alpha) emission from SN 1987A observed with the Space Telescope Imaging Spectrograph (STIS) evidently comes from a reverse shock formed where the outer envelope of SN 1987A strikes ionized gas inside the inner circumstellar ring. The observations can be explained by a simple kinematic model, in which the Ly(Alpha) emission comes from hydrogen atoms with radial velocity approximately 15,000 km s(exp -1) crossing a reverse shock in the shape of a slightly prolate ellipsoid with equatorial radius 4.8 x 10(exp 17) cm or approximately 80% of the distance to the inner surface of the inner ring. N v double Lambda 1239, 1243 emission, if present, has a net luminosity approximately less than 30% times that of the Ly(Alpha) emission. Future STIS observations should enable us to predict the time of impact with the inner ring and to determine unambiguously whether or not N v emission is present. These observations will offer a unique opportunity to probe the structure of SN 1987A's circumstellar environment and the hydrodynamics and kinetics of very fast shocks.

Michael, Eli↗

Galaxy Cluster Shapes and Systematic Errors in the Hubble Constant as Determined by the Sunyaev-Zel'dovich Effect

Imaging of the Sunyaev-Zei'dovich (S-Z) effect in galaxy clusters combined with the cluster plasma x-ray diagnostics can measure the cosmic distance scale to high accuracy. However, projecting the inverse-Compton scattering and x-ray emission along the cluster line-of-sight will introduce systematic errors in the Hubble constant, H$-O$, because the true shape of the cluster is not known. This effect remains present for clusters that are otherwise chosen to avoid complications for the S-Z and x-ray analysis, such as plasma temperature variations, cluster substructure, or cluster dynamical evolution. In this paper we present a study of the systematic errors in the value of H$-0$, as determined by the x-ray and S-Z properties of a theoretical sample of triaxial isothermal 'beta-model' clusters, caused by projection effects and observer orientation relative to the model clusters' principal axes. The model clusters are not generated as ellipsoids of rotation, but have three independent 'core radii', as well as a random orientation to the plane of the sky.

Sulkanen, Martin E.↗

Evidence of Microfossils in Carbonaceous Chondrites

Investigations have been carried out on freshly broken, internal surfaces of the Murchison, Efremovka and Orgueil carbonaceous chondrites using Scanning Electron Microscopes (SEM) in Russia and the Environmental Scanning Electron Microscope (ESEM) in the United States. These independent studies on different samples of the meteorites have resulted in the detection of numerous spherical and ellipsoidal bodies (some with spikes) similar to the forms of uncertain biogenicity that were designated "organized elements" by prior researchers. We have also encountered numerous complex biomorphic microstructures in these carbonaceous chondrites. Many of these complex bodies exhibit diverse characteristics reminiscent of microfossils of cyanobacteria such as we have investigated in ancient phosphorites and high carbon rocks (e.g. oil shales). Energy Dispersive Spectroscopy (EDS) analysis and 2D elemental maps shows enhanced carbon content in the bodies superimposed upon the elemental distributions characteristic of the chondritic matrix. The size, distribution, composition, and indications of cell walls, reproductive and life cycle developmental stages of these bodies are strongly suggestive of biology' These bodies appear to be mineralized and embedded within the meteorite matrix, and can not be attributed to recent surface contamination effects. Consequently, we have interpreted these in-situ microstructures to represent the lithified remains of prokaryotes and filamentous cyanobacteria. We also detected in Orgueil microstructures morphologically similar to fibrous kerite crystals. We present images of many biomorphic microstructures and possible microfossils found in the Murchison, Efremovka, and Orgueil chondrites and compare these forms with known microfossils from the Cambrian phosphate-rich rocks (phosphorites) of Khubsugul, Northern Mongolia.

Hoover, Richard B.↗

Elementary Theoretical Forms for the Spatial Power Spectrum of Earth's Crustal Magnetic Field

