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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Backus Effect on a Perpendicular Errors in Harmonic Models of Real vs. Synthetic Data

Measurements of geomagnetic scalar intensity on a thin spherical shell alone are not enough to separate internal from external source fields; moreover, such scalar data are not enough for accurate modeling of the vector field from internal sources because of unmodeled fields and small data errors. Spherical harmonic models of the geomagnetic potential fitted to scalar data alone therefore suffer from well-understood Backus effect and perpendicular errors. Curiously, errors in some models of simulated 'data' are very much less than those in models of real data. We analyze select Magsat vector and scalar measurements separately to illustrate Backus effect and perpendicular errors in models of real scalar data. By using a model to synthesize 'data' at the observation points, and by adding various types of 'noise', we illustrate such errors in models of synthetic 'data'. Perpendicular errors prove quite sensitive to the maximum degree in the spherical harmonic expansion of the potential field model fitted to the scalar data. Small errors in models of synthetic 'data' are found to be an artifact of matched truncation levels. For example, consider scalar synthetic 'data' computed from a degree 14 model. A degree 14 model fitted to such synthetic 'data' yields negligible error, but amplifies 4 nT (rmss) added noise into a 60 nT error (rmss); however, a degree 12 model fitted to the noisy 'data' suffers a 492 nT error (rmms through degree 12). Geomagnetic measurements remain unaware of model truncation, so the small errors indicated by some simulations cannot be realized in practice. Errors in models fitted to scalar data alone approach 1000 nT (rmss) and several thousand nT (maximum).

Voorhies, C. V.↗
NASA NTRS1992

Bypass transition in compressible boundary layers

Transition to turbulence in aerospace applications usually occurs in a strongly disturbed environment. For instance, the effects of free-stream turbulence, roughness and obstacles in the boundary layer strongly influence transition. Proper understanding of the mechanisms leading to transition is crucial in the design of aircraft wings and gas turbine blades, because lift, drag and heat transfer strongly depend on the state of the boundary layer, laminar or turbulent. Unfortunately, most of the transition research, both theoretical and experimental, has focused on natural transition. Many practical flows, however, defy any theoretical analysis and are extremely difficult to measure. Morkovin introduced in his review paper the concept of bypass transition as those forms of transition which bypass the known mechanisms of linear and non-linear transition theories and are currently not understood by experiments. In an effort to better understand the mechanisms leading to transition in a disturbed environment, experiments are conducted studying simpler cases, viz. the effects of free stream turbulence on transition on a flat plate. It turns out that these experiments are very difficult to conduct, because generation of free stream turbulence with sufficiently high fluctuation levels and reasonable homogeneity is non trivial. For a discussion see Morkovin. Serious problems also appear due to the fact that at high Reynolds numbers the boundary layers are very thin, especially in the nose region of the plate where the transition occurs, which makes the use of very small probes necessary. The effects of free-stream turbulence on transition are the subject of this research and are especially important in a gas turbine environment, where turbulence intensities are measured between 5 and 20 percent, Wang et al. Due to the fact that the Reynolds number for turbine blades is considerably lower than for aircraft wings, generally a larger portion of the blade will be in a laminar transitional state. The effects of large free stream turbulence in compressible boundary layers at Mach numbers are examined both in the subsonic and transonic regime using direct numerical simulations. The flow is computed over a flat plate and curved surface. while many applications operate in the transonic regime. Due the nature of their numerical scheme, a non-conservation formulation of the Navier-Stokes equations, it is a non-trivial extension to compute flow fields in the transonic regime. This project aims at better understanding the effects of large free-stream turbulence in compressible boundary layers at mach number both in the subsonic and transonic regime using direct numerical simulations. The present project aims at computing the flow over a flat plate and curved surface. This research will provide data which can be used to clarify mechanisms leading to transition in an environment with high free stream turbulence. This information is useful for the development of turbulence models, which are of great importance for CFD applications, and are currently unreliable for more complex flows, such as transitional flows.

