Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “microelectronics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 685 records · Page 38

All-optical control of charge-trapping defects in rare-earth doped oxides

Abstract Charge-trapping defects in crystalline solids play important roles in applications ranging from microelectronics, optical storage, sensing and quantum technologies. On one hand, depleting trapped charges in the host matrix reduces charge noise and enhances coherence of solid-state quantum emitters. On the other hand, stable charge traps can enable high-density optical storage systems. Here we report all-optical control of charge-trapping defects via optical charge trapping (OCT) spectroscopy of a rare-earth ion doped oxide (Y 2 O 3 ). Charge trapping is realized by low intensity optical excitation in the 200–375 nm range. Charge detrapping or depletion is carried out by optically stimulated luminescence (OSL) under 532 nm stimulation. Using a Pr-doped Y 2 O 3 polycrystalline ceramic host matrix, we observe charging pathways via the inter-band optical absorption of Y 2 O 3 and via the 4f-5d transitions of Pr 3+ . We demonstrate effective control of the density of trapped charges within the Y 2 O 3 matrix at ambient environment. These results point to a viable method for controlling the local charge environment in rare-earth doped crystals via all-optical means, and pave the way for further development of efficient optical storage technologies with ultrahigh storage capacity, as well as for the localized control of quantum coherence in rare-earth doped solids.

França, Leonardo V. S. [Pritzker School of Molecul↗

Preparation and electrical conductivity of graphitic carbon-infused copper alloys

By electron-beam (e-beam) melting, we prepared 0.4 wt% carbon-infused copper (CuCv4), and a copper control without carbon addition (CuCv0). Scanning electron microscopy and helium ion microscopy (HIM) were performed on the as-solidified surface, fracture surface, and ion-polished surface of the CuCv4 sample. The results revealed that graphitic carbon flakes cover the as-solidified surface, and carbon nanoparticles and clusters exist in the fracture and ion-polished surfaces. HIM on the ion-polished surface revealed a unique ripple-shaped feature, which is possibly associated with the infusion of carbon nanoribbons in the copper matrix. The bulk densities were measured to be 8.86 and 8.53 g/cm 3 , which correspond to relative densities of 98.9% and 96.4% for the CuCv0 and CuCv4 samples, respectively. Also, apparent electrical conductivities were measured to be 56.9 and 57.5 MS/m, respectively, for the e-beam melted CuCv0 and CuCv4 samples. These values correspond to true electrical conductivities of 100.5% IACS (International Annealed Copper Standard) and 107.4% IACS after correction for the porosity. Thus, our results reveal remarkable promise of using covetic copper for the next generation conductors in energy applications from microelectronic devices to high-power transmission cables.

36 MATERIALS SCIENCE↗

Defect-engineered GaN high electron mobility transistors for enhanced radiation tolerance

This study explores the radiation resilience of GaN high-electron-mobility transistors (HEMTs) under various preconditioning treatments—pristine, electro-pulsed, electrically overstressed, and 60 Co gamma-irradiated—with a focus on enhancing survivability in high-radiation environments. Key findings emphasize the gate region’s central role in radiation sensitivity, with increased defect concentrations leading to reduced sensitivity—as determined from reduced single-event transient intensities during pulsed-laser studies—and impacting charge-transport dynamics. Notably, the most sensitive region shifted as a function of bias state, with the drain side of the gate being most sensitive under negative gate bias and the source side under unbiased conditions due to two-dimensional electron gas disruptions. These insights clarify the mechanisms influencing radiation sensitivity in microelectronics and highlight the potential of defect and strain engineering to enhance the radiation hardness of GaN HEMTs across various operational states, providing valuable guidance for applications in space, defense, and other radiation-rich environments.

36 MATERIALS SCIENCE↗

Point defects in semiconductors: Friends and foes for quantum technologies

Point defects in semiconductors are both a curse and a blessing in microelectronics: they enable the control of electrical conductivity through doping, yet can also act as trapping and recombination centers that degrade device performance. In quantum information science, defects play a similarly dual role. They can be harnessed as spin–photon interfaces enabling the coupling of electronic and nuclear spins to light and the creation of distributed entanglement for quantum networks or used as atomistic scale sensors for quantum sensing. At the same time, defects are a major source of decoherence for superconducting qubits, one of the leading quantum computing platforms. This article discusses how a deeper materials-level understanding of defects can guide the design of improved quantum devices for communication, sensing, and computation.

