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Journal articles on the topic 'Schrödinger Poisson Solver'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Kosina, H., and C. Troger. "SPIN – A Schrödinger-Poisson Solver Including Nonparabolic Bands." VLSI Design 8, no. 1-4 (1998): 489–93. http://dx.doi.org/10.1155/1998/39231.

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Nonparabolicity effects in two-dimensional electron systems are quantitatively analyzed. A formalism has been developed which allows to incorporate a nonparabolic bulk dispersion relation into the Schrödinger equation. As a consequence of nonparabolicity the wave functions depend on the in-plane momentum. Each subband is parametrized by its energy, effective mass and a subband nonparabolicity coefficient. The formalism is implemented in a one-dimensional Schrödinger-Poisson solver which is applicable both to silicon inversion layers and heterostructures.

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2

Mina, Mattia, David F. Mota, and Hans A. Winther. "SCALAR: an AMR code to simulate axion-like dark matter models." Astronomy & Astrophysics 641 (September 2020): A107. http://dx.doi.org/10.1051/0004-6361/201936272.

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We present a new code, SCALAR, based on the high-resolution hydrodynamics and N-body code RAMSES, to solve the Schrödinger equation on adaptive refined meshes. The code is intended to be used to simulate axion or fuzzy dark matter models where the evolution of the dark matter component is determined by a coupled Schrödinger-Poisson equation, but it can also be used as a stand-alone solver for both linear and non-linear Schrödinger equations with any given external potential. This paper describes the numerical implementation of our solver and presents tests to demonstrate how accurately it oper

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3

Karner, Markus, Andreas Gehring, Stefan Holzer, et al. "A multi-purpose Schrödinger-Poisson Solver for TCAD applications." Journal of Computational Electronics 6, no. 1-3 (2007): 179–82. http://dx.doi.org/10.1007/s10825-006-0077-7.

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4

Khoie, R. "A Study of Transconductance Degradation in HEMT Using a Self-consistent Boltzmann-Poisson-Schrödinger Solver." VLSI Design 6, no. 1-4 (1998): 73–77. http://dx.doi.org/10.1155/1998/27462.

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A self-consistent Boltzmann-Poisson-Schrödinger Solver is used to study the transconductance degradation in high electron mobility transistor (HEMT), which has extensively been reported by both experimental [1]-[8] and computational [9]-[ 13] researchers. As the gate voltage of a HEMT device is increased, its transconductance increases until it reaches a peak value, beyond which, the transconductance is degraded rather sharply with further increase in applied gate bias. We previously reported a two-subband self-consistent Boltzmann-Poisson- Schrödinger Solver for HEMT. [14] We further incorpor

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5

Ramey, S., and R. Khoie. "Formulation of a Self-Consistent Model for Quantum Well pin Solar Cells: Dark Behavior." VLSI Design 8, no. 1-4 (1998): 419–22. http://dx.doi.org/10.1155/1998/61791.

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A self-consistent numerical simulation model for a pin single-cell solar cell is formulated. The solar cell device consists of a p–AlGaAs region, an intrinsic i–AlGaAs/GaAs region with several quantum wells, and a n–AlGaAs region. Our simulator solves a field-dependent Schrödinger equation self-consistently with Poisson and drift-diffusion equations. The field-dependent Schrödinger equation is solved using the transfer matrix method. The eigenfunctions and eigenenergies obtained are used to calculate the escape rate of carriers from the quantum wells, the capture rates of carriers by the wells

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6

Mauser, Norbert J., and Yong Zhang. "Exact Artificial Boundary Condition for the Poisson Equation in the Simulation of the 2D Schrödinger-Poisson System." Communications in Computational Physics 16, no. 3 (2014): 764–80. http://dx.doi.org/10.4208/cicp.110813.140314a.

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AbstractWe study the computation of ground states and time dependent solutions of the Schrödinger-Poisson system (SPS) on a bounded domain in 2D (i.e. in two space dimensions). On a disc-shaped domain, we derive exact artificial boundary conditions for the Poisson potential based on truncated Fourier series expansion in θ, and propose a second order finite difference scheme to solve ther-variable ODEs of the Fourier coefficients. The Poisson potential can be solved within(MNlogN) arithmetic operations whereM,Nare the number of grid points inr-direction and the Fourier bases. Combined with the

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7

Mantas, José M., and Francesco Vecil. "Hybrid OpenMP-CUDA parallel implementation of a deterministic solver for ultrashort DG-MOSFETs." International Journal of High Performance Computing Applications 34, no. 1 (2019): 81–102. http://dx.doi.org/10.1177/1094342019879985.

