In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NL...In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived.Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.展开更多
In this paper, we investigate a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices. We mainly show the long-time behavior of solutions to the one-dimensional bipolar quantum drift-diffusi...In this paper, we investigate a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices. We mainly show the long-time behavior of solutions to the one-dimensional bipolar quantum drift-diffusion model in a bounded domain. That is, we prove the existence of the global attractor for the solution.展开更多
In this study, we consider the one-dimensional bipolar quantum drift-diffusion model, which consists of the coupled nonlinear fourth-order parabolic equation and the electric field equation. We first show the global e...In this study, we consider the one-dimensional bipolar quantum drift-diffusion model, which consists of the coupled nonlinear fourth-order parabolic equation and the electric field equation. We first show the global existence of the strong solution of the initial boundary value problem in the quarter plane. Moreover, we show the self-similarity property of the strong solution of the bipolar quantum drift-diffusion model in the large time. Namely, we show the unique global strong solution with strictly positive density to the initial boundary value problem of the quantum drift-diffusion model, which in large time, tends to have a self-similar wave at an algebraic time-decay rate. We prove them in an energy method.展开更多
In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the ...In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.展开更多
This paper is devoted to the long time behavior for the Drift-diffusion semiconductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants ...This paper is devoted to the long time behavior for the Drift-diffusion semiconductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants and generation-recombination term is the Auger model; as well as the semigroup S(t) denned by the solutions map is differential. Moreover the upper bound of Hausdorff dimension for the attractor is given.展开更多
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.
Based on the nonlinear drift-diffusion(NLDD)model,the coupled behavior between the mechanical and electrical fields in piezoelectric semiconductor(PS)PN junctions under two typical loading conditions is investigated.T...Based on the nonlinear drift-diffusion(NLDD)model,the coupled behavior between the mechanical and electrical fields in piezoelectric semiconductor(PS)PN junctions under two typical loading conditions is investigated.The governing equations for the general shell structure of the PS PN junction are derived within the framework of virtual work principles and charge continuity conditions.The distributions of the electromechanical coupling field are obtained by the Fourier series expansion and the differential quadrature method(DQM),and the nonlinearity is addressed with the iterative method.Several numerical examples are presented to investigate the effects of mechanical loading on the charge carrier transport characteristics.It is found that the barrier height of the heterojunction can be effectively modulated by mechanical loading.Furthermore,a nonlinearity index is introduced to quantify the influence of nonlinearity in the model.It is noted that,when the concentration difference between the two sides is considerable,the nonlinear results differ significantly from the linear results,thereby necessitating the adoption of the NLDD model.展开更多
In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions（close t...In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions（close to equilibrium）of the problem converge to the unique stationary solution.展开更多
In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-...In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-dimensional (1-D) PIN diode structure simulation achieved by solving the drift diffusion model (DDM). Backward Euler algorithm is used for the discretization of the proposed model. The aim is to accomplish time-domain integration. Also, finite different method (FDM) is considered to achieve space-Domain mesh. We introduced an iterative scheme to solve the obtained matrix systems, which combines the Gummel’s iteration with an efficient direct numerical UMFPACK method. The obtained solutions of the proposed algorithm provide the time and space distribution of the unknown functions like electrostatic potential and carrier’s concentration for the PIN diode. As second case, the finite-difference time-domain (FDTD) technique is adopted to analyze the entire 3-D structure of the stripline circuit including the lumped element PIN diode. The microwave circuit is located in an unbounded medium, requiring absorbing boundaries to avoid nonphysical reflections. Active device results were presented and show a good agreement with other reference. Electromagnetic results are qualitatively in agreement with other results obtained using SILVACO-TCAD.展开更多
The quasineutral limit and the mixed layer problem of a three-dimensional drift-diffusion model is discussed in this paper. For the Neumann boundaries and the general initial data, the quasineutral limit is proven rig...The quasineutral limit and the mixed layer problem of a three-dimensional drift-diffusion model is discussed in this paper. For the Neumann boundaries and the general initial data, the quasineutral limit is proven rigorously with the help of the weighted energy method, the matched asymptotic expansion method of singular perturbation problem and the entropy production inequality.展开更多