Vandervegt, J. J.↗
NASA NTRS2015

Real-Time On-Board Airborne Demonstration of High-Speed On-Board Data Processing for Science Instruments (HOPS)

The project called High-Speed On-Board Data Processing for Science Instruments (HOPS) has been funded by NASA Earth Science Technology Office (ESTO) Advanced Information Systems Technology (AIST) program since April, 2012. The HOPS team recently completed two flight campaigns during the summer of 2014 on two different aircrafts with two different science instruments. The first flight campaign was in July, 2014 based at NASA Langley Research Center (LaRC) in Hampton, VA on the NASA's HU-25 aircraft. The science instrument that flew with HOPS was Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS) CarbonHawk Experiment Simulator (ACES) funded by NASA's Instrument Incubator Program (IIP). The second campaign was in August, 2014 based at NASA Armstrong Flight Research Center (AFRC) in Palmdale, CA on the NASA's DC-8 aircraft. HOPS flew with the Multifunctional Fiber Laser Lidar (MFLL) instrument developed by Excelis Inc. The goal of the campaigns was to perform an end-to-end demonstration of the capabilities of the HOPS prototype system (HOPS COTS) while running the most computationally intensive part of the ASCENDS algorithm real-time on-board. The comparison of the two flight campaigns and the results of the functionality tests of the HOPS COTS are presented in this paper.

Beyon, Jeffrey Y.↗
NASA NTRS2017

Shed Vortex Structure and Phase-Averaged Velocity Statistics in Symmetric/Asymmetric Turbulent Flat Plate Wakes

The near wake of a flat plate is investigated via direct numerical simulations (DNS). Many earlier experimental investigations have used thin plates with sharp trailing edges and turbulent boundary layers to create the wake. This results in large theta divided by D (sub TE) values (theta is the boundary layer momentum thickness towards the end of the plate and D (sub TE) is the trailing edge thickness). In the present study the emphasis is on relatively thick plates with circular trailing edges (CTE) resulting in theta divided by D values less than one (D is the plate thickness and the diameter of the CTE), and vigorous vortex shedding. The Reynolds numbers based on the plate length and D are 1.255 x 10 (sup 6) and 10,000, respectively. Two cases are computed; one with turbulent boundary layers on both the upper and lower surfaces of the plate (statistically the same, symmetric wake, Case TT) and, a second with turbulent and laminar boundary layers on the upper and lower surfaces, respectively (asymmetric case, Case TL). The data and understanding obtained is of considerable engineering interest, particularly in turbomachinery where the pressure side of an airfoil can remain laminar or transitional because of a favorable pressure gradient and the suction side is turbulent. Shed-vortex structure and phase-averaged velocity statistics obtained in the two cases are compared here. The upper negative shed vortices in Case TL (turbulent separating boundary layer) are weaker than the lower positive ones (laminar separating boundary layer) at inception (a factor 1.27 weaker in terms of peak phase-averaged spanwise vorticity at first appearance of a peak). The upper vortices weaken rapidly as they travel downstream. A second feature of interest in Case TL is a considerable increase in the peak phase-averaged, streamwise normal intensity (random component) with increasing streamwise distance (x divided by D) that occurs nears the positive vortex cores. This behavior is observed for a few diameters in the near wake. This is counter to Case TT where the peak value essentially decreases with increasing x divided by D. Both these effects are examined in detail and the important contributors are identified.

direct numerical simulations↗
NASA NTRS2009

Desktop Application Program to Simulate Cargo-Air-Drop Tests

The DSS Application is a computer program comprising a Windows version of the UNIX-based Decelerator System Simulation (DSS) coupled with an Excel front end. The DSS is an executable code that simulates the dynamics of airdropped cargo from first motion in an aircraft through landing. The bare DSS is difficult to use; the front end makes it easy to use. All inputs to the DSS, control of execution of the DSS, and postprocessing and plotting of outputs are handled in the front end. The front end is graphics-intensive. The Excel software provides the graphical elements without need for additional programming. Categories of input parameters are divided into separate tabbed windows. Pop-up comments describe each parameter. An error-checking software component evaluates combinations of parameters and alerts the user if an error results. Case files can be created from inputs, making it possible to build cases from previous ones. Simulation output is plotted in 16 charts displayed on a separate worksheet, enabling plotting of multiple DSS cases with flight-test data. Variables assigned to each plot can be changed. Selected input parameters can be edited from the plot sheet for quick sensitivity studies.

