Hydrodynamic Model For Semiconductor Devices Research Articles

Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

A high order multi-resolution WENO numerical scheme for solving viscous quantum hydrodynamic model for semiconductor devices

In this article, fifth order finite volume multi-resolution weighted essentially non-oscillatory (MR-WENO) scheme is developed for solving one-dimensional non linear viscous quantum hydrodynamical model for semiconductor devices with constant temperature. This non linear model consists of three equations, two equations for the current density and electron density, and third equation is the Poisson equation. The first two equations include the viscous and quantum correction terms. Further, numerical technique is used to obtain the solution due to high non linearity of considered model. The multi-resolution technique is used to reduce the computational cost of high resolution numerical scheme. In the procedure of derivation of the MR-WENO scheme unequal central spatial stencils are used and linear weights can be chosen any positive numbers with only restriction that their total sum is one. Various numerical test problems are considered to check the validity and accuracy of the derived numerical scheme. Further, the results obtained from considered numerical scheme are compared with those of kinetic flux vector splitting numerical scheme.

Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the uniform estimates of density, we then prove the entropy solutions converge to the corresponding unique stationary solution exponentially with time. We generalize the existing results to the variable coefficient damping case.

Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices

We are concerned with the global existence and large time behavior of entropy solutions to the one dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space and time variables by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy solution converges to the corresponding unique stationary solution exponentially in time. No any smallness condition is assumed on the initial data and doping profile. Moreover, the novelty in this paper is about the unform bound with respect to time for the weak solutions of the isentropic Euler-Possion system.

Large time behavior framework for the time-increasing weak solutions of bipolar hydrodynamic model of semiconductors

In this paper, we consider an isentropic Euler-Poisson equations for the bipolar hydrodynamic model of semiconductor devices, which has a non-flat doping profile and insulating boundary conditions. Using a technical energy method and an entropy dissipation estimate, we present a framework for the large time behavior of time-increasing weak entropy solutions. It is shown that the weak solutions converge to the stationary solutions in $L^2$ norm with exponential decay rate. No regularity and smallness conditions are assumed.

Steady states and interface transmission conditions for heterogeneous quantum–classical 1-D hydrodynamic model of semiconductor devices

We study a hybrid model linking the quantum hydrodynamics equation with classical hydrodynamics deriving the transmission conditions between the two PDE systems modeling the quantum and the classical dynamics. These conditions are derived under the assumption of constant scaled temperature and assuming a current jump across the interface between the classical and the quantum region. In Section 2.2 we shall give a heuristic and physically plausible explanation of this assumption.Because of this fact we produce not a weak solution on the whole device domain, but a piecewise smooth solution.

Weak solutions to isothermal hydrodynamic model for semiconductor devices

In this paper, the Cauchy problem of the isothermal hydrodynamic model for semiconductor devices is investigated. The existence of global weak entropy solutions with large initial data is obtained by using a modified fractional step Lax–Friedrichs scheme and the theory of compensated compactness. As a byproduct, the existence of entropy solutions to the Cauchy problem of the isentropic hydrodynamic model for a semiconductor with infinite mass is also proved.

Numerical simulation of shock wave phenomena in hydrodynamic model of semiconductor devices

We propose a finite element method to investigate the phenomena of shock wave and to simulate the hydrodynamic model in semiconductor devices. An introduction of this model is discussed first. Then some scaling factors and a relationship between the changing variables are discussed. And then, we use a finite element method (P 1-iso-P 2 element) to discrete the equations. Some boundary conditions are also discussed. Finally, a sub-micron n +-n-n + silicon diode and Si MESFET device are simulated and the results are analyzed. Numerical results show that electronic fluids are transonic under some conditions.

Asymptotic profile in a multi-dimensional stationary nonisentropic hydrodynamic semiconductor model

We study the irrotational subsonic stationary solutions of a multi-dimensional nonisentropic hydrodynamic model for semiconductor devices. This model consists of the continuous equations for the electron density, the electron current density and electron temperature, coupled the Poisson equation of the electrostatic potential. In some domain supplemented by the proper boundary conditions, we investigate the zero-electron-mass limit, the zero-relaxation-time limit and the Debye-length (quasi-neutral) limit, respectively. We show the strong convergence of the sequence of solutions and give the associated error estimates.

Asymptotic profile in a one-dimensional steady-state nonisentropic hydrodynamic model for semiconductors

We study the stationary flow for a one-dimensional nonisentropic hydrodynamic model for semiconductor devices. This model consists of the continuous equations for the electron density, the electron current density and electron temperature, coupled the Poisson equation of the electrostatic potential. In a bounded interval supplemented by the proper boundary conditions, we investigate the zero-electron-mass limit, the zero-relaxation-time limit and the Debye-length (quasi-neutral) limit, respectively. We show the strong convergence of the sequence of solutions and give the associated convergence rate.

