Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipol...Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.展开更多
The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order...The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder＇s fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion （DD） model are studied.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
The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditi...The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.展开更多
The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,th...The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.展开更多
A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in...A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the global existence and semiclassical limit are obtained, in which semiclassieal limit describes the relation between quantum and classical drift-diffusion models, Furthermore, in the case of constant doping, we prove the weak solution exponentially approaches its constant steady state as time increases to infinity.展开更多
This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time an...This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary condition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.展开更多
Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semicon- ductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diff...Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semicon- ductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diffusion model. In addition, we also proved the global existence of weak solutions.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
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
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
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.
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
Perovskite quantum dot light-emitting diodes(Pe-QLEDs)have shown immense application potential in display and lighting fields due to their narrow full-width at half maximum(FWHM)and high photoluminescence quantum yiel...Perovskite quantum dot light-emitting diodes(Pe-QLEDs)have shown immense application potential in display and lighting fields due to their narrow full-width at half maximum(FWHM)and high photoluminescence quantum yield(PLQY).Despite significant advancements in their performance,challenges such as defects and ion migration still hinder their long-term stability and operational efficiency.To address these issues,various optimization strategies,including ligand engineering,interface passivation,and self-assembly strategy,are being actively researched.This review focuses on the synthesis methods,challenges and optimization of perovskite quantum dots,which are critical for the commercialization and large-scale production of high-performance and stable Pe-QLEDs.展开更多
Implementing quantum wireless multi-hop network communication is essential to improve the global quantum network system. In this paper, we employ eight-level GHZ states as quantum channels to realize multi-hop quantum...Implementing quantum wireless multi-hop network communication is essential to improve the global quantum network system. In this paper, we employ eight-level GHZ states as quantum channels to realize multi-hop quantum communication, and utilize the logical relationship between the measurements of each node to derive the unitary operation performed by the end node. The hierarchical simultaneous entanglement switching(HSES) method is adopted, resulting in a significant reduction in the consumption of classical information compared to multi-hop quantum teleportation(QT)based on general simultaneous entanglement switching(SES). In addition, the proposed protocol is simulated on the IBM Quantum Experiment platform(IBM QE). Then, the data obtained from the experiment are analyzed using quantum state tomography, which verifies the protocol's good fidelity and accuracy. Finally, by calculating fidelity, we analyze the impact of four different types of noise(phase-damping, amplitude-damping, phase-flip and bit-flip) in this protocol.展开更多
The quantum confinement effect fundamentally alters the optical and electronic properties of quantum dots(QDs),making them versatile building blocks for next-generation light-emitting diodes(LEDs).This study investiga...The quantum confinement effect fundamentally alters the optical and electronic properties of quantum dots(QDs),making them versatile building blocks for next-generation light-emitting diodes(LEDs).This study investigates how quantum confinement governs the charge transport,exciton dynamics,and emission efficiency in QD-LEDs,using CsPbI_(3) QDs as a model system.By systematically varying QD sizes,we reveal size-dependent trade-offs in LED performance,such as enhanced efficiency for smaller QDs but increased brightness and stability for larger QDs under high current densities.Our findings offer critical insights into the design of high-performance QD-LEDs,paving the way for scalable and energy-efficient optoelectronic devices.展开更多
The preparation of red,green,and blue quantum dot(QD)pixelated arrays with high precision,resolution,and brightness poses a significant challenge on the development of advanced micro-displays for virtual,augmented,and...The preparation of red,green,and blue quantum dot(QD)pixelated arrays with high precision,resolution,and brightness poses a significant challenge on the development of advanced micro-displays for virtual,augmented,and mixed reality applications.Alongside the controlled synthesis of high-performance QDs,a reliable QD patterning technology is crucial in overcoming this challenge.Among the various methods available,photolithography-based patterning technologies show great potentials in producing ultra-fine QD patterns at micron scale.This review article presents the recent advancements in the field of QD patterning using photolithography techniques and explores their applications in micro-display technology.Firstly,we discuss QD patterning through photolithography techniques employing photoresist(PR),which falls into two categories:PRassisted photolithography and photolithography of QDPR.Subsequently,direct photolithography techniques based on photo-induced crosslinking of photosensitive groups and photo-induced ligand cleavage mechanisms are thoroughly reviewed.Meanwhile,we assess the performance of QD arrays fabricated using these photolithography techniques and their integration into QD light emitting diode display devices as well as color conversionbased micro light emitting diode display devices.Lastly,we summarize the most recent developments in this field and outline future prospects.展开更多
基金Supported by NSFC (10541001, 10571101, 10401019, and 10701011)by Basic Research Foundation of Tsinghua University
文摘Semiclassical limit to the solution of transient bipolar quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical bipolar drift-diffusion model. In addition, the authors also prove the existence of weak solution.
文摘The weak solutions to the stationary quantum drift-diffusion equations （QDD） for semiconductor devices are investigated in one space dimension. The proofs are based on a reformulation of the system as a fourth-order elliptic boundary value problem by using an exponential variable transformation. The techniques of a priori estimates and Leray-Schauder＇s fixed-point theorem are employed to prove the existence. Furthermore, the uniqueness of solutions and the semiclassical limit δ→0 from QDD to the classical drift-diffusion （DD） model are studied.
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the National Natural Science Foundation of China(Nos.10401019,10701011,10541001)
文摘The semiclassical limit in the transient quantum drift-diffusion equations with isentropic pressure in one space dimension is rigorously proved. The equations are supplemented with homogeneous Neumann boundary conditions. It is shown that the semiclassical limit of this solution solves the classical drift-diffusion model. In the meanwhile, the global existence of weak solutions is proved.