In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model.The model consists of five nonlinear elliptic equations,and two of them describe q...In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model.The model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi levels.We propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction equations.The IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations.Moreover,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi levels.The Poisson equation of electrical potential is solved with standard Lagrangian finite elements.We prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete problem.Numerical experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.展开更多
针对常用进港航班排序数学模型(总延迟时间最小和总延迟成本最小)中存在的问题,选取空中延误成本、旅客延误成本、后续延误成本以及环境污染成本4个指标综合建立一种改进的总延迟成本最小数学模型。在分析已有的基于模拟退火的粒子群算...针对常用进港航班排序数学模型(总延迟时间最小和总延迟成本最小)中存在的问题,选取空中延误成本、旅客延误成本、后续延误成本以及环境污染成本4个指标综合建立一种改进的总延迟成本最小数学模型。在分析已有的基于模拟退火的粒子群算法(SA-PSO:particle swarm optimization based on simulated annealing)优化进港航班排序时寻优能力不足、收敛速度慢的基础上,采用一种线性微分递减(LDD:linear differential decrease)的退火策略,从而可以有效地解决进港航班排序问题。实验结果表明,与FCFS(first come first serve)、PSO以及SA-PSO算法相比,LDD-SA-PSO算法在进港航班优化问题上具有较好的寻优能力和收敛速度,同时改进数学模型中参数选择对优化结果也具有明显影响。展开更多
In this study, micro-hollow cathode discharge （MHCD） is investigated by a fluid model with drift-diffusion approximation. The MHC device is a cathode/dielectric/anode sandwich structure with one hole of a diameter D...In this study, micro-hollow cathode discharge （MHCD） is investigated by a fluid model with drift-diffusion approximation. The MHC device is a cathode/dielectric/anode sandwich structure with one hole of a diameter D=200 um. The gas is a Ne/Xe mixture at a pressure p=50-500 Torr. The evolutions of the discharge show that there are two different discharge modes. At larger pD the discharge plasma and high density excited species expand along the cathode surface and, a ringed discharge mode is formed. At smaller pD, the discharge plasma and the excited species expand along the axis of the cathode aperture to form a columnar discharge.展开更多
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
The mixing morphology control plays a crucial role in photovoltaic power generation,yet this specific effect on device performances remains elusive.Here,we employed computational approaches to delineate the photovolta...The mixing morphology control plays a crucial role in photovoltaic power generation,yet this specific effect on device performances remains elusive.Here,we employed computational approaches to delineate the photovoltaic properties of layered heterojunction polymer solar cells with tunable mixing morphologies.One-step quench and two-step quench strategies were proposed to adjust the mixing morphology by thermodynamic and kinetic effects.The computation for the one-step quench revealed that modulating interfacial widths and interfacial roughness could significantly promote the photovoltaic performance of layered heterojunction polymer solar cells.The two-step quench can provide a buffer at a lower temperature before the kinetic quenching,leading to the formation of small-length-scale islands connected to the interface and a further increase in photovoltaic performance.Our discoveries are supported by recent experimental evidence and are anticipated to guide the design of photovoltaic materials with optimal performance.展开更多
The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. The...The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory of the quantum scattering characteristics of the superlattice elementary cell (like e.g.transmission resonances) are shown in order. Two examples are treated with the analyticallycomputation of the diffusion constants.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 12172236, 12202289,and U21A20430)the Science and Technology Research Project of Hebei Education Department of China (No. QN2022083)。
文摘In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived.Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.
基金Supported by the National Natural Science Foundation of China(11671134)
文摘In this paper, we investigate a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices. We mainly show the long-time behavior of solutions to the one-dimensional bipolar quantum drift-diffusion model in a bounded domain. That is, we prove the existence of the global attractor for the solution.
基金Supported by the National Natural Science Foundation of China(11671134)
文摘In this study, we consider the one-dimensional bipolar quantum drift-diffusion model, which consists of the coupled nonlinear fourth-order parabolic equation and the electric field equation. We first show the global existence of the strong solution of the initial boundary value problem in the quarter plane. Moreover, we show the self-similarity property of the strong solution of the bipolar quantum drift-diffusion model in the large time. Namely, we show the unique global strong solution with strictly positive density to the initial boundary value problem of the quantum drift-diffusion model, which in large time, tends to have a self-similar wave at an algebraic time-decay rate. We prove them in an energy method.