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The simulation of ultrashort two-dimensional double gate metal-oxide semiconductor field-effect transistors and similar semiconductor devices through a deterministic mesoscopic, hence accurate, model can be very useful for the industry: It can provide reference results for macroscopic solvers and properly describe weakly charged zones of the device. For the scope of this work, we use a Boltzmann–Schrödinger–Poisson model. Its drawback is being particularly costly from the computational point of view, and a purely sequential code may take weeks to simulate high voltages. In this article, we dev

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8

Cheng, Candong, Joon-Ho Lee, Hisham Z. Massoud, and Qing Huo Liu. "3-D self-consistent Schrödinger-Poisson solver: the spectral element method." Journal of Computational Electronics 7, no. 3 (2008): 337–41. http://dx.doi.org/10.1007/s10825-008-0204-8.

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9

Wang, Lingquan, Deli Wang, and Peter M. Asbeck. "A numerical Schrödinger–Poisson solver for radially symmetric nanowire core–shell structures." Solid-State Electronics 50, no. 11-12 (2006): 1732–39. http://dx.doi.org/10.1016/j.sse.2006.09.013.

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10

Ramayya, E. B., and I. Knezevic. "Self-consistent Poisson-Schrödinger-Monte Carlo solver: electron mobility in silicon nanowires." Journal of Computational Electronics 9, no. 3-4 (2010): 206–10. http://dx.doi.org/10.1007/s10825-010-0341-8.

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11

Claus, Martin, Sven Mothes, Stefan Blawid, and Michael Schröter. "COOS: a wave-function based Schrödinger–Poisson solver for ballistic nanotube transistors." Journal of Computational Electronics 13, no. 3 (2014): 689–700. http://dx.doi.org/10.1007/s10825-014-0588-6.

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12

Hebal, H., Z. Koziol, S. B. Lisesivdin, and R. Steed. "General-purpose open-source 1D self-consistent Schrödinger-Poisson Solver: Aestimo 1D." Computational Materials Science 186 (January 2021): 110015. http://dx.doi.org/10.1016/j.commatsci.2020.110015.

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13

Khoie, R. "A self-consistent numerical method for simulation of quantum transport in high electron mobility transistor; part I: The Boltzmann-Poisson-Schrödinger solver." Mathematical Problems in Engineering 2, no. 3 (1996): 205–18. http://dx.doi.org/10.1155/s1024123x96000324.

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A self-consistent Boltzmann-Poisson-Schrödinger solver for High Electron Mobility Transistor is presented. The quantization of electrons in the quantum well normal to the heterojunction is taken into account by solving the two higher moments of Boltzmann equation along with the Schrödinger and Poisson equations, self-consistently. The Boltzmann transport equation in the form of a current continuity equation and an energy balance equation are solved to obtain the transient and steady-state transport behavior. The numerical instability problems associated with the simulator are presented, and th

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14

Ikeno, Rimon, Hiroshi Ito, and Kunihiro Asada. "One-Dimensional Analysis of Subthreshold Characteristics of SOI-MOSFET Considering Quantum Mechanical Effects." VLSI Design 6, no. 1-4 (1998): 65–67. http://dx.doi.org/10.1155/1998/23890.

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We have been studying on subthreshold characteristics of SOI MOSFETs in terms of substrate bias dependence, using a 1-D Poisson equation on an SOI multi-layer structure for estimating structural parameters of real devices[1]. Here, we consider quantum mechanical effects in the electron inversion layer of thin SOI MOSFETs, implementing a self-consistent solver of Poisson and Schrödinger equations in a 1-D subthreshold simulator. From results of simulations, we have concluded that quantum mechanical effects need to be considered in analizing thin SOI devices.

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15

Tuckerman, Laurette S. "Laplacian Preconditioning for the Inverse Arnoldi Method." Communications in Computational Physics 18, no. 5 (2015): 1336–51. http://dx.doi.org/10.4208/cicp.281114.290615a.