基金Project supported by the National Natural Science Foundation of China(Nos.10631020,10401019)the Basic Research Grant of Tsinghua University.
文摘The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model,a fourth order parabolic system.Using semi-discretization in time and entropy estimate,the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann(or periodic)boundary conditions.Furthermore,by a logarithmic Sobolev inequality,it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.
基金Supported by the Natural Science Foundation of China （No. 10571101, No. 10626030 and No. 10871112）
文摘A fourth order parabolic system, the bipolar quantum drift-diffusion model in semiconductor simulation, with physically motivated Dirichlet-Neumann boundary condition is studied in this paper. By semidiscretization in time and compactness argument, the global existence and semiclassical limit are obtained, in which semiclassieal limit describes the relation between quantum and classical drift-diffusion models, Furthermore, in the case of constant doping, we prove the weak solution exponentially approaches its constant steady state as time increases to infinity.
基金the National Natural Science Foundation of China(No. 10401019)
文摘This paper studies the existence, semiclassical limit, and long-time behavior of weak solutions to the unipolar isentropic quantum drift-diffusion model, a fourth order parabolic system. Semi-discretization in time and entropy estimates give the global existence and semiclassical limit of nonnegative weak solutions to the one-dimensional model with a nonnegative large initial value and a Dirichlet-Neumann boundary condition. Furthermore, the weak solutions are proven to exponentially approach constant steady state as time increases to infinity.
文摘Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semicon- ductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diffusion model. In addition, we also proved the global existence of weak solutions.
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.
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 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 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.
文摘Perovskite quantum dot light-emitting diodes(Pe-QLEDs)have shown immense application potential in display and lighting fields due to their narrow full-width at half maximum(FWHM)and high photoluminescence quantum yield(PLQY).Despite significant advancements in their performance,challenges such as defects and ion migration still hinder their long-term stability and operational efficiency.To address these issues,various optimization strategies,including ligand engineering,interface passivation,and self-assembly strategy,are being actively researched.This review focuses on the synthesis methods,challenges and optimization of perovskite quantum dots,which are critical for the commercialization and large-scale production of high-performance and stable Pe-QLEDs.
基金Project supported by the Open Fund of Anhui Key Laboratory of Mine Intelligent Equipment and Technology (Grant No. ZKSYS202204)the Talent Introduction Fund of Anhui University of Science and Technology (Grant No. 2021yjrc34)the Scientific Research Fund of Anhui Provincial Education Department (Grant No. KJ2020A0301)。
文摘Implementing quantum wireless multi-hop network communication is essential to improve the global quantum network system. In this paper, we employ eight-level GHZ states as quantum channels to realize multi-hop quantum communication, and utilize the logical relationship between the measurements of each node to derive the unitary operation performed by the end node. The hierarchical simultaneous entanglement switching(HSES) method is adopted, resulting in a significant reduction in the consumption of classical information compared to multi-hop quantum teleportation(QT)based on general simultaneous entanglement switching(SES). In addition, the proposed protocol is simulated on the IBM Quantum Experiment platform(IBM QE). Then, the data obtained from the experiment are analyzed using quantum state tomography, which verifies the protocol's good fidelity and accuracy. Finally, by calculating fidelity, we analyze the impact of four different types of noise(phase-damping, amplitude-damping, phase-flip and bit-flip) in this protocol.
基金support from the National Key Research and Development Program of China(2024YFA1207700)National Natural Science Foundation of China(52072141,52102170).
文摘The quantum confinement effect fundamentally alters the optical and electronic properties of quantum dots(QDs),making them versatile building blocks for next-generation light-emitting diodes(LEDs).This study investigates how quantum confinement governs the charge transport,exciton dynamics,and emission efficiency in QD-LEDs,using CsPbI_(3) QDs as a model system.By systematically varying QD sizes,we reveal size-dependent trade-offs in LED performance,such as enhanced efficiency for smaller QDs but increased brightness and stability for larger QDs under high current densities.Our findings offer critical insights into the design of high-performance QD-LEDs,paving the way for scalable and energy-efficient optoelectronic devices.
基金supported by the National Natural Science Foundation of China(62374142,12175189 and 11904302)External Cooperation Program of Fujian(2022I0004)+1 种基金Fundamental Research Funds for the Central Universities(20720190005 and 20720220085)Major Science and Technology Project of Xiamen in China(3502Z20191015).
文摘The preparation of red,green,and blue quantum dot(QD)pixelated arrays with high precision,resolution,and brightness poses a significant challenge on the development of advanced micro-displays for virtual,augmented,and mixed reality applications.Alongside the controlled synthesis of high-performance QDs,a reliable QD patterning technology is crucial in overcoming this challenge.Among the various methods available,photolithography-based patterning technologies show great potentials in producing ultra-fine QD patterns at micron scale.This review article presents the recent advancements in the field of QD patterning using photolithography techniques and explores their applications in micro-display technology.Firstly,we discuss QD patterning through photolithography techniques employing photoresist(PR),which falls into two categories:PRassisted photolithography and photolithography of QDPR.Subsequently,direct photolithography techniques based on photo-induced crosslinking of photosensitive groups and photo-induced ligand cleavage mechanisms are thoroughly reviewed.Meanwhile,we assess the performance of QD arrays fabricated using these photolithography techniques and their integration into QD light emitting diode display devices as well as color conversionbased micro light emitting diode display devices.Lastly,we summarize the most recent developments in this field and outline future prospects.
