Parabolic Approximation Research Articles

Simulation of silicon conical field effect GAA nanotransistors with stack SiO2/HfO2 dielectric of gate

The issues of modeling the electrophysical characteristics of a silicon conical field effect GAA nanotransistor are discussed. An analytical model of the drain current of a transistor with a fully enclosing conical gate with a stack sub-gate oxide SiO2/HfO2 has been developed, taking into account the effect of the charge of the interphase trap at the Si/SiO2 interface. To simulate the potential distribution in a conical working area under the condition of constant trap density, an analytical solution of the Poisson equation was obtained using the method of parabolic approximation in a cylindrical coordinate system with appropriate boundary conditions. The potential model was used to develop an expression for the GAA drain current of a nanotransistor with a stack gate oxide. The key electrophysical characteristics are numerically investigated depending on the density of traps and the thicknesses of SiO2 and HfO2 layers.

Is Quantum Above-Barrier Reflection Important for Molecular Barrier Crossing Rates?

Understanding quantum tunneling and above-barrier reflection effects on unimolecular and bimolecular reaction rate constants remains challenging to this very day. In many applications, especially when considering moderate-to-high temperatures, the "standard" procedure is to use the parabolic barrier approximation. Recent work has shown though that this may be insufficient, and one cannot ignore anharmonicity. In this work, we study the analytic theory, including anharmonicity obtained when expanding the thermal rate up to order ℏ4. Such theories need high-order derivatives of the potential at the barrier top. We show that such derivatives are computed straightforwardly for six different reactions. We suggest a straightforward methodology for assessing whether the parabolic barrier approximation is valid and show that when the reaction asymmetry is large, this may lead to significant quantum above-barrier reflection and transmission coefficients, which are less than unity.

Impact of underlap layer on DC and RF/analog performance of asymmetric junctionless dual material double gate MOSFET for low-power analog amplifier design

Impact of underlap layer is analytically investigated on asymmetric junctionless dual material double gate MOSFET (AJDMDG) to reduce subthreshold slope and threshold voltage, which are two essential requirements with shrinking device dimensions to avoid short channel effects. The model utilizes two-dimensional Poisson’s equation with parabolic approximation for determining electrical parameters where dimensional ranges are kept within fabrication limit. Excellent accuracy is found for the obtained analytical outcome, when compared with results obtained from TCAD ATLAS simulator. Comparative study is extended for conventional junctionless DMDG (JDMDG) and underlap asymmetric junctionless single material DGFET (UAJDG) device, having identical dimensional parameters and biasing ranges; where the present structure exhibits superior performance in terms of threshold voltage, subthreshold slope and DIBL of 34.57%, 62.85% and 69.85% respectively compared to JDMDG and 12.50%, 26.08% and 40.25% respectively w.r.t UAJDG structure. Supremacy of the proposed architecture is further established with RF/analog Figures of Merit (FOMs), which are essential for designing low power analog amplifier.

Fast permeability measurement for tight reservoir cores using only initial data of the one chamber pressure pulse decay test

In this study, a mathematical model for fast determination of the permeabilities of tight rocks using measurements taken from the initial period of the One Chamber Pressure Pulse Decay (OC-PPD) test is presented. The model applies to measurements taken both before and after the pressure pulse front has reached the downstream end of the specimen. The analytical solutions for the pressure decay in the upstream chamber are derived based on a parabolic arc approximation of pore pressure distribution along the test specimen. This approximation allows converting the initial–boundary value problem of fluid diffusion in the specimen, governed by partial differential equations, to a system of ordinary differential equations that can be easily solved by explicit formulae. Thus, an explicit formula for the pressure decay rate is obtained, which enables inverse analysis of the initial experimental data to estimate the rock permeability. The proposed method expedites the pulse decay test as it does not require the system to reach equilibrium. The method is validated with three sets of experimental data of the OC-PPD test using helium as the diffusing fluid, for which the relative error of the permeability is found to be less than 6%. This method is particularly useful if the equilibrium time of the pulse decay test for rock specimens with permeabilities in the range of nano-Darcy takes hours or days.

