Joseph W. Jerome

Classical and Quantum Hydrodynamic Device Models and Energy Transport

We study simulations of then+-n-n+ diode, by means of higher moment models, derived from the Boltzmann
equation. We emply such realistic assumptions as energy dependent mobility functions, with doping dependent
low field mobility. It is known that a critical role is played in the hydrodynamic model by the heat conduction
term. When the standard choice of the Wiedemann-Franz law is made for the conductivity, and constant low field
mobility values are used, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime
has in the past been achieved by empirical modification of this law. In this paper, we consider the effect of
representing the heat flux by the sum of two terms. It is found that the effect is negligible with respect to
overshoot in comparison to that achieved by employing a doping dependent low field mobility. We also compare
the hydrodynamic model to recently introduced energy transport models. Finally, in low temperature regimes, we
study the dependence of shock formation on the momentum relaxation time representations and on the heat
conduction term. The algorithms employed for both models are the essentially nonoscillatory (ENO) shock
capturing algorithms.

Chi-Wang Shu

The Response of the Hydrodynamic Model
to Heat Conduction, Mobility,
and Relaxation Expressions

We discuss the basis of a set of quantum hydrodynamic equations and the use of this set of equations in thetwo-dimensional simulation of quantum effects in deep submicron semiconductor devices. The equations areobtained from the Wigner function equation-of-motion. Explicit quantum correction is built into these equationsby using the quantum mechanical expression of the moments of the Wigner function, and its physical implicationis clearly explained. These equations are then applied to numerical simulation of various small semiconductordevices, which demonstrate expected quantum effects, such as barrier penetration and repulsion. These effectsmodify the electron density distribution and current density distribution, and consequently cause a change of thetotal current flow by 10-15 per cent for the simulated HEMT devices. Our work suggests that the inclusion ofquantum effects into the simulation of deep submicron and ultra-submicron semiconductor devices is necessary.

Jing-Rong  Zhou

David K. Ferry

2-D Simulation of Quantum Effects in SmallSemiconductor Devices Using QuantumHydrodynamic Equations

According to different assumptions in deriving carrier and energy flux equations, macroscopic semiconductor
transport models from the moments of the Boltzmann transport equation (BTE) can be divided into two main
categories: the hydrodynamic (HD) model which basically follows Bløtekjer's approach [1, 2], and the Energy
Transport (ET) model which originates from Strattton's approximation [3, 4]. The formulation, discretization,
parametrization and numerical properties of the HD and ET models are carefully examined and compared. The
well-known spurious velocity spike of the HD model in simple nin structures can then be understood from its
formulation and parametrization of the thermoelectric current components. Recent progress in treating negative
differential resistances with the ET model and extending the model to thermoelectric simulation is summarized.
Finally, we propose a new model denoted by DUET (Dual ET)which accounts for all thermoelectric effects in
most modern devices and demonstrates very good numerical properties. The new advances in applicability and
computational efficiency of the ET model, as well as its easy implementation by modifying the conventional
drift-diffusion (DD) model, indicate its attractiveness for numerical simulation of advanced semiconductor
devices

Edwin C. Kan

Zhiping Yu

Robert W. Dutton

Datong Chen

Umberto Ravaioli

Formulation of Macroscopic Transport
Models for Numerical Simulation
of Semiconductor Devices

Basing on a general formulation of the hydrodynamic model for semiconductor devices [1], a consistent approachto the solution of the model equations is proposed, along with a method for selezting the closure condition. Thedefinition of the coefficients of the hydrodynamic and energy-transport models is then re-examined in order tomake a comparison between them possible. Finally, the closure condition is discussed and compared with othersproposed in the literature.

Massimo  Rudan

Giorgio  Baccarani

On the Structure and Closure-Conditionof the Hydrodynamic Model

Transport in one- and two-dimensional semiconductor device structures is considered using a set of quantumcorrected hydrodynamic equations. Simple one-dimensional simulations demonstrate the need to include quantumeffects in structures with sharp interfaces. Application to a two-dimensional quantum well HEMT structure isthen considered. A brief discussion of the computational procedure is also presented.

J.  P. Kreskovsky

H. L. Grubin

Electron Transport Using the QuantumCorrected Hydrodynamic Equations

In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for
semiconductor devices in two space dimensions. The method combines a standard mixed finite element method,
used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous
Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of
conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing
the performance of the new method are displayed, and the results compared with those obtained by using
Essentially Nonoscillatory (ENO) finite difference schemes. From the perspective of device modeling, these
methods are robust, since they are capable of encompassing broad parameter ranges, including those for which
shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but
we have tested them much more generally with considerable success.

Zhangxin Chen

Bernardo Cockburn

Mixed-RKDG Finite Element Methods
for the 2-D Hydrodynamic Model
for Semiconductor Device Simulation

Hydrodynamic or continuum descriptions of electron transport have long been used for modeling and simulating
semiconductor devices. In this paper, we use classical field theory ideas to discuss the physical foundations of such
descriptions as applied specifically to high-field transport regimes. The classical field theory development of these
types of models is of interest because it differs significantly from and may be viewed as complementary to
conventional derivations based on the Boltzmann equation: After outlining the general field theoretic principles
upon which our development of fluid-based high-field transport descriptions is based, we study several specific
models both analytically and using numerical simulation. These models provide an overall framework for
understanding and extending various theories which have appeared in the literature. Most importantly, they
emphasize the importance of including memory or history effects and viscosity in describing high-field transport.
In all of this our aim is a unified and synoptic view unencumbered with microscopic details. Obtaining quantitative
agreement with specific experiments and/or microscopic simulations is only of secondary importance. We share
the view that continuum approaches can provide succinct and computationally-efficient models needed for current
and future semiconductor device analysis and engineering. At the same time, we believe that these models need
not be phenomenological but can be given solid physical foundation in macroscopic principles.

M. G. Ancona

Hydrodynamic Models of Semiconductor
Electron Transport at High Fields

The phenomenon of resonant tunneling is simulated and analyzed in the quantum hydrodynamic (QHD) modelfor semiconductor devices. Simulations of a parabolic well resonant tunneling diode at 77 K are presented whichshow multiple regions of negative differential resistance (NDR) in the current-voltage curve. These are the firstsimulations of the QHD equations to show multiple regions of NDR.Resonant tunneling (and NDR) depend on the quantum interference of electron wavefunctions and thereforeon the phases of the wavefunctions. An analysis of the QHD equations using a moment expansion of theWigner-Boltzmann equation indicates how phase information is retained in the hydrodynamic equations.

Carl L. Gardner

Resonant Tunneling in the QuantumHydrodynamic Model

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VLSI Design

Classical and Quantum Hydrodynamic Device Models and Energy Transport

Classical and Quantum Hydrodynamic Device Models and Energy Transport

Articles

Classical and Quantum Hydrodynamic Device Models and Energy Transport

The Response of the Hydrodynamic Model to Heat Conduction, Mobility, and Relaxation Expressions

2-D Simulation of Quantum Effects in Small Semiconductor Devices Using Quantum Hydrodynamic Equations

Formulation of Macroscopic Transport Models for Numerical Simulation of Semiconductor Devices

On the Structure and Closure-Condition of the Hydrodynamic Model

Electron Transport Using the Quantum Corrected Hydrodynamic Equations

Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation

Hydrodynamic Models of Semiconductor Electron Transport at High Fields

Resonant Tunneling in the Quantum Hydrodynamic Model