Zhu, Yizhi [Rice University, Houston, TX (United S↗

Investigation of Donor and Acceptor Ion Implantation in AlN

AlGaN alloys with high Al composition and AlN based electronic devices are attractive for high voltage, high temperature applications, including microwave power sources, power switches and communication systems. AlN is of particular interest because of its wide bandgap of ~6.1eV which is ideal for power electronic device applications in extreme environments which requires high dose ion implantation. One of the major challenges that need to be addressed to achieve full utilization of AlN for opto and microelectronic applications is the development of a doping strategy for both donors and acceptors. Ion implantation is a particularly attractive approach since it allows for selected-area doping of semiconductors due to its high spatial and dose control and its high throughput capability. Active layers in the semiconductor are created by implanting a dopant species followed by very high temperature annealing to reduce defects and thereby activate the dopants. Recovery of implant damage in AlN requires excessively high temperature. In this SBIR program we began the investigation by simulation of ion beam implantation profiles for Mg, Ge and Si in AlN over wide dose and energy ranges. Si and Ge are implanted to achieve the n-type doping, Mg is investigated as a p-type doping. The simulation of implantation profiles were performed in collaboration between NRL and Agnitron using a commercial software known as Stopping and Range of Ions in Matter (SRIM). The simulation results were then used as the basis for ion implantation of AlN samples. The implanted samples were annealed by an innovative technique under different conditions and evaluated along the way. Raman spectroscopy and XRD were used to determine the crystal quality of the implanted samples, demonstrating the effectiveness of annealing in removing implant induced damage. Additionally, SIMS was used to verify that a nearly uniform doping profile was achieved near the sample surface. The electrical characteristics of the implanted samples were evaluated by TLM and Hall techniques. Generally, the implanted samples before and after annealing were found to be very resistive. Further work is required before the superior properties of AlN can be fully utilized.

24 POWER TRANSMISSION AND DISTRIBUTION↗

High speed radiation tolerant data links

This project was slated to design and develop Rad-Hard IP components for 1Gb/s links and supporting hardware designs such as PLL, SER/DES, pad drivers and receivers and custom protocol hardware for the 1Gb/s channel. Also included in the proposal was a study of a hardened memory to be used as a packet buffer for channel and data concentrator components to meet the 1 Gb/s specification. Over the course of the proposal, technology change and innovation of hardware designs lead us away from the 1 Gb/s goal to contemplate much higher performance link IP which, we believed better met the goals of physics experiments. Note that CERN microelectronics had managed to create a 4.7 Gb/s link designed to drive optical fibers and containing infrastructure for connecting much lower bandwidth front-end devices. Our own work to that point had shown the possibility of constructing a link with much lower power, lower physical overhead but of equivalent performance that could be designed to integrate directly onto the front-end ASIC (ADC and data encoding) designs. Substantial overall power savings and experimental simplicity could be achieved by eliminating data transmission to data concentrators and data concentrators and related hardened buffering themselves, with conversion to optical media at a removed distance from the experiment core. We had already developed and tested Rad-Hard SER/DES components (1Gb in 130nm standard cells) and redundant Pad Drivers/Receivers (3+ Gb/s designed and measured performance), and had a viable 1Gb/s link design based on redundant a stuttered clock receiver and classical PLL, so the basic goals of the proposal had been achieved. Below, in chronological order, are the products and tools we constructed, as well as our tests and publications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Toward Molecular Engineering of Polymer Glasses