The effect of hydrostatic pressure, temperature and impurity factor on linear and nonlinear optical properties of InxGa1-xAs tuned quantum dot with modified Gaussian potential under the action of a vertical magnetic field

This study presents a detailed theoretical analysis of the effects of hydrostatic pressure, temperature, impurity factors, and external electric fields on the optical properties of InxGa1-xAs tuned quantum dot. A uniform magnetic field, directed perpendicular to the quantum dot plane, is applied. The system is excited using a monochromatic electromagnetic field, considering electron intersubband transitions. Energy levels and wave functions are determined using the parabolic band approximation and effective mass approximation. The linear and nonlinear optical absorption coefficients and refractive index changes are computed using the compact-density matrix approach and the iterative method. Numerical results indicate that the peaks of the linear and nonlinear optical absorption coefficients and refractive index changes shift towards lower energies (red shift) and higher energies (blue shift) under varying hydrostatic pressure, temperature, and impurity factor strength. Additionally, the peak values of the absorption coefficients and refractive index changes increase or decrease based on these parameter variations. These results have significant implications for the design and optimization of quantum dot-based optoelectronic devices.

Equation of state of hot neutron star matter using finite range simple effective interaction

The equation of state (EoS) of hot neutron star matter (NSM) of n+p+e+μ composition in β-equilibrium is studied for both neutrino-free isothermal and neutrino-trapped isoentropic conditions, using the formalism where the thermal evolution is built upon its zero-temperature predictions in a self-consistent manner. The accuracy of the parabolic approximation, often used in the finite temperature calculation of hot NSM, is verified by comparing with the results obtained from the exact evaluation in the neutrino-free NSM. The EoS of neutrino-trapped isoentropic matter at low entropic condition, relevant to the core-collapsing supernovae, is formulated. In the isoentropic matter, the particle fractions and EoS have marginal variance as entropy per particle vary between 1 and 3 (in the unit of k B), but the temperature profile shows marked variation. The isentropes are found to be much less sensitive to the nuclear matter incompressibility, but have large dependence on the slope parameter L. The bulk properties of the neutron stars predicted by the isoentropic EoSs for different entropy are calculated. A model calculation for the early stage evolution of protoneutron star to neutron star configuration is also given.

Modulation of nonlinear optical rectification, second, and third harmonic generation coefficients in n-type quadruple δ-doped GaAs quantum wells under external fields

The paper theoretically explores the variations in nonlinear optical rectification (NOR), second (SHG), and third harmonic generation (THG) coefficients of an n-type quadruple δ-doped GaAs quantum well in the presence of electric, magnetic, and THz laser fields. The energies of subbands and associated wave functions are derived through the solution of the Schrödinger equation, utilizing effective mass and parabolic band approximations. The findings indicate that the applied external electric and magnetic fields significantly influence both the magnitudes and the positions of the peaks in NOR, SHG, and THG concerning the incident photon energies. In addition to the influences of electric and magnetic fields, subjecting the system to an intense laser field results in noticeable changes in the THG, SHG, and NOR coefficients. These numerical findings regarding the optical properties of quadruple δ-doped quantum wells in the presence of external fields could offer valuable guidance for experimental studies.

An inverse Gauss curvature flow to the Lp-Gauss Minkowski problem

In this paper, we confirm the existence of asymmetric smooth solutions to the Lp-Gauss Minkowski problem for p>0 by a class of inverse Gauss curvature flows. Furthermore, asymmetric weak solution for p>0 is obtained by a parabolic approximation method.

Direct Determination of Carrier Parameters in Indium Tin Oxide Nanocrystals.

We develop here a comprehensive experimental approach to independently determine charge carrier parameters, namely, carrier density and mass, in plasmonic indium tin oxide nanocrystals. Typically, in plasmonic nanocrystals, only the ratio between these two parameters is accessible through optical absorption experiments. The multitechnique methodology proposed here combines single particle and ensemble optical and magneto-optical spectroscopies, also using 119Sn solid-state nuclear magnetic resonance spectroscopy to probe the surface depletion layer. Our methodology overcomes the limitations of standard fitting approaches based on absorption spectroscopy and ultimately gives access to carrier effective mass directly on the NCs, discarding the use of literature value based on bulk or thin film materials. We found that mass values depart appreciably from those measured on thin films; consequently, we found carrier density values that are different from reported literature values for similar systems. The effective mass was found to deviate from the parabolic approximation at a high carrier density. Finally, the dopant activation and defect diagram for ITO NCs for tin doping between 2.5 and 15% are determined. This approach can be generalized to other plasmonic heavily doped semiconductor nanostructures and represents, to the best of our knowledge, the only method to date to characterize the full Drude parameter space of 0-D nanosystems.