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AbstractMany physical processes are described by elliptic or parabolic partial differential equations. For linear stability problems associated with such equations, the inverse Laplacian provides a very effective preconditioner. In addition, it is also readily available in most scientific calculations in the form of a Poisson solver or an implicit diffusive timestep. We incorporate Laplacian preconditioning into the inverse Arnoldi method, using BiCGSTAB to solve the large linear systems. Two successful implementations are described: spherical Couette flow described by the Navier-Stokes equati

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16

Kim, Joong-sik, and Taeyoung Won. "Device Optimization of Multiple-Channel Field Effect Transistor with Two Dimensional Poisson–Schrödinger Solver." Japanese Journal of Applied Physics 45, no. 6B (2006): 5474–77. http://dx.doi.org/10.1143/jjap.45.5474.

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17

Odili, D. I., Y. Wu, P. A. Childs, and D. C. Herbert. "Modeling charge transport in graphene nanoribbons and carbon nanotubes using a Schrödinger-Poisson solver." Journal of Applied Physics 106, no. 2 (2009): 024509. http://dx.doi.org/10.1063/1.3174430.

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18

Pourfath, M., H. Kosina, and S. Selberherr. "A fast and stable Poisson-Schrödinger solver for the analysis of carbon nanotube transistors." Journal of Computational Electronics 5, no. 2-3 (2006): 155–59. http://dx.doi.org/10.1007/s10825-006-8836-z.

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19

Pourghaderi, M. Ali, Wim Magnus, Bart Sorée, Kristin De Meyer, Marc Meuris, and Marc Heyns. "General 2D Schrödinger-Poisson solver with open boundary conditions for nano-scale CMOS transistors." Journal of Computational Electronics 7, no. 4 (2008): 475–84. http://dx.doi.org/10.1007/s10825-008-0257-8.

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20

FOSSUM, JERRY G. "A SIMULATION-BASED PREVIEW OF EXTREMELY SCALED DOUBLE-GATE CMOS DEVICES AND CIRCUITS." International Journal of High Speed Electronics and Systems 12, no. 02 (2002): 563–72. http://dx.doi.org/10.1142/s0129156402001460.

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This paper gives a simulation-based preview of device-design issues and performance of extremely scaled DG CMOS. A suite of simulation tools, including a 2D numerical device simulator, a 1D numerical Poisson-Schrödinger solver, and a generic, physics/process-based DG MOSFET compact model in Spice, is applied to both asymmetrical-and symmetrical-gate DG CMOS devices and circuits to provide physical insight at the device and circuit levels. The results give added motivation as well as preliminary guidance for the development of DG CMOS.

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21

Glembocki, Orest J., Marek Skowronski, S. M. Prokes, D. Kurt Gaskill, and Joshua D. Caldwell. "Observation of Free Carrier Redistribution Resulting from Stacking Fault Formation in Annealed 4H-SiC." Materials Science Forum 527-529 (October 2006): 347–50. http://dx.doi.org/10.4028/www.scientific.net/msf.527-529.347.

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Bulk n+-4H-SiC wafers (n=1-2×1019 cm-3) containing annealing-induced stacking faults were examined by Raman scattering. The coupled plasmon-LO mode was observed to shift in a manner consistent with 1018 cm-3 doping in the 4H-SiC. Numerical simulations were performed using a self-consistent Poisson-Schrödinger solver and agree well with the experimental observations of carrier transfer from the 4H-SiC into the 3C-SiC stacking faults. The Raman data also shows that the 3C stacking faults induce a tensile strain on the surrounding 4H-SiC regions.

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22

Wang, Lingquan, Peter M. Asbeck, and Yuan Taur. "Self-consistent 1-D Schrödinger–Poisson solver for III–V heterostructures accounting for conduction band non-parabolicity." Solid-State Electronics 54, no. 11 (2010): 1257–62. http://dx.doi.org/10.1016/j.sse.2010.06.018.

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23

Cassan, Eric. "On the reduction of direct tunneling leakage through ultrathin gate oxides by a one-dimensional Schrödinger–Poisson solver." Journal of Applied Physics 87, no. 11 (2000): 7931–39. http://dx.doi.org/10.1063/1.373477.

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24

Vecil, Francesco, José M. Mantas, María J. Cáceres, Carlos Sampedro, Andrés Godoy, and Francisco Gámiz. "A parallel deterministic solver for the Schrödinger–Poisson–Boltzmann system in ultra-short DG-MOSFETs: Comparison with Monte-Carlo." Computers & Mathematics with Applications 67, no. 9 (2014): 1703–21. http://dx.doi.org/10.1016/j.camwa.2014.02.021.