Smooth Quantum Hydrodynamic Model vs. NEMO Simulation of Resonant Tunneling Diodes

The smooth quantum hydrodynamic model is an extension of the classical hydrodynamic model for semiconductor devices which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. Smooth QHD model simulations of the current-voltage curves of resonant tunneling diodes are presented which exhibit negative differential resistance—the experimental signal for quantum resonance effects—and are compared with the experimentally verified current-voltage curves predicted by the simulator NEMO, which uses a non-equilibrium Green function method.

An efficient preconditioning technique for numerical simulation of hydrodynamic model semiconductor devices

AbstractWe investigate the application of preconditioned generalized minimal residual (GMRES) algorithm to the equations of hydrodynamic model of semiconductor devices. An introduction to such a model is presented. We use finite‐element method P1‐isoP2 element to discretize the equations. A preconditioning technique is proposed. The CPU times are presented for n+‐n‐n+ diodes and 0.25 μm gate length Si MESFETs by using the preconditioned GMRES algorithm and the GMRES algorithm. The numerical results show that the preconditioning technique accelerates effectively the velocity of convergence. Copyright © 2003 John Wiley & Sons, Ltd.

Convergent Iterative Schemes for a Non-isentropic Hydrodynamic Model for Semiconductors

Two iterative schemes for the solution of the one-dimensional stationary full hydrodynamic model for semiconductor devices are studied. This model consists of a system of balance equations for the electron density, temperature, and the electric field. The first iterative scheme relies on a decoupling of the equations in the spirit of the well-known Gummeliteration for the standard drift diffusion model. Convergence is proven in the case of small deviations from the equilibrium state. Secondly, a full Newton-iteration is analyzed and its local second order convergence is proven.

A relaxation scheme for the hydrodynamic equations for semiconductors

In this paper, we shall study numerically the hydrodynamic model for semiconductor devices, particularly in a one-dimensional n + nn + diode. By using a relaxation scheme, we explore the effects of various parameters, such as the low field mobility, device length, and lattice temperature. The effect of different types of boundary conditions is discussed. We also establish numerically the asymptotic limits of the hydrodynamic model towards the energy-transport and drift-diffusion models. This verifies the theoretical results in the literature.

Resonant tunneling in the smooth quantum hydrodynamic model for semiconductor devices

The “smooth” quantum hydrodynamic (QHD) model is an extension of the classical hydrodynamic model for semiconductor devices which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. Smooth QHD model simulations of the resonant tunneling diode exhibit negative differential resistance—the experimental signal for quantum resonance effects. Resonant tunneling is analyzed in fluid dynamical terms from the point of view of the smooth QHD transport equations.

Numerical simulation of the smooth quantum hydrodynamic model for semiconductor devices

An extension of the classical hydrodynamic model for semiconductor devices to include quantum transport effects is reviewed. This “smooth” quantum hydrodynamic (QHD) model is derived specifically to handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. A conservative upwind discretization of the one-dimensional (1D) steady-state smooth QHD equations is outlined. Smooth QHD model simulations of the resonant tunneling diode are presented which exhibit enhanced negative differential resistance when compared with simulations using the original O(ℏ 2) QHD model.

The Chapman-Enskog Expansion and the Quantum Hydrodynamic Model for Semiconductor Devices

A “smooth” quantum hydrodynamic (QHD) model for semiconductor devices is derived by a Chapman-Enskog expansion of the Wigner-Boltzmann equation which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. A dispersive quantum contribution to the heat flux term in the QHD model is introduced.

Hydrodynamic Device Simulationwith New State Variables Specially Chosen fora Block Gummel Iterative Approach

A new numerical formulation for solving the hydrodynamic model of semiconductor devices is presented. The method is based on using new variables to transform the conventional hydrodynamic equations into forms which facilitate numerical evaluation with a block Gummel approach. To demonstrate the new method, we apply it to model a 0.35 μm 2‐D LDD MOSFET, where robust convergence properties are observed.

Incompletely Parabolic Systems from Friedrichs Theory Point of View

An incompletely parabolic system of partial differential equations consist of one parabolic subsystem coupled to a hyperbolic subsystem. For the initial-boundary value problem, it has been shown, by requiring that a solution remains bounded at any time by the data, that boundary conditions which make both subsystems well-posed render the global system well-posed too. In this paper, we establish the same type of result with the help of the notion of semi-admissible boundary conditions in the theory of Friedrichs positive systems of differential equations. Our aim is not to obtain the same results of existence and uniqueness as those for the Cauchy problem, but rather to find a way to establish boundary conditions on the subsystems which can be used for the global system too. The theory is illustrated by the two examples of the compressible Navier–Stokes equations and of the hydrodynamic model for semiconductor devices, both in two space dimensions.

Subsonic solutions of hydrodynamic model for semiconductors

This paper is concerned with the existence and uniqueness of the steady-state solution of hydrodynamic model for semiconductor devices. Boundary conditions are prescribed by vorticity on inflow boundary as well as by electron density, temperature, and normal component of electron velocity on whole boundary. If the ambient temperature is large, and if both vorticity on inflow boundary and the variation of density on boundary are small, a unique subsonic solution exists.