Study of biocapacity areas to reduce ecological footprint deficits: A case study of Turkey

Our world has had difficulty meeting humans' needs in recent years. To ensure that the world can sustain its inhabitability and self-sufficiency in terms of natural resources, it is required to make the total amount of biocapacity areas equal to or higher than the ecological footprint. An analytical study has been carried out to remedy the biocapacity deficit by utilizing this information for Turkey and then these areas are optimized with heuristic optimization techniques. As a result, Artificial Bee Colony provides better objective function results (fewer errors) compared to Particle Swarm Optimization and Global Optimization Method Based on Clustering and Parabolic Approximation in terms of minimum, maximum, average value, and standard deviation. The rates of change according to the current situation of the biocapacity areas in 2016 are 277.97 %, 30.28 %, −29.28 %, 14.97 %, and −44.85 % for cropland, grazing land, forestland, fishing grounds, and built-up land, respectively. Depending on the population growth, these rates should additionally change by 83.24 %, −0.69 %, 3.97 %, 6.22 %, and −14.24 % respectively in 2050. The developed model can be used in industry or within the frame of government development policy and thus the balance between ecological footprint and biocapacity can be kept under control.

Hydrostatic pressure and temperature dependent optical properties of double inverse parabolic quantum well under the magnetic field

In this study, we investigated the combined effects of structure parameters such as size and geometry, as well as hydrostatic pressure, temperature, and magnetic field on the electronic and optical properties of a double inverse parabolic quantum well within the framework of the effective mass and parabolic band approximations. It is very important to consider the effects of temperature and hydrostatic pressure, especially in practical applications involving quantum wells such as semiconductor devices and optoelectronics. The results obtained are in good agreement with the literature. Understanding how these factors affect the electronic and optical properties of semiconductor heterostructures helps to optimize the performance and stability of devices operating under different environmental conditions.

Threshold voltage modeling based comparative performance exploration of Junctionless and Junction-Based High-K gate stack Dual-Material Cylindrical Gate-All-Around Macaroni MOSFET

This paper presents explicit threshold voltage modeling based comparative threshold voltage exploration of Junctionless (JL) and Junction-based (JB) High-K gate stack (HKGS) Dual-Material (DM) Cylindrical Gate-all-around (CGAA) Macaroni (Mac.) MOSFET. Based on Young’s popular Parabolic Potential Approximation (PPA), device features like inner potential has been formulated. Based on the expression of inner potential, threshold voltage has been extracted. Other major short channel effects like Drain-induced barrier lowering (DIBL) and subthreshold swing (SS) have also been analyzed. Device parameters such as inner, outer radii, channel lengths, type of high-k gate oxide, source/drain doping for JB device, etc. have also been varied to examine their effects on device parameters. Finally mathematical outputs have been corroborated with simulation outputs from Atlas.

Hydrostatic pressure and temperature effects on nonlinear optical properties in harmonic-Gaussian asymmetric double quantum wells

The paper examines the linear and non-linear optical characteristics of an electron in harmonic Gaussian asymmetrical double quantum wells, taking into account thermodynamic variables such as temperature and hydrostatic pressure. Numerical calculations by considering the effective mass and parabolic band approximation are performed. The electron contained within an asymmetric double well generated by the sum of a parabolic and Gaussian potential has its eigenvalues and eigenfunctions determined using the diagonalization approach. For nonlinear optical coefficients, the density matrix expansion is used. Wavefunctions and energy levels vary as an effect of the applied fields. In harmonic Gaussian asymmetrical double quantum wells, the total optical absorption coefficient (TOAC), the relative refractive index changes (RRIC), and second harmonic generation (SHG) have all been theoretically investigated. The magnitude and position of the resonant peaks are significantly influenced by the hydrostatic pressure and temperature effects. With controllable coupling and externally applied hydrostatic pressure and temperature, the potential model presented in this study can be used to simulate and manipulate the optical and electronic properties of the asymmetric double-quantum heterostructures, such as double quantum dots and wells.