Glass formation has been central to fabrication technologies since the dawn of civilization. Glasses not only encompass window panes, the insulation in our homes, the optical fibers supplying our cable TV, and vessels for eating and drinking, but they also include a vast array of ‘‘plastic’’ polymeric materials. Glasses find applications in high technology (e.g., producing microelectronic materials, etc., amorphous semiconductors), and recent advances have created ‘‘plastic metallic glasses’’ that are promising for fabricating everyday structural materials. Many commercially relevant systems, such as microemulsions and colloidal suspensions, have complex molecular structures and thus solidify by glass formation. Despite the importance of understanding the fundamental nature of glass formation for the synthesis of new materials, a predictive molecular theory has been lacking. Much of our understanding of glass formation derives from the analysis of experimental data, a process that has uncovered a number of interesting universal behaviors, namely, relations between properties that are independent of molecular details. However, these empirically derived relations and their limitations remain to be understood on the basis of theories, and, more importantly, there is strong need for theories of the explicit variation with molecular system to enable the rational design and tailoring of new materials. We have recently developed the generalized entropy theory, the only analytic, theory that enables describing the dependence of the properties of glass-formation on monomer molecular structures. These properties include the two central quantities of glass formation, the glass transition temperature and the glass fragility parameter, material dependent properties that govern how a material may be processed (e.g., by extrusion, ink jet, molding, etc.) Our recent works, which are further described below, extend the studies of glass formation in polymer systems to test the theory by directly comparing between the predictions of our generalized entropy theory with experiment and with simulations and to expand the vistas of the theory to describe a wider range of important systems (e.g. glass formation in binary blends and systems with specific interactions) and phenomena that are describable by the generalized entropy theory. In addition, we have addressed longstanding fundamental problems associated with the validity of the Adam-Gibbs theory, one of the underpinnings of the general entropy theory. Theoretical advances to enable describing the properties of glass-formation over a wider class of important polymeric systems, included semi-flexible systems, the more general situation of specific interactions, and more. Our recent work removes the simplest approximation uses the simplest model in which the interaction is approximated by a single, monomer average. Thus, the theory has been extended to allow some variations of the energy parameters between the atoms within the monomers. The theory has also been extended to include all the contributions from chain semi-flexibility. Both projects are extremely difficult, but the payback is that the process of solving the problems developed strong theoretical skills in Dr. Xu, who has recently begun a postdoc position at ORNL. The theory has also been extended to describe glass formation in partially miscible blends, with good general agreement with experiment. Again, the development of the theory presented an extremely difficult problem, but the payback is the development of a theory for a very important class of systems. Another project provides an extremely simple approximation for certain properties of glass formation in polymer melts and should make the theory more accessible to everyone.

36 MATERIALS SCIENCE↗

Corrosion Monitors for Embedded Evaluation

We have developed and characterized novel in-situ corrosion sensors to monitor and quantify the corrosive potential and history of localized environments. Embedded corrosion sensors can provide information to aid health assessments of internal electrical components including connectors, microelectronics, wires, and other susceptible parts. When combined with other data (e.g. temperature and humidity), theory, and computational simulation, the reliability of monitored systems can be predicted with higher fidelity.

47 OTHER INSTRUMENTATION↗

Sandia QIS Capabilities.

Sandia National Laboratories has developed a broad set of capabilities in quantum information science (QIS), including elements of quantum computing, quantum communications, and quantum sensing. The Sandia QIS program is built atop unique DOE investments at the laboratories, including the MESA microelectronics fabrication facility, the Center for Integrated Nanotechnologies (CINT) facilities (joint with LANL), the Ion Beam Laboratory, and ASC High Performance Computing (HPC) facilities. Sandia has invested $75 M of LDRD funding over 12 years to develop unique, differentiating capabilities that leverage these DOE infrastructure investments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Modeling the self-assembly of ordered nanoporous materials

This report describes progress on a collaborative project on the multiscale modeling of the assembly processes in the synthesis of nanoporous materials. Such materials are of enormous importance in modern technology with application in the chemical process industries, biomedicine and biotechnology as well as microelectronics. The project focuses on two important classes of materials: i) microporous crystalline materials, such as zeolites, and ii) ordered mesoporous materials. In the first case the pores are part of the crystalline structure, while in the second the structures are amorphous on the atomistic length scale but where surfactant templating gives rise to order on the length scale of 2 - 20 nm. We have developed a modeling framework that encompasses both these kinds of materials. Our models focus on the assembly of corner sharing silica tetrahedra in the presence of structure directing agents. We emphasize a balance between sufficient realism in the models and computational tractibility given the complex many-body phenomena. We use both on-lattice and off-lattice models and the primary computational tools are Monte Carlo simulations with sampling techniques and ensembles appropriate to specific situations. Our modeling approach is the first to capture silica polymerization, nanopore crystallization, and mesopore formation through computer-simulated self assembly.