The magnetic field produced by magnetization in Earth's crust and lithosphere can be distinguished from the field produced by electric currents in Earth's core because the spatial magnetic power spectrum of the crustal field differs from that of the core field. Theoretical forms for the spectrum of the crustal field are derived by treating each magnetic domain in the crust as the point source of a dipole field. The geologic null-hypothesis that such moments are uncorrelated is used to obtain the magnetic spectrum expected from a randomly magnetized, or unstructured, spherical crust of negligible thickness. This simplest spectral form is modified to allow for uniform crustal thickness, ellipsoidality, and the polarization of domains by an periodically reversing, geocentric axial dipole field from Earth's core. Such spectra are intended to describe the background crustal field. Magnetic anomalies due to correlated magnetization within coherent geologic structures may well be superimposed upon this background; yet representing each such anomaly with a single point dipole may lead to similar spectral forms. Results from attempts to fit these forms to observational spectra, determined via spherical harmonic analysis of MAGSAT data, are summarized in terms of amplitude, source depth, and misfit. Each theoretical spectrum reduces to a source factor multiplied by the usual exponential function of spherical harmonic degree n due to geometric attenuation with attitude above the source layer. The source factors always vary with n and are approximately proportional to n(exp 3) for degrees 12 through 120. The theoretical spectra are therefore not directly proportional to an exponential function of spherical harmonic degree n. There is no radius at which these spectra are flat, level, or otherwise independent of n.

Voorhies, C.↗

Summary of Research Report

Ten papers, published in various publications, on buckling, and the effects of imperfections on various structures are presented. These papers are: (1) Buckling mode localization in elastic plates due to misplacement in the stiffner location; (2) On vibrational imperfection sensitivity on Augusti's model structure in the vicinity of a non-linear static state; (3) Imperfection sensitivity due to elastic moduli in the Roorda Koiter frame; (4) Buckling mode localization in a multi-span periodic structure with a disorder in a single span; (5) Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling; (6) Derivation of multi-dimensional ellipsoidal convex model for experimental data; (7) Passive control of buckling deformation via Anderson localization phenomenon; (8)Effect of the thickness and initial im perfection on buckling on composite cylindrical shells: asymptotic analysis and numerical results by BOSOR4 and PANDA2; (9) Worst case estimation of homology design by convex analysis; (10) Buckling of structures with uncertain imperfections - Personal perspective.

Elishakoff, Isaac↗

Time of Arrival Retrievals on an Oblate Spheroidal Earth

The current National Lightning Detection Network (NLDN) retrieval algorithm is based on a chi sq minimization. This numerical approach finds the lightning ground strike location on an ellipsoidal Earth that optimally agrees with multiple station time of arrival (TOA) measurements and, if available, magnetic bearing data. In addition, an analytic solution for determining lightning ground strike locations on a spherical Earth using only TOA data has been recently introduced. In the current work, a quasi-analytic approach is suggested for determining lightning ground strike locations on an oblate spheroidal Earth by perturbing the spherical model results proposed by Koshak. Latitude, longitude, time, and the associated perturbed quantities are related through terms in a Taylor series. The correction terms may be considered collectively as a vector which may be calculated by an overconstrained inversion. Expressions for the derivatives contained in the Taylor series are given in terms of elliptic integrals.

Solakiewicz, Richard J.↗

A Spherical Earth Solution for TOA Lightning Location Retrieval

With the advent of high-speed digital computers, the method of chi square minimization is a highly practical means for analyzing a wide variety of (otherwise intractable) nonlinear inversion problems in applied mathematical physics. Little thought or effort is required to apply the chi square method to obtain quick and reasonable estimates of a solution, and the method offers a means to assess retrieval errors. Because the method is simple and practical it is sometimes hastily applied to problems that can be solved by formal analytic or quasi-analytic means. Presently, Global Atmospherics Inc. (GAI) finds the minimum of a chi square function to analyze time-of-arrival (TOA) and magnetic bearing data derived from the National Lightning Detection Network (NLDN); ellipsoidal Earth geometry is assumed. An analytic solution to this problem has not yet been attained, but the consideration and solving of less general problem statements might eventually lead to a final solution. In the present study, the problem of retrieving lightning ground-strike location on a spherical Earth surface using a network of 4 or more time-of-arrival (TOA) sensors is considered. It is shown that this problem has an analytic solution and therefore does not require the use of nonlinear estimation theory (such as the chi square method mentioned above). The mathematical robustness of the analytic solution is tested using computer-generated lightning sources and simulated TOA measurement errors. A quasi-analytic extension of the spherical Earth solution for an oblate spheroidal Earth geometry is considered in a related study. The incorporation of magnetic bearing information into these analytic solutions would lead to a general and elegant analytic retrieval scheme that would most likely replace the chi square estimation theory currently employed by Global Atmospherics Inc. (GAI).