Simultaneous effects of the position dependent mass and magnetic field on quantum well with the improved Tietz potential

In this study, we explored the synergistic impact of position-dependent mass and magnetic field on the electronic and optical properties of quantum wells, featuring an enhanced Tietz potential confinement incorporating both standard Morse and improved Rosen–Morse potentials, as influenced by variations in the structural parameter. Calculations were conducted within the framework of effective mass and parabolic band approximations. The diagonalization method was employed, selecting a wave function basis of trigonometric orthonormal functions to determine the eigenvalues and eigenfunctions of the confined electron potential. Our findings reveal that alterations in the sizes and shapes of the quantum wells, magnetic field strength, geometric asymmetry, and confinement parameters lead to significant variations in electron energies, transition between electron states, and the absorption spectrum. These outcomes offer valuable insights for investigating the electronic and structural properties of materials and devising novel materials with tailored optical characteristics.

A method for rapid estimation of residual stresses in metal samples produced by additive manufacturing

The mechanical methods for measuring residual stresses typically rely on so-called destructive techniques where some stress components can be determined based on part deflection after material removal (cutting, etching, drilling, etc.). While these methods don't provide a comprehensive representation of residual stresses within the entire part, they can be readily applied in most manufacturing labs. In this study, we propose an efficient method for determining residual stress within additively manufactured cylindrical samples of stainless steel. The method is based on the assumption of a relation between the axial component of residual stress (normal to cross-section) and the cylinder radius. The general form of this relation is proposed based on data from numerical simulations using linear, parabolic or piecewise approximations. The parameters for the proposed relation are defined using equilibrium equations for total force and moment. The proposed method relies on an experiment with a mechanical cut along the cylinder. Consequently, the deflection of the cylinder halves after the cut allows for obtaining the equivalent bending moment.

A fuzzy computing approach to aggregate expert opinions using parabolic and exparabolic approximation procedures for solving multi-criteria group decision-making problems

AbstractTriangular fuzzy numbers (TFNs) are widely used for selection problems to determine expert opinions using linguistic expressions. Some aggregation procedures are developed to determine expert opinions more accurately. However, there is a need for a simple and more useful procedure to solve the selection problems more suitably. For this purpose, our study offers a triangular, exparabolic, and parabolic area calculation-based approximation approach for TFNs to aggregate the possible hedges (very and more or less) for TFNs. Hence, this aggregation procedure provides a tuning opportunity for classical TFN expressions to capture possible tuning processes to reflect the hesitancies of experts. The technique for order preferences by similarity to ideal solution (TOPSIS) method is applied in the two studies from extant literature, and suitable alternatives are determined as a result of the ranking process. Finally, a comparative analysis is presented to illustrate the efficiency of the proposed procedure. The conventional TOPSIS model’s ranking scores are very close for exemplified examples (i.e., 0.5308, 0.4510, 0.4550 and 0.5304, 0.4626, 0.4940), but the proposed model’s result has fluctuated for the same examples (i.e., 0.346, 0,669, 0,567 and 0.208, 0.991, 0.148). So, the main advantage of the proposed aggregation procedure is the alternative ranking scores separation capability analyzed with their linguistic diversification.

Time-resolved analysis of dual-gate FETs with non-parabolic energy dispersion for THz applications

The investigation of charge carrier transport in state-of-the-art nanoelectronic devices based on III/V semiconductors proves to be challenging, even more so when the highly non-parabolic energy dispersion exhibited by these materials is taken into account. Unlike the common approach of neglecting this behavior by the use of the parabolic band approximation, a novel combination of a tight-binding approach with a quantum Liouville-type equation is introduced here, where any arbitrary energy dispersion can effectively be included. This leads to a discretization based on the atomic structure without the need for finite difference approximations of the Hamiltonian. Because this allows for the stationary as well as the transient simulation of quantum charge carrier transport, it is well suited for the analysis of ultrathin FETs such as dual-gate FETs when it is combined with a mode-space approach. We demonstrate that the parabolic approximation not only vastly underestimates the current densities when compared to the non-parabolic case but also fails to capture transient effects such as gain compression when amplifier operation is considered.