36 MATERIALS SCIENCE↗

Optical-based spectroscopic methods for measuring chemical, optical, and physical properties of thin polymer waveguide films

Non-destructive optical-based spectroscopic methods are needed for analyzing “real world” devices that consist of thin polymer waveguide films. Many applications (e.g., sensors, microelectronics, optics, and biomedical applications, etc.) utilize thin polymer waveguide films, and non-destructive characterization methods based on Fourier transform (FT)-plasmon waveguide spectroscopy (PWR) and scanning angle (SA) Raman spectroscopy are used to extract optical, physical, and chemical properties simultaneously. The FT-PWR method measures reflected light at polymer waveguide interface as both the incident frequency (wavelength) and incident angle are scanned. This method uses p- and s-polarized light to simultaneously extract the polymer waveguide thickness and apparent anisotropic indices of refraction. Polystyrene waveguide films ranging from 360 to 800 nm are used to demonstrate the method and it has an average 0.4% relative error when compared to profilometry and atomic force microscopy measurements. SA Raman spectroscopy is used to measure mixed waveguide polymer films consisting of polystyrene-block-poly(methyl methacrylate) and homopolymer poly(methyl methacrylate) (PS-b-PMMA:PMMA), and poly(2-vinylnapthalene)-block-poly(methyl methacrylate) (P2VN-b-PMMA). PMMA homopolymer is added to the PS-b-PMMA solutions to vary the chemical composition. The chemical composition of each mixed film is quantified (SA Raman peak amplitude ratios) and averaged over all incident angles and is termed the Raman amplitude ratio (rps). This parameter is used to calculate the refractive index of each mixed waveguide polymer film. The refractive index is an input parameter for sum square electric field (SSEF) calculations, which are used to model SA Raman spectra as a function of incident angle to extract the film thickness. The mixed polymer waveguide film thicknesses ranged from 495 to 971 nm, and the SA Raman spectroscopy method has an average 5% difference between the values determined by profilometry. The SA Raman spectroscopy method developed for mixed polymer waveguide films is used to measure the chemical composition and extract interface locations in bilayer and trilayer films consisting of PMMA/PS or PMMA/PS/PMMA, respectively. The rps value is averaged over angle ranges corresponding to waveguide mode 0 and waveguide mode 1 for the bilayer and trilayer films, respectively. Six multilayer films are analyzed and their total thicknesses range from 330 to 1260 nm. Iterative SSEF calculations are used to model the SA Raman spectra as a function of incident angle, and the best fit to the experimental data is used to extract the total thickness and interface location(s). The method has an axial spatial resolution of 7 to 80 nm and provides comparable values to films measured by profilometry with an average 8% and 7% difference for the bilayer and trilayer films, respectively.