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25

PALANICHAMY, VIMALA, and N. B. BALAMURUGAN. "ANALYTICAL MODELING OF DRAIN CURRENT, CAPACITANCE AND TRANSCONDUCTANCE IN SYMMETRIC DOUBLE-GATE MOSFETs CONSIDERING QUANTUM EFFECTS." International Journal of Nanoscience 12, no. 01 (2013): 1350005. http://dx.doi.org/10.1142/s0219581x13500051.

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An analytical model for double-gate (DG) MOSFETs considering quantum mechanical effects is proposed in this paper. Schrödinger and Poisson's equations are solved simultaneously using a variational approach. Solving the Poisson and Schrödinger equations simultaneously reveals quantum effects (QME) that influence the performance of DG MOSFETs. This model is developed to provide an analytical expression for inversion charge distribution function for all regions of device operation. This expression is used to calculate the other important parameters like inversion layer centroid, inversion charge,

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26

Mak, Man Kwong, Chun Sing Leung, and Tiberiu Harko. "The effects of the dark energy on the static Schrödinger–Newton system — An Adomian Decomposition Method and Padé approximants based approach." Modern Physics Letters A 36, no. 06 (2021): 2150038. http://dx.doi.org/10.1142/s0217732321500383.

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The Schrödinger–Newton system is a nonlinear system obtained by coupling together the linear Schrödinger equation of quantum mechanics with the Poisson equation of Newtonian mechanics. In this work, we will investigate the effects of a cosmological constant (dark energy or vacuum fluctuation) on the Schrödinger–Newton system, by modifying the Poisson equation through the addition of a new term. The corresponding Schrödinger–Newton-[Formula: see text] system cannot be solved exactly, and therefore for its study one must resort to either numerical or semianalytical methods. In order to obtain a

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27

Mordkovich, V. N., K. K. Abgaryan, D. L. Reviznikov, and A. V. Leonov. "Simulation of Hall field elements based on nanoscale silicon-on-insulator heterostructures." Izvestiya Vysshikh Uchebnykh Zavedenii. Materialy Elektronnoi Tekhniki = Materials of Electronics Engineering 23, no. 2 (2020): 109–15. http://dx.doi.org/10.17073/1609-3577-2020-2-109-115.

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The article is devoted to the issues of numerical simulation of field Hall sensors based on the "silicon on insulator" structure with two control gates. To solve the problem, a two-level local-one-dimensional computational model is used. At the first level, a series of one-dimensional Schrödinger—Poisson equations are solved, which describe the distribution of the electron density across the heterostructure in different sections. The obtained information is transmitted to the second level, where the current characteristics of the element are calculated. The numerical simulation results are com

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28

Guo, Hui, and Tao Wang. "Infinitely Many Solutions for the Nonlinear Schrödinger–Poisson System with Broken Symmetry." Advanced Nonlinear Studies 21, no. 3 (2021): 579–92. http://dx.doi.org/10.1515/ans-2021-2132.

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Abstract In this paper, we consider the following Schrödinger–Poisson system with perturbation: { - Δ ⁢ u + u + λ ⁢ ϕ ⁢ ( x ) ⁢ u = | u | p - 2 ⁢ u + g ⁢ ( x ) , x ∈ ℝ 3 , - Δ ⁢ ϕ = u 2 , x ∈ ℝ 3 , \left\{\begin{aligned} \displaystyle-\Delta u+u+\lambda\phi(x)u&\displaystyle=% |u|^{p-2}u+g(x),&&\displaystyle x\in\mathbb{R}^{3},\\ \displaystyle-\Delta\phi&\displaystyle=u^{2},&&\displaystyle x\in\mathbb{R}^{3% },\end{aligned}\right. where λ > 0 {\lambda>0} , p ∈ ( 3 , 6 ) {p\in(3,6)} and the radial general perturbation term g ⁢ ( x ) ∈ L p p - 1 ⁢ ( ℝ 3 ) {g(x)\in L

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29

SHAMAROV, N. N. "POISSON–MASLOV TYPE FORMULAS FOR SCHRÖDINGER EQUATIONS WITH MATRIX-VALUED POTENTIALS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 10, no. 04 (2007): 641–49. http://dx.doi.org/10.1142/s0219025707002877.