基金Supported by the National Natural Science Foundation of China(11171223)
文摘In this paper, we study the classical drift-diffusion model arising from the semiconductor device simulation, which is the simplest macroscopic model describing the dynamics of the electron and the hole. We prove the global existence of strong solutions for the initial boundary value problem in the quarter plane. In particular, we show that in large time, these solutions tend to the nonlinear diffusion wave which is different from the steady state, at an algebraic time-decay rate. As far as we know, this is the first result about the nonlinear diffusion wave phenomena of the solutions for the one-dimensional drift-diffusion model in the quarter plane.
基金This work is supported by the Funds of the Nature Science Research of Henan(10371111).
文摘This paper is devoted to the long time behavior for the Drift-diffusion semiconductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants and generation-recombination term is the Auger model; as well as the semigroup S(t) denned by the solutions map is differential. Moreover the upper bound of Hausdorff dimension for the attractor is given.
基金Supported the National Natural Science Foundation of China（10471080） Supported by the Natural Science Foundation of Henan Province（2004110008）
文摘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.
基金supported by the National Key Research and Development Program of China(No.2023YFE0111000)the National Natural Science Foundation of China(Nos.12372151,12302200,12172171,12172183,and U24A2005)+6 种基金the Natural Science Foundation of Jiangsu Province of China(No.BK20230873)the China Postdoctoral Science Foundation(No.2023M731671)the Jiangsu Funding Program for Excellent Postdoctoral Talent(No.2023ZB156)the Shenzhen Science and Technology Program(No.JCYJ20230807142004009)the Jiangsu Association for Science&Technology Youth Science&Technology Talents Lifting Projectthe Russian Ministry of Science and Higher Education(No.075-15-2023-580)the Shenzhen Longhua Science and Technology Innovation Special Funding(Industrial Sci-Tech Innovation Center of Low-Altitude Intelligent Networking)。
文摘Based on the nonlinear drift-diffusion(NLDD)model,the coupled behavior between the mechanical and electrical fields in piezoelectric semiconductor(PS)PN junctions under two typical loading conditions is investigated.The governing equations for the general shell structure of the PS PN junction are derived within the framework of virtual work principles and charge continuity conditions.The distributions of the electromechanical coupling field are obtained by the Fourier series expansion and the differential quadrature method(DQM),and the nonlinearity is addressed with the iterative method.Several numerical examples are presented to investigate the effects of mechanical loading on the charge carrier transport characteristics.It is found that the barrier height of the heterojunction can be effectively modulated by mechanical loading.Furthermore,a nonlinearity index is introduced to quantify the influence of nonlinearity in the model.It is noted that,when the concentration difference between the two sides is considerable,the nonlinear results differ significantly from the linear results,thereby necessitating the adoption of the NLDD model.
基金Supported by the Financial Project of Key Youth in College of Henan Province
文摘In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions（close to equilibrium）of the problem converge to the unique stationary solution.
文摘In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-dimensional (1-D) PIN diode structure simulation achieved by solving the drift diffusion model (DDM). Backward Euler algorithm is used for the discretization of the proposed model. The aim is to accomplish time-domain integration. Also, finite different method (FDM) is considered to achieve space-Domain mesh. We introduced an iterative scheme to solve the obtained matrix systems, which combines the Gummel’s iteration with an efficient direct numerical UMFPACK method. The obtained solutions of the proposed algorithm provide the time and space distribution of the unknown functions like electrostatic potential and carrier’s concentration for the PIN diode. As second case, the finite-difference time-domain (FDTD) technique is adopted to analyze the entire 3-D structure of the stripline circuit including the lumped element PIN diode. The microwave circuit is located in an unbounded medium, requiring absorbing boundaries to avoid nonphysical reflections. Active device results were presented and show a good agreement with other reference. Electromagnetic results are qualitatively in agreement with other results obtained using SILVACO-TCAD.
文摘The quasineutral limit and the mixed layer problem of a three-dimensional drift-diffusion model is discussed in this paper. For the Neumann boundaries and the general initial data, the quasineutral limit is proven rigorously with the help of the weighted energy method, the matched asymptotic expansion method of singular perturbation problem and the entropy production inequality.