36 MATERIALS SCIENCE↗

The Flotation Chemistry of Nonsulfide Minerals

Particulate separations are of considerable significance in many areas of technology ranging from pharmaceutics and microelectronics, to mining and construction materials industries. In addition, particulate separation technology is of critical importance in the environmental area, for example, the development of advanced water treatment processes for the 21st century will rely on more efficient particulate separation techniques. In this regard it is most appropriate that the Separations Program of the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences, of DOE supports basic science research in the area of particulate separations. One such particulate separation process of special importance is froth flotation, a physico-chemical process that is used to separate particles in an aqueous suspension via differences in hydrophobicity as established by the interaction of various reagents at the solid/water, solid/gas and water/gas interfaces. Surfactants, called collectors, are added to a suspension to selectively adsorb at the surface of specific particles, rendering these particles hydrophobic. Regulators are employed to promote collector adsorption at the desired surfaces, while preventing such reactions at other surfaces. When air is dispersed into the suspension, the bubbles generated attach to the hydrophobic particles. The resulting bubble/particle aggregates float to the suspension surface and are collected in a froth phase as a concentrate. The remaining hydrophilic particles are retained in suspension and discharged as a tailings product. Clearly, particulate separation by froth flotation is an outstanding example of applied surface chemistry, and is used in the food, petroleum, pulp/paper, and mineral industries. The use of flotation technology is perhaps most significant in the mineral industry where, in the U. S. alone, over 500,000 tons/day of nonsulfide minerals are processed. The estimated value of all nonfuel mineral materials processed in the United States during 2015 totaled $630 billion. It is evident that particle separation by flotation is an important process that is used in many of the mineral industries. Understanding of the interfacial chemistry for the development of improved flotation separations is required for more effective production and utilization of our mineral resources, especially the critical minerals as identified in the 2017 USGS report, “Critical Mineral Resources of the United States – Economic and Environmental Geology and Prospects for Future Supply.” In this regard, a research program has been in progress with DOE support from Grant DE-FGO2-93ER14315 to study the fundamental interfacial chemistry features in nonsulfide mineral flotation systems in order to increase our understanding and provide for improved separation efficiencies and energy economy in the processing of our mineral resources. Significant contributions have been made to the flotation chemistry of flotation separations in many areas, including, salt minerals; collector adsorption; wetting, surface forces, bubble attachment; interfacial water structure; phyllosilicate minerals, and critical mineral resources such as rare earth minerals and lithium resources. The research results summarized herein have resulted in more than 225 publications, the education of 28 PhD graduate students, and impressive recognition with university, national, and international awards. For example, among many other awards, Distinguished Professor Jan Miller, PI, was elected to be a member of the National Academy of Engineering (1993) and the National Academy of Inventors (2014). In 2015 he received the University of Utah’s most prestigious award presented annually to a faculty member, the Rosenblatt Prize for Excellence. Research Professor Xuming Wang was selected by SME to be a Henry Krumb Lecturer (2013-2014), and many of the student researchers involved in the program received national awards from AIME, ICE, IPMI, SME, and TMS. It is evident that the flotation separation research program has been quite successful. Unfortunately, the flotation chemistry research for mineral particle separation has been terminated even though the renewal proposal received excellent reviews with recommended funding. The need for continued support of minerals separation research is of critical importance as recognized by 1) the recent 2017 USGS report, “Critical Mineral Resources of the United States – Economic and Environmental Geology and Prospects for Future Supply,” and by 2) the 20 December 2017 executive order from President Trump to increase the discovery, production, and domestic refining of critical minerals. In view of our research accomplishments, the excellent reviews of the renewal proposal, and the expressed need for attention to the production of critical minerals, termination of “The Flotation Chemistry of Nonsulfide Minerals” research program by DOE is not appropriate, and continued support should be reconsidered.

58 GEOSCIENCES↗

Revealing Nanoscale Energy Flow Using Ultrafast THz to X-ray Beams (Final Technical Report)

We developed novel spectroscopic methods and made use of them to study energy flow and material properties on nanometer length scales and ultrafast time scales. Access to short length scales was provided through the use of light beams with short wavelengths (EUV through hard x-ray spectral ranges) and/or fabricated structural elements with nanometer dimensions. Recent advances in tabletop high harmonic generation of extreme ultraviolet (EUV) pulses were exploited to measure thermal transport and acoustic vibrations using time-resolved diffraction from photoexcited periodic nanostructures, revealing new physics that arises at length scales of tens to hundreds of nm. The tabletop EUV sources as well as the FERMI free electron laser at FERMI-Elettra in Trieste were used to generate as well as measure nanoscale thermoelastic responses without the need for patterned nanostructures, with the short length scale coming from optical interference patterns formed by crossing pairs of beams in transient grating experiments. We also used EUV and optical sources to excite and monitor ultrahigh-frequency acoustic waves (coherent phonons) at ultraflat interfaces and multilayer structures, extending our measurements of the highest-frequency coherent acoustic waves observed to date. Our measurements of acoustic properties allowed direct calculation of thermal conductivities which can be compared with our measurements of thermal transport and with first-principles calculations. Terahertz-frequency acoustic measurements can also be used to reveal complex relaxation dynamics in glass-forming liquids and partially disordered solids. Acoustic measurements were used to investigate the confinement effect in ultrathin liquid layers and to characterize mechanical properties of ultrathin solid layers. The methods we developed have broad fundamental applications and may also enable new practical metrology for use in nanoelectronics, just as earlier methods we developed have found commercial applications in microelectronics metrology.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Attack detection and strategy optimization in game-theoretic trust models