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Cauchy problems for Schrödinger equations with matrix-valued potentials are explicitly solved under following assumptions:. — equations are written in momentum form;. — the potentials are Fourier transformed matrix-valued measures with, in general, noncommuting values;. — initial Cauchy data are good enough. The solutions at time t are presented in form of integrals over some spaces of piecewise continuous mappings of the segment [0, t] to a finite-dimensional momentum space, and measures of the integration are countably additive but matrix-valued (resulting in matrices of ordinary Lebesgue in

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30

MARMO, GIUSEPPE, and GAETANO VILASI. "SYMPLECTIC STRUCTURES AND QUANTUM MECHANICS." Modern Physics Letters B 10, no. 12 (1996): 545–53. http://dx.doi.org/10.1142/s0217984996000602.

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Canonical coordinates for the Schrödinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schrödinger equation, considered as a classical field theory, shares with Liouville completely integrable field theories the existence of a recursion operator which allows for the infinitely many conserved functionals pairwise commuting with respect to the corresponding Poisson bracket. The approach may provide a good starting point to get a clear interpretation of Quantum Mechanics in the general setting, provided by Stone–von Neumann theorem, of Symplecti

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31

ŞAHİN, MEHMET, and MEHMET TOMAK. "SELF-CONSISTENT CALCULATION OF SEMICONDUCTOR HETEROJUNCTIONS USING QUANTUM GENETIC ALGORITHM." International Journal of Modern Physics B 16, no. 26 (2002): 3883–93. http://dx.doi.org/10.1142/s0217979202014759.

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In this study, we have investigated the ground state energy level of electrons in modulation doped GaAs / Al x Ga 1 - x As heterojunctions. For this purpose, Schrödinger and Poisson equations are solved self consistently using quantum genetic algorithm (QGA). In this way, we have found the potential profile, the ground state subband energy and their corresponding envelope functions, Fermi level, and the amount of tunneling charge from barrier to channel region. Their dependence on various device parameters are also examined.

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32

Ueno, H., S. Yamakawa, C. Hamaguchi, and K. Miyatsuji. "Monte Carlo Simulation of HEMT based on Self-Consistent Method." VLSI Design 6, no. 1-4 (1998): 13–16. http://dx.doi.org/10.1155/1998/41787.

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Device simulation of HEMT (High Electron Mobility Transistor) has been carried out by ensemble Monte Carlo simulation, where two-dimensional motion of electrons confined in GaAs region at GaAs/AIGaAs heterointerface is taken into account. In order to develop a realistic device simulator of HEMT, we divide the channel region in meshes, and Schrödinger and Poisson equations are solved self-consistently to obtain electronic states of the twodimensional electrons in a mesh. In addition the real space transfer from GaAs layer into AIGaAs barrier layer is taken into account.

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33

JOVANOVIĆ, D., R. FEDELE, F. TANJIA, S. DE NICOLA, and M. BELIĆ. "Coherent quantum hollow beam creation in a plasma wakefield accelerator." Journal of Plasma Physics 79, no. 4 (2013): 397–403. http://dx.doi.org/10.1017/s0022377813000111.

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AbstractA theoretical investigation of the propagation of a relativistic electron (or positron) particle beam in an overdense magnetoactive plasma is carried out within a fluid plasma model, taking into account the individual quantum properties of beam particles. It is demonstrated that the collective character of the particle beam manifests mostly through the self-consistent macroscopic plasma wakefield created by the charge and the current densities of the beam. The transverse dynamics of the beam–plasma system is governed by the Schrödinger equation for a single-particle wavefunction derive

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34

ABOU-ELNOUR, ALI. "PERFORMANCE LIMITS OF SIMULATION MODELS FOR NOISE CHARACTERIZATION OF MM WAVE DEVICES." Fluctuation and Noise Letters 07, no. 03 (2007): L299—L312. http://dx.doi.org/10.1142/s0219477507003957.