Koshak, William J,↗

Mars Global Reference Atmospheric Model (Mars-GRAM) Version 3.8: Users Guide

Mars Global Reference Atmospheric Model (Mars-GRAM) Version 3.8 is presented and its new features are discussed. Mars-GRAM uses new values of planetary reference ellipsoid radii, gravity term, and rotation rate (consistent with current JPL values) and includes centrifugal effects on gravity. The model now uses NASA Ames Global Circulation Model low resolution topography. Curvature corrections are applied to winds and limits based on speed of sound are applied. Altitude of the F1 ionization peak and density scale height, including effects of change of molecular weight with altitude are computed. A check is performed to disallow temperatures below CO2 sublimination. This memorandum includes instructions on obtaining Mars-GRAM source code and data files and running the program. Sample input and output are provided. An example of incorporating Mars-GRAM as an atmospheric subroutine in a trajectory code is also given.

Justus, C. G.↗

Postseismic Deformation after the 1964 Great Alaskan Earthquake: Collaborative Research with Goddard Space Flight Center

The purpose of this project was to carry out GPS observations on the Kenai Peninsula, southern Alaska, in order to study the postseismic and contemporary deformation following the 1964 Alaska earthquake. All of the research supported in this grant was carried out in collaboration with Dr. Steven Cohen of Goddard Space Flight Center. The research funding from this grant primarily supported GPS fieldwork, along with the acquisition of computer equipment to allow analysis and modeling of the GPS data. A minor amount of salary support was provided by the PI, but the great majority of the salary support was provided by the Geophysical Institute. After the expiration of this grant, additional funding was obtained from the National Science Foundation to continue the work. This grant supported GPS field campaigns in August 1995, June 1996, May-June and September 1997, and May-June 1998. We initially began the work by surveying leveling benchmarks on the Kenai peninsula that had been surveyed after the 1964 earthquake. Changes in height from the 1964 leveling data to the 1995+ GPS data, corrected for the geoid-ellipsoid separation, give the total elevation change since the earthquake. Beginning in 1995, we also identified or established sites that were suitable for long-term surveying using GPS. In the subsequent annual GPS campaigns, we made regular measurements at these GPS marks, and steadily enhanced our set of points for which cumulative postseismic uplift data were available. From 4 years of Global Positioning System (GPS) measurements, we find significant spatial variations in present-day deformation between the eastern and western Kenai peninsula, Alaska. Sites in the eastern Kenai peninsula and Prince William Sound move to the NNW relative to North America, in the direction of Pacific-North America relative plate motion. Velocities decrease in magnitude from nearly the full plate rate in southern Prince William Sound to about 30 mm/yr at Seward and to about 5 mm/yr near Anchorage. In contrast, sites in the western Kenai peninsula move to the SW, in a nearly trenchward direction, with a velocity of about 20 mm/yr. The data are consistent with the shallow plate interface offshore and beneath the eastern Kenai and Prince William Sound being completely locked or nearly so, with elastic strain accumulation resulting in rapid motion in the direction of relative plate motion of sites in the overriding plate. The velocities of sites in the western Kenai, along strike to the southwest, are opposite in sign with those predicted from elastic strain accumulation. These data are incompatible with a significant locked region in this segment of the plate boundary. Trenchward velocities are found also for some sites in the Anchorage area. We interpret the trenchward velocities as being caused by a continuing postseismic transient from the 1964 great Alaska earthquake.

Freymueller, Jeffrey T.↗

Nontangent, Developed Contour Bulkheads for a Single-Stage Launch Vehicle

Dry weights for single-stage launch vehicles that incorporate nontangent, developed contour bulkheads are estimated and compared to a baseline vehicle with 1.414 aspect ratio ellipsoidal bulkheads. Weights, volumes, and heights of optimized bulkhead designs are computed using a preliminary design bulkhead analysis code. The dry weights of vehicles that incorporate the optimized bulkheads are predicted using a vehicle weights and sizing code. Two optimization approaches are employed. A structural-level method, where the vehicle's three major bulkhead regions are optimized separately and then incorporated into a model for computation of the vehicle dry weight, predicts a reduction of4365 lb (2.2 %) from the 200,679-lb baseline vehicle dry weight. In the second, vehicle-level, approach, the vehicle dry weight is the objective function for the optimization. For the vehicle-level analysis, modified bulkhead designs are analyzed and incorporated into the weights model for computation of a dry weight. The optimizer simultaneously manipulates design variables for all three bulkheads to reduce the dry weight. The vehicle-level analysis predicts a dry weight reduction of 5129 lb, a 2.6% reduction from the baseline weight. Based on these results, nontangent, developed contour bulkheads may provide substantial weight savings for single stage vehicles.