Cuthbert, Peter↗
NASA NTRSDate not supplied

3D Localization of Defects in Facility Inspection

Wind tunnels are crucial facilities that support the aerospace industry. However, these facilities are large, complex, and pose unique maintenance and inspection requirements. Manual inspections to identify defects such as cracks, missing fasteners, leaks, and foreign objects are important but labor and schedule intensive. Our goal is to utilize small Unmanned Aircraft Systems (sUAS) and computer vision-based analysis to automate the inspection of the interior and exterior of NASA’s critical wind tunnel facilities. We detect missing fasteners as our defect class, and detect existing fasteners to provide potential future missing fastener sites for preventative maintenance. These detections are done on both 2D raw images and in 3D space to provide a visual reference and real world location to facilitate repairs. A dataset was created consisting of images taken along a grid-like pattern of an interior tunnel section in the AEDC National Full-Scale Aerodynamics Complex (NFAC) at NASA Ames Research Center. Our method uses object detection to create image level bounding boxes of the fasteners and missing fasteners, then uses photogrammetry to create a mapping from 2D image locations to 3D real world locations. The image level bounding boxes and the 2D to 3D mapping are then combined to determine the 3D location of the defects. We describe the data collection, photogrammetry, and computer vision techniques used for object detection as well as a quantitative analysis of the method.

Small Unmanned Aircraft Systems (sUAS)↗
NASA NTRSDate not supplied

Transonic Lift and Drag Predictions using Wall Modelled Large Eddy Simulations

Wall-modelled Large Eddy Simulations (WMLES) of the NASA Common Research Model (CRM) at transonic conditions and various angles of attacks leading up to and including shock-induced flow separation are performed using the LAVA computational framework. The simulations are shown to accurately predict the lift curve slope and the onset of separation characterized by the break in the pitching moment. Furthermore, careful assessment of skin-friction drag at cruise condition and its subsequent decrease with increasing angles of attack are shown to be in agreement with viscous sublayer resolving Reynolds Averaged Navier Stokes(RANS) simulations. The small differences between WMLES and RANS appear to be of the same order as differences seen between two RANS models at the cruise-point. Some sensitivity is observed to the coefficient used in the subgrid scale model, although this can be reconciled by noting the low chord- and shock-incidence Reynolds numbers (Rex≈106) seen in the outboard regions of the wing, along with the uncertainties associated with tripping and the numerical transition that occurs near the leading edge. Among the primary drawbacks seen in the WMLES predictions is the subdued increase in wave-drag with increasing angle-of-attack and the shock intensity when compared with experimental data. Preliminary assessment suggests that additional span- and stream-wise grid resolution is likely needed in mid- and out-board portions of the wing to better resolve the shock-induced separated flow and to further investigate prediction accuracy of unsteady temporal characteristics of the problem.

ARMD↗
NASA NTRS1995

A Coupled-Cluster Study of the Molecular Structure, Vibrational Spectrum, and Heats of Formation of XONO2 (X=H, F, Cl)

The equilibrium structures, harmonic vibrational frequencies, dipole moments, and IR intensities of nitric acid, fluorine nitrate, and chlorine nitrate have been investigated by using the singles and doubles coupled cluster method that also includes a perturbational estimate of the effects of connected triple excitations, CCSD(T). A standard triple-zeta double-polarized basis set was utilized. The equilibrium geometries and vibrational spectra of HONO2 and ClONO2 are shown to be in excellent agreement with the available experimental data. The ab initio vibrational spectrum of FONO2 is also shown to be in excellent agreement with experiment. Unlike the FOOF and FON molecules, but similar to the cis- and trans-FONO molecules, FONO2 is shown to possess normal bond distances. The bonding in FONO2 is shown to be more similar to that in ClONO2 than that in HONO2, although there are still significant differences, especially in the partial atomic charges as deduced from Mulliken populations. This causes FONO2 to possess almost no dipole moment, which is very different to both HONO2 and ClONO2. By using large atomic natural orbital basis sets, CCSD(T) energies are computed for four isodesmic reactions in order to determine an accurate heat of formation for FONO2. Our best estimate for DELTA H(raised circle) (sub f,298) is 3.1 plus or minus 2.0 kcal/mol, indicating that the F-ONO2 bond energy is 31.3 kcal/mol.