Trust in a microelectronics-based systems can be characterized as the level of confidence that the system is free of subversive alterations inserted by a malicious adversary during system development. Outkin et al. recently developed GPLADD, a game-theoretic framework that enables trust analysis through a set of mathematical models that represent multi-step attack graphs and contention between system attackers and defenders. This paper extends GPLADD to include detection of attacks on development processes and defender decision processes that occur in response to detection events. The paper provides mathematical details for implementing attack detection and demonstrates the models on an example system. The authors further demonstrate how optimal defender strategies vary when solution concepts and objective functions are modified.

97 MATHEMATICS AND COMPUTING↗

Workshop on Advanced Computing for Connected and Automated Vehicles

To safely and reliably operate without a human driver, connected and automated vehicles (CAVs) require more advanced computing hardware and software solutions than are implemented today in vehicles that provide driver-assistance features. A workshop was held to discuss advanced microelectronics and computing approaches that can help meet future energy and computational requirements for CAVs. Workshop questions were posed as follows: will highly automated vehicles be viable with conventional computing approaches or will they require a step-change in computing; what are the energy requirements to support on-board sensing and computing; and what advanced computing approaches could reduce the energy requirements while meeting their computational requirements? At present, there is no clear convergence in the computing architecture for highly automated vehicles. However, workshop participants generally agreed that there is a need to improve the computing performance per watt by at least 10x to advance the degree of automation. Participants suggested that DOE and the national laboratories could play a near-term role by developing benchmarks for determining and comparing CAV computing performance, developing public data sets to support algorithm and software development, and contributing precompetitive advancements in energy efficient computing.

33 ADVANCED PROPULSION SYSTEMS↗

Final report of Sandia National Laboratories (SNL) contribution to IAEA CRP F11016 on ''Utilization of ion accelerators for studying and modeling of radiation induced defects in semiconductors and insulator''

This is the final report of Sandia National Laboratories’ activities within the International Atomic Energy Agency (IAEA) Collaboration Research Project (CRP) F11016. The goal of this CRP is to study the effects of radiation on semiconductors and insulators with the emphasis on the effect of displacement damage due to MeV energy ions on the performance of semiconductor detectors and microelectronic devices. The devices used in this study were received from the university of Helsinki, but some other commercial diodes from Hamatsu were investigated, too. SNL’s role in the project was to perform irradiation, C-­V and Ion Beam Induced Charge (IBIC) measurements on the devices. In addition we performed Binary Collision Approximation (BCA) calculations to estimate the ionization and damage of the ions used in the experiment by the members of the CRP and created a TCAD model of the irradiation of the devices.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Evaluation & Development of Algorithms & Techniques for Streaming Detector Readout

The advancement in microelectronics capabilities, computing, and data science in the last decade has been remarkable. With the start of the 12 GeV Science Program at Jefferson Lab (JLab) and the conceptual detector design for the upcoming Ion Collider (EIC) in mind, we have evaluated and developed the possibility of evolving and improving the existing nuclear science research workflow based on these advances. Specifically, we have prototyped components of streaming readout.

43 PARTICLE ACCELERATORS↗

Mapping Stochastic Devices to Probabilistic Algorithms

Probabilistic and Bayesian neural networks have long been proposed as a method to incorporate uncertainty about the world (both in training data and operation) into artificial intelligence applications. One approach to making a neural network probabilistic is to leverage a Monte Carlo sampling approach that samples a trained network while incorporating noise. Such sampling approaches for neural networks have not been extensively studied due to the prohibitive requirement of many computationally expensive samples. While the development of future microelectronics platforms that make this sampling more efficient is an attractive option, it has not been immediately clear how to sample a neural network and what the quality of random number generation should be. This research aimed to start addressing these two fundamental questions by examining basic “off the shelf” neural networks can be sampled through a few different mechanisms (including synapse “dropout” and neuron “dropout”) and examine how these sampling approaches can be evaluated both in terms of evaluating algorithm effectiveness and the required quality of random numbers.

97 MATHEMATICS AND COMPUTING↗