Wu, K. Chauncey↗

Antarctic Rebound and the Time-Dependence of the Earth's Shape

Great strides have been made during the past 30 years in refining models of the last global glaciation. The refinements draw upon a vastly expanded relative sea level and sedimentary core record. Furthermore, we now possess a sharpened understanding of the mechanisms that drive climate changes associated with deglaciation. Some 15 years ago, using only 5.5 years of ranging data, analyses of the drift in LAGEOS I node acceleration was used to infer that postglacial rebound was responsible for a secular change in the Earth's ellipsoidal shape (Yoder et al., .1983]. Today there exists a wealth of geodynamics satellite orbit data that constrain the secular time-dependence of the Earth's shape and low order gravity field, which includes mass redistribution from present-day glacier and great ice sheet imbalance and from postglacial rebound. We have shown that an unambiguous determination of the secular variation in the Earth's pear shaped harmonic (l = 3, m = 0) might provide information that bears on the present-day mass balance of Antarctica. This issue is revisited in light of new constraints on glacial loading during the late-Pleistocene and Holocene. An especially critical issue for the interpretation of secular odd degree zonal harmonics, l = 3 to 7, is the timing and magnitude of the deglaciation of Antarctica from Last Glacial Maximum. We explore ways in which the recovery of secular variation in both zonal and non-zonal harmonics for l = 2 through 7 can improve constraints on both rebound and present-day ice sheet balance.

Ivins, Erik R.↗

Surface Change Detection Using Large Footprint Laser Altimetry

Laser altimeters provide a precise and accurate method for mapping topography at fine horizontal and vertical scales. A laser altimeter provides range by measuring the roundtrip flight time of a short pulse of laser light from the laser altimeter instrument to the target surface. The range is then combined with laser beam pointing knowledge and absolute position knowledge to provide an absolute measurement of the surface topography. Newer generations of laser altimeters measure the range by recording the shape and time of the outgoing and received laser pulses. The shape of the return pulse can also provide unique information about the vertical structure of material such as vegetation within each laser footprint. Distortion of the return pulse is caused by the time-distributed reflections adding together and representing the vertical distribution of surfaces within the footprint. Larger footprints (10 - 100m in diameter) can support numerous target surfaces and thus provide the potential for producing complex return pulses. Interpreting the return pulse from laser altimeters has evolved from simple timing between thresholds, range-walk corrections, constant-fraction discriminators, and multi-stop time interval units to actual recording of the time varying return pulse intensity - the return waveform. Interpreting the waveform can be as simple as digitally thresholding the return pulse, calculating a centroid, to fitting one or more gaussian pulse-shapes to the signal. What we present here is a new technique for using the raw recorded return pulse as a raw observation to detect centimeter-level vertical topographic change using large footprint airborne and spaceborne laser altimetry. We use the correlation of waveforms from coincident footprints as an indication of the similarity in structure of the waveforms from epoch to epoch, and assume that low correlation is an indicator of vertical structure or elevation change. Thus, using vertically and horizontally geolocated waveforms as raw observables (i.e., waveforms tied to a common reference ellipsoid), we assess whether epoch-to-epoch vertical ground motion results in a decrease in the correlation of coincident waveforms over time, and whether this can be used to quantify the magnitude of the deformation. Results of computer models and an example over an area of eroded beachfront will be presented.

Blair, J. Bryan↗

X-Ray and UV Orbital Phase Dependence in LMC X-3

The black-hole binary LMC X-3 is known to be variable on time scales of days to years. We investigated X-ray and ultraviolet variability in the system as a function of the 1.7 d binary orbit using a 6.4 day observation with the Rossi X-ray Timing Explorer (RXTE) in 1998 December. An abrupt 14 % flux decrease lasting nearly an entire orbit was followed by a return to previous flux levels. This behavior occurred twice at nearly the same binary phase, but is not present in consecutive orbits. When the X-ray flux is at lower intensity, a periodic amplitude modulation of 7 % is evident in data folded modulo the orbital period. The higher intensity data show weaker correlation with phase. This is the first report of X-ray variability at the orbital period of LMC X-3. Archival RXTE observations of LMC X-3 during a high flux state in 1996 December show similar phase dependence. An ultraviolet light curve obtained with the High Speed Photometer (HSP) on the Hubble Space Telescope (HST) shows a phase dependent variability consistent with that observed in the visible, ascribed to the ellipsoidal variation of the visible star. The X-ray spectrum of LMC X-3 is acceptably represented by a phenomenological disk black-body plus a power law. Changes in the spectrum of LMX X-3 during our observations are compatible with earlier observations during which variations in the 2-10 keV flux are closely correlated with the disk geometry spectral model parameter.