Lee, Timothy J.↗
NASA NTRS2020

Leveraging Google Earth Engine User Interface for Semiautomated Wetland Classification in the Great Lakes Basin at 10 m With Optical and Radar Geospatial Datasets

As one of the world’s largest freshwater ecosystems,the Great Lakes Basin houses hundreds of thousands of acres of wetlands that support a variety of crucial ecological and environmental functions at the local, regional, and global levels.Monitoring these wetlands is critical to conservation and restoration efforts, however current methods that rely on field monitoring are labor-intensive, costly, and often outdated. In this study, we present a graphical user interface constructed in Google Earth Engine called the Wetland Extent Tool (WET),which allows semi-automatic wetland classification according to a user-input area of interest and date range. WET composites datasets and conducts multi source, moderate resolution processing utilizing Landsat 8 OLI, Sentinel-2 MSI, Sentinel-1 C-SAR, and Shuttle Radar Topography Mission (SRTM) datasets to classify wetlands in the entire Great Lakes Basin. We evaluated classification results of wetlands, uplands, and open water from May-September 2019, and tested whether SRTM elevation, slope,or the Dynamic Surface Water Extent produced the most accurate results in each Great Lake Basin in conjunction with optical indices and radar composites. We found that elevation produced the most accurate classification in Lake Erie, Michigan,and Ontario, while slope performed best in Lake Huron and Superior. Lake Erie, Michigan, Ontario, and Huron achieved high overall accuracy and identification of wetlands. WET leverages cloud-computing for multi source processing of moderate resolution remote sensing data, and employs a user interface in Google Earth Engine that wetland managers and conservationists can use to monitor wetland extent in the Great Lakes Basin in near real-time.

Vanessa L Valenti↗
NASA NTRS2004

Extraction of Martian valley networks from digital topography

We have developed a novel method for delineating valley networks on Mars. The valleys are inferred from digital topography by an autonomous computer algorithm as drainage networks, instead of being manually mapped from images. Individual drainage basins are precisely defined and reconstructed to restore flow continuity disrupted by craters. Drainage networks are extracted from their underlying basins using the contributing area threshold method. We demonstrate that such drainage networks coincide with mapped valley networks verifying that valley networks are indeed drainage systems. Our procedure is capable of delineating and analyzing valley networks with unparalleled speed and consistency. We have applied this method to 28 Noachian locations on Mars exhibiting prominent valley networks. All extracted networks have a planar morphology similar to that of terrestrial river networks. They are characterized by a drainage density of approx.0.1/km, low in comparison to the drainage density of terrestrial river networks. Slopes of "streams" in Martian valley networks decrease downstream at a slower rate than slopes of streams in terrestrial river networks. This analysis, based on a sizable data set of valley networks, reveals that although valley networks have some features pointing to their origin by precipitation-fed runoff erosion, their quantitative characteristics suggest that precipitation intensity and/or longevity of past pluvial climate were inadequate to develop mature drainage basins on Mars.

