Quantum Hydrodynamic Model For Semiconductors Research Articles

Existence and uniqueness of steady states to semiconductor bipolar full quantum hydrodynamic model

In this paper, we are concerned with the existence and uniqueness of subsonic steady states to the one-dimensional bipolar full quantum hydrodynamic model for semiconductors in a bounded interval. The main result is proved by perturbation arguments combined with Banach's Fixed Point Theorem. Moreover, we also obtain the uniform estimates of steady states with respect to the physical parameters appear in the model, which comes in useful for discussing the relaxation time limit and semi-classical limit in future study.

Large time behavior of solutions to 1-dimensional bipolar quantum hydrodynamic model for semiconductors

In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained.

Quasineutral limit of bipolar quantum hydrodynamic model for semiconductors

This paper is concerned with the quasineutral limit of the bipolar quantum hydrodynamic model for semiconductors. It is rigorously proved that the strong solutions of the bipolar quantum hydrodynamic model converge to the strong solution of the so-called quantum hydrodynamic equations as the Debye length goes to zero. Moreover, we obtain the convergence of the strong solutions of bipolar quantum hydrodynamic model to the strong solution of the compressible Euler equations with damping if both the Debye length and the Planck constant go to zero simultaneously.

Some limit analysis in a one-dimensional stationary quantum hydrodynamic model for semiconductors

In this paper, we study the steady-state hydrodynamic equations for isothermal states including the quantum Bohn potential. The one-dimensional equations for the electron current density and the particle density are coupled self-consistently to the Poisson equation for the electric potential. The quantum correction can be interpreted as a dispersive regularization of the classical hydrodynamic equations. In a bounded interval supplemented by the proper boundary conditions, we investigate the zero-electron-mass limit, the zero-relaxation-time limit, the Debye-length (quasi-neutral) limit, and some combined limits, respectively. For each limit, we show the strong convergence of the sequence of solutions and give the associated convergence rate.

Quasineutral limit of the viscous quantum hydrodynamic model for semiconductors

The quasineutral limit (zero-Debye-length limit) of viscous quantum hydrodynamic model for semiconductors is studied in this paper. By introducing new modulated energy functional and using refined energy analysis, it is shown that, for well-prepared initial data, the smooth solution of viscous quantum hydrodynamic model converges to the strong solution of incompressible Navier–Stokes equations as the Debye length goes to zero.

Semiclassical and relaxation limits of bipolar quantum hydrodynamic model for semiconductors

The global in-time semiclassical and relaxation limits of the bipolar quantum hydrodynamic model for semiconductors are investigated in R 3 . We prove that the unique strong solution exists and converges globally in time to the strong solution of classical bipolar hydrodynamical equation in the process of semiclassical limit and that of the classical drift–diffusion system under the combined relaxation and semiclassical limits.

STEADY-STATE SOLUTIONS AND ASYMPTOTIC LIMITS ON THE MULTI-DIMENSIONAL SEMICONDUCTOR QUANTUM HYDRODYNAMIC MODEL

In this paper we study the steady-state quantum hydrodynamic model for semiconductors. The existence of solutions on the bipolar QHD model is obtained in the case of sufficiently small relaxation time. Uniqueness results are showed both in the thermal equilibrium states and the scaled Planck constant being large enough. The relaxation time and dispersive limit are performed on the bipolar and unipolar equations, respectively. In a sense, we have made a complete answer to the original unsolved problems of the steady-state QHD model.

Exponential decay to a quantum hydrodynamic model for semiconductors

This paper deals with large-time behavior of solutions for a viscous bipolar quantum hydrodynamic model with third-order terms. By applying the entropy method, we prove exponential decays of solutions towards constant steady states for the one-dimensional and the multi-dimensional cases. The argument is based on a series of a priori estimates. As a byproduct, the decay of solutions for the viscous hydrodynamic model is obtained as well.

Numerical approximation of the viscous quantum hydrodynamic model for semiconductors

The viscous quantum hydrodynamic equations for semiconductors with constant temperature are numerically studied. The model consists of the one-dimensional Euler equations for the electron density and current density, including a quantum correction and viscous terms, coupled to the Poisson equation for the electrostatic potential. The equations can be derived formally from a Wigner–Fokker–Planck model by a moment method. Two different numerical techniques are used: a hyperbolic relaxation scheme and a central finite-difference method. By simulating a ballistic diode and a resonant tunneling diode, it is shown that numerical or physical viscosity changes significantly the behavior of the solutions. Moreover, the current-voltage characteristics show multiple regions of negative differential resistance and hysteresis effects.

Zero Debye Length Asymptotic of the Quantum Hydrodynamic Model for Semiconductors

In the present paper we consider the zero Debye length asymptotic of solutions of isentropic quantum hydrodynamic equations for semiconductors at nano-size and show that the current density consists of the divergence free vector field involved in the incompressible Euler equation and highly oscillating gradient vector field caused by the highly electric fields for small Debye length. This means that the quantum effects possibly may not dominate the charge transport within the channel of semiconductor devices (for instance MOSFET) of nano-size for isentropic quantum fluids.

Existence and Asymptotic Behavior of Multi-Dimensional Quantum Hydrodynamic Model for Semiconductors

This paper is devoted to the study of the existence and the time-asymptotic of multi-dimensional quantum hydrodynamic equations for the electron particle density, the current density and the electrostatic potential in spatial periodic domain. The equations are formally analogous to classical hydrodynamics but differ in the momentum equation, which is forced by an additional nonlinear dispersion term, (due to the quantum Bohm potential) and are used in the modelling of quantum effects on semiconductor devices. We prove the local-in-time existence of the solutions, in the case of the general, nonconvex pressure-density relation and large and regular initial data. Furthermore we propose a ‘‘subsonic’’ type stability condition related to one of the classical hydrodynamical equations. When this condition is satisfied, the local-in-time solutions exist globally in-time and converge time exponentially toward the corresponding steady-state. Since for this problem classical methods like, for instance, the Friedrichs theory for symmetric hyperbolic systems cannot be used, we investigate via an iterative procedure an extended system, which incorporates the one under investigation as a special case. In particular the dispersive terms appear in the form of a fourth-order wave type equation.

On a steady-state quantum hydrodynamic model for semiconductors

A third order quantum perturbation of the stress tensor, and a relaxation approximation to represent averaged collisions, are employed as perturbations of the isentropic model for a collisionless plasma. The model is self-consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. As formulated, the model is a reduced version of the quantum hydrodynamic model for semiconductors. Existence is demonstrated for the model, which is shown to be equivalent to a non-standard integro-differential equation. An unusual boundary condition, with the important physical interpretation of specifying the quantum potential at the (current) inflow boundary, is identified as essential for the theory.

Thermal equilibrium states of the quantum hydrodynamic model for semiconductors in one dimension

The thermal equilibrium of the quantum hydrodynamic model for semiconductors is investigated in one space dimension. Existence is obtained using a fixed point argument. Uniqueness is proved for small values of the scaled Planck constant. The classical limit is also carried out.