基金supported by National Key R&D Program of China 2019YFA0709600 and 2019YFA0709602Weiying Zheng was supported in part by National Key R&D Program of China 2019YFA0709600 and 2019YFA0709602the National Science Fund for Distinguished Young Scholars 11725106,and the NSFC major grant 11831016.
文摘In this paper,we propose a positivity-preserving finite element method for solving the three-dimensional quantum drift-diffusion model.The model consists of five nonlinear elliptic equations,and two of them describe quantum corrections for quasi-Fermi levels.We propose an interpolated-exponential finite element(IEFE)method for solving the two quantum-correction equations.The IEFE method always yields positive carrier densities and preserves the positivity of second-order differential operators in the Newton linearization of quantum-correction equations.Moreover,we solve the two continuity equations with the edge-averaged finite element(EAFE)method to reduce numerical oscillations of quasi-Fermi levels.The Poisson equation of electrical potential is solved with standard Lagrangian finite elements.We prove the existence of solution to the nonlinear discrete problem by using a fixed-point iteration and solving the minimum problem of a new discrete functional.A Newton method is proposed to solve the nonlinear discrete problem.Numerical experiments for a three-dimensional nano-scale FinFET device show that the Newton method is robust for source-to-gate bias voltages up to 9V and source-to-drain bias voltages up to 10V.
文摘针对常用进港航班排序数学模型(总延迟时间最小和总延迟成本最小)中存在的问题,选取空中延误成本、旅客延误成本、后续延误成本以及环境污染成本4个指标综合建立一种改进的总延迟成本最小数学模型。在分析已有的基于模拟退火的粒子群算法(SA-PSO:particle swarm optimization based on simulated annealing)优化进港航班排序时寻优能力不足、收敛速度慢的基础上,采用一种线性微分递减(LDD:linear differential decrease)的退火策略,从而可以有效地解决进港航班排序问题。实验结果表明,与FCFS(first come first serve)、PSO以及SA-PSO算法相比,LDD-SA-PSO算法在进港航班优化问题上具有较好的寻优能力和收敛速度,同时改进数学模型中参数选择对优化结果也具有明显影响。
基金supported by National Natural Science Foundation of China （No. 11005009）
文摘In this study, micro-hollow cathode discharge （MHCD） is investigated by a fluid model with drift-diffusion approximation. The MHC device is a cathode/dielectric/anode sandwich structure with one hole of a diameter D=200 um. The gas is a Ne/Xe mixture at a pressure p=50-500 Torr. The evolutions of the discharge show that there are two different discharge modes. At larger pD the discharge plasma and high density excited species expand along the cathode surface and, a ringed discharge mode is formed. At smaller pD, the discharge plasma and the excited species expand along the axis of the cathode aperture to form a columnar discharge.
基金supported by NSFC (40906048) the Tianyuan Foundation of Mathematics (11026211)+1 种基金 the Natural Science Foundation of the Jiangsu Higher Education Institutions (09KJB110005)the Science Research Foundation of NUIST (20080295)
文摘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.
基金financially supported by the National Natural Science Foundation of China(Nos.21774032,51833003 and 51621002)。
文摘The mixing morphology control plays a crucial role in photovoltaic power generation,yet this specific effect on device performances remains elusive.Here,we employed computational approaches to delineate the photovoltaic properties of layered heterojunction polymer solar cells with tunable mixing morphologies.One-step quench and two-step quench strategies were proposed to adjust the mixing morphology by thermodynamic and kinetic effects.The computation for the one-step quench revealed that modulating interfacial widths and interfacial roughness could significantly promote the photovoltaic performance of layered heterojunction polymer solar cells.The two-step quench can provide a buffer at a lower temperature before the kinetic quenching,leading to the formation of small-length-scale islands connected to the interface and a further increase in photovoltaic performance.Our discoveries are supported by recent experimental evidence and are anticipated to guide the design of photovoltaic materials with optimal performance.
基金Project supported by the TMR network No.ERB FMBX CT97 0157 on‘Asymptotic methods in kinetic theory'of the European Community,the LIAMA(Laboratoire d'Informatique,Automatique et Mathematiques Appliquees),the PRA(Programme de Recherches Avancees),the Aust
文摘The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory of the quantum scattering characteristics of the superlattice elementary cell (like e.g.transmission resonances) are shown in order. Two examples are treated with the analyticallycomputation of the diffusion constants.