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Based on Boltzmann transport equation, the drift-diffusion, hydrodynamic, and Monte-Carlo physical simulators are accurately developed. For each simulator, the model equations are self-consistently solved with Poisson equation, and with Schrödinger equation when quantization effects take place, in one and two-dimensions to characterize the operation and optimize the structure of mm-wave devices. The effects of the device dimensions, biasing conditions, and operating frequencies on the accuracy of results obtained from the simulators are thoroughly investigated. Based on physical understanding

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35

KIM, H. J., and K. S. YI. "MAGNETIZATION OF DIGITALLY Mn-DOPED DILUTED MAGNETIC SEMICONDUCTOR QUANTUM WELLS." International Journal of Modern Physics B 18, no. 27n29 (2004): 3757–60. http://dx.doi.org/10.1142/s0217979204027414.

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We present spin-resolved electronic properties of digitally Mn -doped diluted magnetic semiconductor (DMS) quantum wells (QWs) with an emphasis on the control of spontaneous magnetization and spin carrier distributions in terms of QW structure parameters and doping profiles of the magnetic ions. A combined Schrödinger and Poisson equation is solved numerically to obtain self-consistent subband wavefunctions and energies of the holes in the DMS QWs. Self-consistent spin-resolved subband structure shows that (i) the spatial distributions of the majority and minority spin carriers are separated i

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36

Du, Dianlou, and Xiao Yang. "Algebraic-geometrical solutions of three (2 + 1)-dimensional nonlinear equations via Hamiltonian approach." International Journal of Geometric Methods in Modern Physics 12, no. 03 (2015): 1550038. http://dx.doi.org/10.1142/s0219887815500383.

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The algebraic-geometrical solutions of three (2 + 1)-dimensional equations (including mKP equation and coupled mKP equation) are discussed by Hamiltonian approach. First, the Poisson structure on CN × RN is introduced to give a Hamiltonian system associated with the derivative nonlinear Schrödinger (DNLS) hierarchy. The Hamiltonian system is proved to be Liouville integrable, accordingly the solutions of three (2 + 1)-dimensional nonlinear equations can be solved by three compatible Hamiltonian flows. Second, the canonical separated variables and Hamilton–Jacobi theory is used to definite acti

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37

Kevkić, Tijana, and Vladica Stojanović. "Approximate Solution of Coupled Schrödinger and Poisson Equation in Inversion Layer Problem: An Approach Based on Homotopy Perturbations." Zeitschrift für Naturforschung A 74, no. 6 (2019): 457–67. http://dx.doi.org/10.1515/zna-2018-0495.

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AbstractIn this paper, the homotopy perturbation method (HPM) is applied to the coupled set of Schrödinger–Poisson (SP) equations in inversion layer problem for obtaining the approximate analytical solution. Inversion layer of n-type is considered, and the electric quantum limit is assumed. By introducing some dimensionless quantities, the SP system has been turned into one which can be solved along the infinite interval. After some appropriate transformations, the infinite interval has been reduced to finite one $(0,1)$, and recurrence series of the HPM approximate solutions of the coupled SP

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38

Gil-Corrales, John A., Juan A. Vinasco, Adrian Radu, et al. "Self-Consistent Schrödinger-Poisson Study of Electronic Properties of GaAs Quantum Well Wires with Various Cross-Sectional Shapes." Nanomaterials 11, no. 5 (2021): 1219. http://dx.doi.org/10.3390/nano11051219.

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Quantum wires continue to be a subject of novel applications in the fields of electronics and optoelectronics. In this work, we revisit the problem of determining the electron states in semiconductor quantum wires in a self-consistent way. For that purpose, we numerically solve the 2D system of coupled Schrödinger and Poisson equations within the envelope function and effective mass approximations. The calculation method uses the finite-element approach. Circle, square, triangle and pentagon geometries are considered for the wire cross-sectional shape. The features of self-consistent band prof

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39

Qin, Jian, Quanbin Zhou, Biyan Liao, and Hong Wang. "Modeling of 2DEG characteristics of InxAl1−xN/AlN/GaN-Based HEMT Considering Polarization and Quantum Mechanical Effect." Electronics 7, no. 12 (2018): 410. http://dx.doi.org/10.3390/electronics7120410.

