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The Finite Element Solutions to the Semiconductor Equations
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作者 管平 王文胜 《Journal of Southeast University(English Edition)》 EI CAS 1999年第1期75-80,共6页
In this paper, the approximation of stationary equations of the semiconductor devices with mixed boundary conditions is considered. Two schemes are proposed for the system. One is Glerkin discrete scheme, the other is... In this paper, the approximation of stationary equations of the semiconductor devices with mixed boundary conditions is considered. Two schemes are proposed for the system. One is Glerkin discrete scheme, the other is hybrid variable discrete scheme. A convergence analysis is also given. 展开更多
关键词 semiconductor equations finite element Galerkin method hybrid variable method
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EXISTENCE OF WEAK SOLUTIONS TO A DEGENERATE STEAD-STATE SEMICONDUCTOR EQUATIONS
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作者 吴斌 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期960-968,共9页
In this paper, we consider a degenerate steady-state drift-diffusion model for semiconductors. The pressure function used in this paper is ()(s) = s~α(α 〉 1). We present existence results for general nonlinea... In this paper, we consider a degenerate steady-state drift-diffusion model for semiconductors. The pressure function used in this paper is ()(s) = s~α(α 〉 1). We present existence results for general nonlinear diffhsivities for the degenerate Dirichlet-Neumann mixed boundary value problem. 展开更多
关键词 STEADY-STATE degenerate semiconductor equations drift-diffusion model
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On Global Boundedness of Solutions for the Drift-diffusion Semiconductor Equations
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作者 GUO Xiu-lan ZHANG Yu-lan LI Gong-sheng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第4期590-596,共7页
This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.
关键词 drift-diffusion model semiconductor equations global boundedness stampac-chia recurrence method
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ON EXISTENCE, UNIQUENESS AND REGULARITY OF STEADY STATE SOLUTIONS TO THE BASIC SEMICONDUCTOR EQUATIONS
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作者 王元明 樊继山 《Acta Mathematica Scientia》 SCIE CSCD 1995年第2期180-188,共9页
Ealstence and regularity of steady state solutions to the basic semiconductor equations with the non-monotone net recombination rate are proved. A sufficient condition for the uniqueness of the steady state solutions ... Ealstence and regularity of steady state solutions to the basic semiconductor equations with the non-monotone net recombination rate are proved. A sufficient condition for the uniqueness of the steady state solutions is given. The uniqueness result is very general which contains almost all known conclusions. 展开更多
关键词 semiconductor equations EXISTENCE UNIQUENESS regularity.
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Existence of Weak Solutions to a Class of Semiconductor Equations with Fast Diffusion Term
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作者 Bin WU 《Journal of Mathematical Research and Exposition》 CSCD 2010年第5期855-862,共8页
In this paper, we consider the transient drift-diffusion model with fast diffusion term. This problem is not only degenerate but also singular. We present the existence result for the Neumann boundary value problem wi... In this paper, we consider the transient drift-diffusion model with fast diffusion term. This problem is not only degenerate but also singular. We present the existence result for the Neumann boundary value problem with general nonlinear diffusivities. 展开更多
关键词 semiconductor equations fast diffusion term.
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Interference of harmonics emitted by different tunneling momentum channels in laser fields
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作者 Ling-Yu Zhang Zhuo-Xuan Xie +2 位作者 Can Wang Xin-Lei Ge Jing Guo 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第9期366-372,共7页
By numerically solving the semiconductor Bloch equation(SBEs),we theoretically study the high-harmonic generation of ZnO crystals driven by one-color and two-color intense laser pulses.The results show the enhancement... By numerically solving the semiconductor Bloch equation(SBEs),we theoretically study the high-harmonic generation of ZnO crystals driven by one-color and two-color intense laser pulses.The results show the enhancement of harmonics and the cut-off remains the same in the two-color field,which can be explained by the recollision trajectories and electron excitation from multi-channels.Based on the quantum path analysis,we investigate contribution of different ranges of the crystal momentum k of ZnO to the harmonic yield,and find that in two-color laser fields,the intensity of the harmonic yield of different ranges from the crystal momentum makes a big difference and the harmonic intensity is depressed from all k channels,which is related to the interferences between harmonics from symmetric k channels. 展开更多
关键词 high-order harmonic generation the semiconductor Bloch equation k-resolvedinter-bandhar-monic spectrum four-step semiclassical model
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High-order harmonic generation of ZnO crystals in chirped and static electric fields
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作者 张玲玉 何永林 +5 位作者 谢卓璇 高芳艳 徐清芸 葛鑫磊 罗香怡 郭静 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第1期335-343,共9页
High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduce... High harmonic generation in ZnO crystals under chirped single-color field and static electric field are investigated by solving the semiconductor Bloch equation(SBE). It is found that when the chirp pulse is introduced, the interference structure becomes obvious while the harmonic cutoff is not extended. Furthermore, the harmonic efficiency is improved when the static electric field is included. These phenomena are demonstrated by the classical recollision model in real space affected by the waveform of laser field and inversion symmetry. Specifically, the electron motion in k-space shows that the change of waveform and the destruction of the symmetry of the laser field lead to the incomplete X-structure of the crystal-momentum-resolved(k-resolved) inter-band harmonic spectrum. Furthermore, a pre-acceleration process in the solid four-step model is confirmed. 展开更多