Stepinski, T. F.↗
NASA NTRS2003

Resonance Effects in the NASA Transonic Flutter Cascade Facility

Investigations of unsteady pressure loadings on the blades of fans operating near the stall flutter boundary are carried out under simulated conditions in the NASA Transonic Flutter Cascade facility (TFC). It has been observed that for inlet Mach numbers of about 0.8, the cascade flowfield exhibits intense low-frequency pressure oscillations. The origins of these oscillations were not clear. It was speculated that this behavior was either caused by instabilities in the blade separated flow zone or that it was a tunnel resonance phenomenon. It has now been determined that the strong low-frequency oscillations, observed in the TFC facility, are not a cascade phenomenon contributing to blade flutter, but that they are solely caused by the tunnel resonance characteristics. Most likely, the self-induced oscillations originate in the system of exit duct resonators. For sure, the self-induced oscillations can be significantly suppressed for a narrow range of inlet Mach numbers by tuning one of the resonators. A considerable amount of flutter simulation data has been acquired in this facility to date, and therefore it is of interest to know how much this tunnel self-induced flow oscillation influences the experimental data at high subsonic Mach numbers since this facility is being used to simulate flutter in transonic fans. In short, can this body of experimental data still be used reliably to verify computer codes for blade flutter and blade life predictions? To answer this question a study on resonance effects in the NASA TFC facility was carried out. The results, based on spectral and ensemble averaging analysis of the cascade data, showed that the interaction between self-induced oscillations and forced blade motion oscillations is very weak and can generally be neglected. The forced motion data acquired with the mistuned tunnel, when strong self-induced oscillations were present, can be used as reliable forced pressure fluctuations provided that they are extracted from raw data sets by an ensemble averaging procedure.

Lepicovsky, J.↗
NASA NTRS2013

Advanced Optical Diagnostics for Ice Crystal Cloud Measurements in the NASA Glenn Propulsion Systems Laboratory

A light extinction tomography technique has been developed to monitor ice water clouds upstream of a direct connected engine in the Propulsion Systems Laboratory (PSL) at NASA Glenn Research Center (GRC). The system consists of 60 laser diodes with sheet generating optics and 120 detectors mounted around a 36-inch diameter ring. The sources are pulsed sequentially while the detectors acquire line-of-sight extinction data for each laser pulse. Using computed tomography algorithms, the extinction data are analyzed to produce a plot of the relative water content in the measurement plane. To target the low-spatial-frequency nature of ice water clouds, unique tomography algorithms were developed using filtered back-projection methods and direct inversion methods that use Gaussian basis functions. With the availability of a priori knowledge of the mean droplet size and the total water content at some point in the measurement plane, the tomography system can provide near real-time in-situ quantitative full-field total water content data at a measurement plane approximately 5 feet upstream of the engine inlet. Results from ice crystal clouds in the PSL are presented. In addition to the optical tomography technique, laser sheet imaging has also been applied in the PSL to provide planar ice cloud uniformity and relative water content data during facility calibration before the tomography system was available and also as validation data for the tomography system. A comparison between the laser sheet system and light extinction tomography resulting data are also presented. Very good agreement of imaged intensity and water content is demonstrated for both techniques. Also, comparative studies between the two techniques show excellent agreement in calculation of bulk total water content averaged over the center of the pipe.

Bencic, Timothy J.↗
NASA NTRS2021

A NICER View of the Massive Pulsar PSR J0740+6620 Informed by Radio Timing and XMM-Newton Spectroscopy

We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be-+12.390.981.30km and-+2.0720.0660.067Me respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is=-+TlogK5.99100.060.05([])for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters(within the prior support)and can thus be computed from the posterior samples.

Millisecond pulsars↗
NASA NTRS1992

The Language Research Center's Computerized Test System for environmental enrichment and psychological assessment

In the spring of 1987, we undertook to provide environmental enrichment to nonhuman primate subjects in ways that would complement and even contribute to the bio-behaviorial science that justified the monkeys' captivity. Of course, the psychological well-being of captive primates--and indeed all research species-- has been an area of intense research activity since the 1985 amendment of the Animal Welfare Act. This mandate for researchers to ensure the psychological, as well as physical, fitness of experimental animals catalyzed the humane and scientific interests of the research community. The contemporary literature is replete with proposed means both of assaying and of providing enrichment and well-being. Notwithstanding, consensus on either assessment or intervention has yet to be reached. The paradigm we employed was modelled after successful efforts with chimpanzees. An automated test system was constructed in which subjects responded to computer tasks by manipulating a joystick. The tasks, interactive game-like versions of many of the classic testing paradigms of cognitive and comparative psychology, permitted the controlled presentation of stimuli and demands without the required presence of a human experimenter. Despite significant barriers to the success, rhesus monkeys (Macaca mulatta) and a variety of other primate species (including, of course, humans) have mastered the skills necessary for testing in this paradigm. Previous experiments have illustrated the utility of the test system for addressing questions of learning, memory, attention, perception, and motivation. Additional data have been reported to support the contention that the Language Research Center's Computerized Test System (LRC-CTS) serves its other raison d'etre--providing environmental enrichment and assessing psychological well-being. This paper is designed to augment previous descriptions of the technology and the paradigm for scientists and caretakers interested in environmental enrichment and performance assessment with primates.