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A comprehensive model for 2DEG characteristics of InxAl1−xN/AlN/GaN heterostructure has been presented, taking both polarization and bulk ionized charge into account. Investigations on the 2DEG density and electron distribution across the heterostructure have been carried out using solutions of coupled 1-D Schrödinger-Poisson equations solved by an improved iterative scheme. The proposed model extends a previous approach allowing for estimating the quantum mechanical effect for a generic InAlN/GaN-based HEMT within the range of the Hartree approximation. A critical AlN thickness (~2.28 nm) is

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40

Jafarzadeh, Hossein, Elnaz Ahmadi Sangachin, and Seyyed Hossein Asadpour. "Controlling of group velocity via terahertz signal radiation in a defect medium doped by four-level InGaN/GaN quantum dot nanostructure." Modern Physics Letters B 29, no. 20 (2015): 1550104. http://dx.doi.org/10.1142/s0217984915501043.

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In this paper, we propose a novel scheme for controlling the group velocity of transmitted and reflected pulse from defect medium doped with four-level InGaN/GaN quantum dot nanostructure. Quantum dot nanostructure is designed numerically by Schrödinger and Poisson equations which solve self consistently. By size control of quantum dot and external voltage, one can design a four-level quantum dot with appropriate energy levels which can be suitable for controlling the group velocity of pulse transmission and reflection from defect slab with terahertz signal field. It is found that in the prese

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41

WANG, ZHENG-CHUAN, LING LI, and JIE GAO. "ELECTRON–ELECTRON INTERACTIONS IN THE QUANTUM DOT INDUCED BY THE SURFACE ACOUSTIC WAVE." Modern Physics Letters B 18, no. 19n20 (2004): 1029–34. http://dx.doi.org/10.1142/s0217984904007517.

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In order to study the higher order quantized plateaus in the acoustoelectric current induced by the surface acoustic wave (SAW), we consider in this paper, the Coulomb interaction of electrons trapped in the SAW-induced quantum dot at the Hartree approximation level. The Hartree self-consistent potential that originates from the electron–electron interactions in the quantum dot satisfies the Poisson equation and can be solved numerically together with the Schrödinger equation; following which, the conventional tunneling mechanism can be used to interpret the step-like acoustoelectric current,

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42

FARACLAS, ELIAS, RICHARD T. WEBSTER, GEORGE BRANDES, and A. F. M. ANWAR. "DEPENDENCE OF RF PERFORMANCE OF GaN/AlGaN HEMTS UPON AlGaN BARRIER LAYER VARIATION." International Journal of High Speed Electronics and Systems 14, no. 03 (2004): 750–55. http://dx.doi.org/10.1142/s0129156404002788.

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The dependence of microwave performance of GaN/AlGaN High Electron Mobility Transistors (HEMTs), namely the unity gain current cut-off frequency (fT) and the maximum oscillation frequency (fMAX), are reported as a function of the mole fraction of Al and the thickness of the barrier AlGaN layer. The parameters are computed using a physics-based model and compared to experimental results. Schrödinger and Poisson's equations are solved self-consistently to relate the applied gate bias to the channel electron concentration. The contributions of both spontaneous and piezoelectric polarizations towa

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Verma, Yogesh Kumar, Varun Mishra, and Santosh Kumar Gupta. "A Physics-Based Analytical Model for MgZnO/ZnO HEMT." Journal of Circuits, Systems and Computers 29, no. 01 (2019): 2050009. http://dx.doi.org/10.1142/s0218126620500097.

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In this paper, a physics-based compact model is developed for novel MgZnO/ZnO high-electron-mobility transistor (HEMT). Poisson’s equation coupled with 1D Schrödinger equation is solved self-consistently in the triangular quantum well to derive an expression of two-dimensional electron gas (2DEG) density with respect to gate voltage at the heterointerface of barrier (MgZnO) and buffer (ZnO) layers. A compact mathematical framework has been devised further for the first time for ZnO-based HEMT to the best of our knowledge using the expression of 2DEG density to compute surface potential, gate c

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Patil, Dnyaneshwar S., and E. P. Samuel. "Analysis of Optical Properties of GaN/AlGaN Quantum Well Ultra-Violet Laser Diode Using 6X6 Hamiltonian." Materials Science Forum 638-642 (January 2010): 1653–58. http://dx.doi.org/10.4028/www.scientific.net/msf.638-642.1653.

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The Quantum well structures have exhibited significant utility in the fabrication of advanced laser devices. The Gallium nitride semiconductor and its alloy particularly AlGaN based quantum structures are having important applications in optical data storage systems and the visible displays. Due to tailoring of wide band gap energy the spectrum obtained is from visible to ultraviolet wavelength range. We had thoroughly investigated the influence of Aluminum mole fraction variation in AlxGa1-xN under a biased condition for GaN/AlGaN based quantum heterostructure optical properties. Here, we had

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Danielewski, Marek, and Lucjan Sapa. "Foundations of the Quaternion Quantum Mechanics." Entropy 22, no. 12 (2020): 1424. http://dx.doi.org/10.3390/e22121424.

