The Finite Element Solutions to the Semiconductor Equations

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.

EXISTENCE OF WEAK SOLUTIONS TO A DEGENERATE STEAD-STATE SEMICONDUCTOR EQUATIONS

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.

On Global Boundedness of Solutions for the Drift-diffusion Semiconductor Equations

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.

ON EXISTENCE， UNIQUENESS AND REGULARITY OF STEADY STATE SOLUTIONS TO THE BASIC SEMICONDUCTOR EQUATIONS

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.

Existence of Weak Solutions to a Class of Semiconductor Equations with Fast Diffusion Term

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.

Interference of harmonics emitted by different tunneling momentum channels in laser fields

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.

High-order harmonic generation of ZnO crystals in chirped and static electric fields

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.

ASYMPTOTIC BEHAVIOR OF TIME-DEPENDENT SOLUTIONS TO SEMICONDUCTOR EQUATIONS

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.

Role of Bloch oscillation in high-order harmonic generation from periodic structure

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.

A Semi-Lagrangian Deterministic Solver for the Semiconductor Boltzmann-Poisson System

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.

Asymptotic Preserving Schemes for Semiconductor Boltzmann Equation in the Diffusive Regime

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.

Implicit-Explicit Runge-Kutta Schemes for the Boltzmann-Poisson System for Semiconductors

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.