Non-NASA Center↗
NASA NTRS2018

Integrating Cloud-Based Workflows in Continental-Scale Cropland Extent Classification

Accurate information on cropland spatial distribution is required for global-scale assessments and agricultural land use policies. Cloud computing platforms such as Google Earth Engine (GEE) provide unprecedented opportunities for large-scale classifications of Landsat data. We developed a novel method to fuse pixel-based random forest classification of continental-scale Landsat data on GEE and an object-based segmentation approach known as recursive hierarchical segmentation (RHSeg). Using our fusion method, we produced a continental-scale cropland extent map for North America at 30m spatial resolution for the nominal year 2010. The total cropland area for North America was estimated at 275.18 million hectares (Mha). The overall accuracies of the map are>90% across the continent. This map also compares well with the United States Department of Agriculture (USDA) cropland data layer (CDL), Agriculture and Agri-food Canada (AAFC) annual crop inventory (ACI), and the Mexican government agency Servicio de Informacion Agroalimentaria y Pesquera (SIAP)'s agricultural boundaries. Furthermore, our map compared well with sub-country statistics including state-wise and county-wise cropland statistics in regression models resulting in R2 > 0.84. This key contribution paves the way for more detailed products such as crop intensity, crop type, and crop irrigation, and provides a method for creating high-resolution cropland extent maps for other countries where spatial information about croplands are not as prevalent.

Massey, Richard↗
NASA NTRS1988

Psychological tools for knowledge acquisition

Knowledge acquisition is said to be the biggest bottleneck in the development of expert systems. The problem is getting the knowledge out of the expert's head and into a computer. In cognitive psychology, characterizing metal structures and why experts are good at what they do is an important research area. Is there some way that the tools that psychologists have developed to uncover mental structure can be used to benefit knowledge engineers? We think that the way to find out is to browse through the psychologist's toolbox to see what there is in it that might be of use to knowledge engineers. Expert system developers have relied on two standard methods for extracting knowledge from the expert: (1) the knowledge engineer engages in an intense bout of interviews with the expert or experts, or (2) the knowledge engineer becomes an expert himself, relying on introspection to uncover the basis of his own expertise. Unfortunately, these techniques have the difficulty that often the expert himself isn't consciously aware of the basis of his expertise. If the expert himself isn't conscious of how he solves problems, introspection is useless. Cognitive psychology has faced similar problems for many years and has developed exploratory methods that can be used to discover cognitive structure from simple data.

Rueter, Henry H.↗
NASA NTRS1994

Theoretical investigation of wave-vector-dependent analytical and numerical formulations of the interband impact-ionization transition rate for electrons in bulk silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E. Scholl, and M. Rudan (1993), and a more exact, numerical method of Y. Wang and K. F. Brennan (1994). Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formular, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with the completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to the overlap intergrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such the transition rate may be overestimated at those points for which 'near vertical,' small change in k, transitions occur.

Kolnik, Jan↗
NASA NTRS1994

Theoretical Investigation of Wave-Vector-Dependent Analytical and Numerical Formulations of the Interband Impact-Ionization Transition Rate for Electron in Bulk Silicon and GaAs

The electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E Scholl, and M. Rudan, and a more exact, numerical method of Y. Wang and K. F. Brennan. Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formula, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with (he completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to (he overlap integrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such [he transition rate may be overestimated at those points for which "near vertical," small change in k, transitions occur.

Kolnik, Jan↗