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We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of

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KORDROSTAMI, ZOHEIR, M. HOSSEIN SHEIKHI, and ABBAS ZARIFKAR. "DESIGN DEPENDENT CUTOFF FREQUENCY OF NANOTRANSISTORS NEAR THE ULTIMATE PERFORMANCE LIMIT." International Journal of Modern Physics B 26, no. 32 (2012): 1250196. http://dx.doi.org/10.1142/s0217979212501962.

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We have studied the effect of different structural designs of double gate MOSFETs (DG–MOSFETs) and carbon nanotube field effect transistors (CNTFETs) on the cutoff frequency (fT). The effects of metallic contacts with Schottky barriers, gate work function, dual material gate (DMG), halo doped channel and lightly doped drain and source (LDDS) architectures on the fT have been investigated for DG–MOSFETs and CNTFETs and the design dependent fT for both types of transistors has been studied for the first time. The simulations are based on the Schrödinger–Poisson solvers developed for each nanotra

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Davies, Elliot Y., and Philip Mocz. "Fuzzy dark matter soliton cores around supermassive black holes." Monthly Notices of the Royal Astronomical Society 492, no. 4 (2020): 5721–29. http://dx.doi.org/10.1093/mnras/staa202.

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ABSTRACT We explore the effect of a supermassive black hole (SMBH) on the density profile of a fuzzy dark matter (FDM) soliton core at the centre of a dark matter (DM) halo. We numerically solve the Schrödinger–Poisson equations, treating the black hole as a gravitational point mass, and demonstrate that this additional perturbing term has a ‘squeezing’ effect on the soliton density profile, decreasing the core radius, and increasing the central density. In the limit of large black hole mass, the solution approaches one akin to the hydrogen atom, with radius inversely proportional to the black

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Sadi, Toufik, Cristina Medina-Bailon, Mihail Nedjalkov, et al. "Simulation of the Impact of Ionized Impurity Scattering on the Total Mobility in Si Nanowire Transistors." Materials 12, no. 1 (2019): 124. http://dx.doi.org/10.3390/ma12010124.

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Nanowire transistors (NWTs) are being considered as possible candidates for replacing FinFETs, especially for CMOS scaling beyond the 5-nm node, due to their better electrostatic integrity. Hence, there is an urgent need to develop reliable simulation methods to provide deeper insight into NWTs’ physics and operation, and unlock the devices’ technological potential. One simulation approach that delivers reliable mobility values at low-field near-equilibrium conditions is the combination of the quantum confinement effects with the semi-classical Boltzmann transport equation, solved within the r

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Nakano, Aiichiro, Rajiv K. Kalia, and Priya Vashishta. "Quantum Dynamical Simulation of Many Electron-Phonon Coupled Systems on Parallel Computers." MRS Proceedings 291 (January 1, 1992). http://dx.doi.org/10.1557/proc-291-73.

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ABSTRACTA quantum dynamical simulation method is developed to investigate coupled many electron-phonon systems. Both electron and phonon wave functions are numerically propagated in time. The method is applied to the study of resonant tunneling of an electron through double quantum dots. Phonon-induced electron localization is observed. The space- splitting Schrödinger solver and dynamical-simulated-annealing Poisson solver are implemented on an 8,192-node MP-1 computer from MasPar.

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Dolgov, Sergey, and Tomáš Vejchodský. "Guaranteed a posteriori error bounds for low-rank tensor approximate solutions." IMA Journal of Numerical Analysis, June 9, 2020. http://dx.doi.org/10.1093/imanum/draa010.

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Abstract We propose a guaranteed and fully computable upper bound on the energy norm of the error in low-rank tensor train (TT) approximate solutions of (possibly) high-dimensional reaction–diffusion problems. The error bound is obtained from Euler–Lagrange equations for a complementary flux reconstruction problem, which are solved in the low-rank TT representation using the block alternating linear scheme. This bound is guaranteed to be above the energy norm of the total error, including the discretization error, the tensor approximation error and the error in the solver of linear algebraic e

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