Dolan, Joseph F.↗

2D Quantum Mechanical Study of Nanoscale MOSFETs

With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density-gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. We present the results of our simulations of MIT 25, 50 and 90 nm "well-tempered" MOSFETs and compare them to those of classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. Surprisingly, the self-consistent potential profile shows lower injection barrier in the channel in quantum case. These results are qualitatively consistent with ID Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and subthreshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.

Svizhenko, Alexei↗

2D Quantum Transport Modeling in Nanoscale MOSFETs

With the onset of quantum confinement in the inversion layer in nanoscale MOSFETs, behavior of the resonant level inevitably determines all device characteristics. While most classical device simulators take quantization into account in some simplified manner, the important details of electrostatics are missing. Our work addresses this shortcoming and provides: (a) a framework to quantitatively explore device physics issues such as the source-drain and gate leakage currents, DIBL, and threshold voltage shift due to quantization, and b) a means of benchmarking quantum corrections to semiclassical models (such as density- gradient and quantum-corrected MEDICI). We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions, oxide tunneling and phase-breaking scattering are treated on equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Quantum simulations are focused on MIT 25, 50 and 90 nm "well- tempered" MOSFETs and compared to classical and quantum corrected models. The important feature of quantum model is smaller slope of Id-Vg curve and consequently higher threshold voltage. These results are quantitatively consistent with I D Schroedinger-Poisson calculations. The effect of gate length on gate-oxide leakage and sub-threshold current has been studied. The shorter gate length device has an order of magnitude smaller current at zero gate bias than the longer gate length device without a significant trade-off in on-current. This should be a device design consideration.

Svizhenko, Alexei↗

Solar Collector With Image-Forming Mirror Cavity to Irradiate Small Central Volume

A unique solar thermal chamber has been designed and fabricated to produce the maximum concentration of solar energy and higher temperature possible. Its primary purpose was for solar plasma propulsion experiments and related material specimen testing above 3000 K. The design not only maximized solar concentration, but also, minimized infrared heat loss. This paper provides the underlying theory and operation of the chamber and initial optical correlation to the actual fabricated hardware. The chamber is placed at the focal point of an existing primary concentrator with a 2.74 m (9 ft) focal length. A quartz lens focuses a small sun image at the inlet hole of the mirrored cavity. The lens focuses two image planes at prescribed positions; the sun at the cavity's entrance hole and the primary concentrator at the junction plane of two surfaces that form the cavity chamber. The back half is an ellipsoid reflector that produces a 1.27 cm diameter final sun image. The image is "suspended in space," 7.1 cm away from the nearest cavity surface, to minimize thermal and contaminate damage to the mirror surfaces. A hemisphere mirror makes up the front chamber and has its center of curvature at the target image, where rays leaving the target are reflected back upon themselves, minimizing radiation losses.

Buchele, Don↗

2-D Modeling of Nanoscale MOSFETs: Non-Equilibrium Green's Function Approach

We have developed physical approximations and computer code capable of realistically simulating 2-D nanoscale transistors, using the non-equilibrium Green's function (NEGF) method. This is the most accurate full quantum model yet applied to 2-D device simulation. Open boundary conditions and oxide tunneling are treated on an equal footing. Electrons in the ellipsoids of the conduction band are treated within the anisotropic effective mass approximation. Electron-electron interaction is treated within Hartree approximation by solving NEGF and Poisson equations self-consistently. For the calculations presented here, parallelization is performed by distributing the solution of NEGF equations to various processors, energy wise. We present simulation of the "benchmark" MIT 25nm and 90nm MOSFETs and compare our results to those from the drift-diffusion simulator and the quantum-corrected results available. In the 25nm MOSFET, the channel length is less than ten times the electron wavelength, and the electron scattering time is comparable to its transit time. Our main results are: (1) Simulated drain subthreshold current characteristics are shown, where the potential profiles are calculated self-consistently by the corresponding simulation methods. The current predicted by our quantum simulation has smaller subthreshold slope of the Vg dependence which results in higher threshold voltage. (2) When gate oxide thickness is less than 2 nm, gate oxide leakage is a primary factor which determines off-current of a MOSFET (3) Using our 2-D NEGF simulator, we found several ways to drastically decrease oxide leakage current without compromising drive current. (4) Quantum mechanically calculated electron density is much smaller than the background doping density in the poly silicon gate region near oxide interface. This creates an additional effective gate voltage. Different ways to. include this effect approximately will be discussed.

Svizhenko, Alexei↗