关键词 high-order harmonic generation the semiconductor Bloch equation k-resolved inter-band harmonic spectrum four-step semiclassical model
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ASYMPTOTIC BEHAVIOR OF TIME-DEPENDENT SOLUTIONS TO SEMICONDUCTOR EQUATIONS
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作者 邢家省 郭秀兰 《Annals of Differential Equations》 1998年第2期241-247,共7页
This paper considers the relationship between the time dependent solutions and the steady state solutions of semiconductor equations under the thermal equilibrium conditions. The asymptotic behavior of the time depend... This paper considers the relationship between the time dependent solutions and the steady state solutions of semiconductor equations under the thermal equilibrium conditions. The asymptotic behavior of the time dependent solution is obtained. 展开更多
关键词 semiconductor equations time dependent solution steady state solution thermal euqilibrium ASYMPTOTIC
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Role of Bloch oscillation in high-order harmonic generation from periodic structure 被引量:1
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作者 Lu Liu Jing Zhao +1 位作者 Jian-Min Yuan Zeng-Xiu Zhao 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第11期60-66,共7页
The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations(SBEs). The main features of harmonic spectrum from SBEs agree we... The high-order harmonic generation from a model solid structure driven by an intense laser pulse is investigated using the semiconductor Bloch equations(SBEs). The main features of harmonic spectrum from SBEs agree well with the result of the time-dependent Schro¨dinger equation(TDSE), and the cut-off energy can be precisely estimated by the recollision model. With increasing the field strength, the harmonic spectrum shows an extra plateau. Based on the temporal population of electron and the time–frequency analysis, the harmonics in the extra plateau are generated by the Bloch oscillation. Due to the ultrafast time response of the Bloch electron, the generated harmonics provide a potential source of shorter isolated attosecond pulse. 展开更多
关键词 high-order harmonic generation attosecond pulse semiconductor Bloch equations time-dependent Schrodinger equation
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Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime
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作者 Jia Deng 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2012年第2期278-296,共19页
As is known,the numerical stiffness arising from the small mean free path is one of the main difficulties in the kinetic equations.In this paper,we derive both the split and the unsplit schemes for the linear semicond... As is known,the numerical stiffness arising from the small mean free path is one of the main difficulties in the kinetic equations.In this paper,we derive both the split and the unsplit schemes for the linear semiconductor Boltzmann equation with a diffusive scaling.In the two schemes,the anisotropic collision operator is realized by the“BGK”-penalty method,which is proposed by Filbet and Jin[F.Filbet and S.Jin,J.Comp.Phys.229(20),7625-7648,2010]for the kinetic equations and the related problems having stiff sources.According to the numerical results,both of the schemes are shown to be uniformly convergent and asymptotic-preserving.Besides,numerical evidences suggest that the unsplit scheme has a better numerical stability than the split scheme. 展开更多
关键词 linear semiconductor Boltzmann equation drift-diffusion limit diffusive relaxation system “BGK”-penalty method
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A Semi-Lagrangian Deterministic Solver for the Semiconductor Boltzmann-Poisson System 被引量:1
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作者 Jose A.Carrillo Armando Majorana Francesco Vecil 《Communications in Computational Physics》 SCIE 2007年第5期1027-1054,共28页
In this paper we develop a deterministic numerical method for solving the Boltzmann transport equation for semiconductors based on a transport-collision timesplitting method.Transport phases are solved by means of acc... In this paper we develop a deterministic numerical method for solving the Boltzmann transport equation for semiconductors based on a transport-collision timesplitting method.Transport phases are solved by means of accurate flux-balance methods while collision steps are computed in the original k-grid.Numerical experiments are shown allowing for a discussion of this method with respect to other present in the literature. 展开更多
关键词 Kinetic equations for semiconductors semi-Lagrangian schemes splitting schemes.
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Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors
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作者 Giacomo Dimarco Lorenzo Pareschi Vittorio Rispoli 《Communications in Computational Physics》 SCIE 2014年第5期1291-1319,共29页
In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation.The relevant scale which characterizes this kind of problems is the diffusive scal... In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation.The relevant scale which characterizes this kind of problems is the diffusive scaling.This means that,in the limit of zero mean free path,the system is governed by a drift-diffusion equation.Our aim is to develop a method which accurately works for the different regimes encountered in general semiconductor simulations:the kinetic,the intermediate and the diffusive one.Moreover,we want to overcome the restrictive time step conditions of standard time integration techniques when applied to the solution of this kind of phenomena without any deterioration in the accuracy.As a result,we obtain high order time and space discretization schemes which do not suffer from the usual parabolic stiffness in the diffusive limit.We show different numerical results which permit to appreciate the performances of the proposed schemes. 展开更多
关键词 IMEX-RK methods asymptotic preserving methods semiconductor Boltzmann equation drift-diffusion limit
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