Scattering of high-energy positively charged particles in ultrashort oriented silicon crystal

In this work, the process of scattering of high-energy positively charged particles in the field of atomic planes of an ultrashort silicon crystal was studied. In the parabolic potential approximation of atomic planes, analytical expressions are found for the dependence of the coordinates and velocities of particles in a crystal on time and initial conditions. The relationship between the particle incidence angle on the crystal and its deflection angle has also been determined. It is shown that, under certain conditions, a beam can be split by an ultrashort crystal into two beams diverging at an angle equal to twice the angle of planar channeling. Published by the American Physical Society 2024

Physics-based modeling of surface potential and leakage current for vertical Ga2O3 FinFET

Gallium oxide (Ga2O3) is a promising ultra-wide bandgap material offering a large bandgap (>4.7 eV) and high critical electric fields. The increasing demand for electronic devices for high-power applications in electric automobiles, high-performance computing, green energy technologies, etc., requires higher voltages and currents with enhanced efficiency. Vertical transistors, such as fin-shaped field-effect transistors (FinFETs) have emerged to meet the growing need with improved current handling capabilities, reduced resistance, and enhanced thermal performance. However, to fully exploit the Ga2O3 power transistors, precise and reliable physics-driven models are crucial. Therefore, a comprehensive surface potential model has been developed in this work for a vertical Ga2O3 FinFET. The electric potential across the channel is explained by analyzing the two-dimensional (2D) Poisson equation employing parabolic approximation. Such a surface potential model is instrumental in determining the performance of the Ga2O3 FinFET as it affects the threshold voltage, the drain current, and fringing capacitance. Exploiting the surface potentials, a fringing capacitance model is derived which is crucial in analyzing the speed of the device in compact integrated circuits. In addition, statistical analysis of the Ga2O3 FinFET using the Monte Carlo simulation technique is performed to determine the leakage current fluctuation due to doping variations. The validation of the analytical model with experimental results confirms the effectiveness and prospects of the developed models in the rapid development and characterization of next-generation high-performance vertical Ga2O3 power transistors.

Verification of artillery fire under the influence of random disturbances for the computer game ARMA 3

Computer gaming occupies a firm place in today's media culture and media business. Computer games are widely used both as a means of entertainment and as an educational tool. Military games traditionally hold a place in computer gaming. However, it is in this sector of gaming that a sharp contradiction is observed between the super-realistic quality of the video component and the limited scope of the game's script component. In particular, in the development of military-themed games, the introduction of modern weapon models is rapidly evolving. At the same time, the experience of military conflicts over the last decade and the new tactical techniques developed are difficult to implement in games. This work demonstrates the possibility of improving the artillery component of ARMA 3. In artillery fire, random disturbances are always present. These disturbances cannot be eliminated during the preparation of the firing. In practice, they are compensated by consecutive ranging shots. Modern artillery firing tactics require the maximum reduction of the firing time of the artillery unit. In this regard, methods for verifying each artillery shot are very relevant. Verification is understood as confirming the effectiveness of a shot immediately after it is made. A method for verifying a shot by recording the flight time of a projectile through three control points is proposed and studied. Based on the recorded flight times by sensors, a system of approximating parabolas is constructed. The solution of the system allows determining the expected point of the projectile's burst before it lands. The deviation of the burst point from the aiming point verifies the quality of the artillery shot. Simulation modeling of the proposed method has been conducted. It is demonstrated that parabolic approximation effectively compensates for random disturbances of the shot. A comparison of the proposed method with the method of compensating disturbances through consecutive ranging shots is made. It is shown that the proposed method significantly reduces the firing time of the weapon and the ammunition expenditure for hitting the target for the ARMA 3 player.