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

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

Joseph W. Jerome

Chi-Wang Shu

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

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.

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

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

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

Classical and Quantum Hydrodynamic Device Models and Energy Transport

Partitioning is an important problem in the design automation of integrated circuits. This problem in many of itsformulation is NP-Hard, and several heuristic methods have been proposed for its solution. To evaluate theeffectiveness of the various partitioning heuristics, it is desirable to have test cases with known optimal solutionsthat are as &#8220;random looking&#8221; as possible. In this paper, we describe several methods for the construction of suchtest cases. All our methods except one use the theory of network flow. The remaining method uses a relationshipbetween a partitioning problem and the geometric clustering problem. The latter problem can be solved inpolynomial time in any fixed dimension.

Youssef   Saab

New Methods for the Construction of TestCases for Partitioning Heuristics

Technology mapping is the final step of logic synthesis which consists of mapping an optimized technology
independent logic network representation into a circuit realization in a given technology. An important component
of the technology mapping problem is the identification of feasible library cells for the realization of the logic
operators in the logic tree. There are two main classes of such matching algorithms. Library-based matching
algorithms [1–4] require that all available physical components be represented explicitly in a pattern library.
Sections of the logic network are then matched against this pattern list for the identification of suitable
components. In contrast, cell generator-based matching techniques [6–8] accept feasibility constraints on the
complexity and quantity of physical components according to limits imposed by the target technology or the
capabilities of the cell generator. Hence, individual patterns are not stored in a library and are instead generated
as needed. In this paper, we present a new cell generator-based constructive matching algorithm. Because the
algorithm builds matched patterns incrementally, very large cell families can be accommodated using time and
space resources that are proportional to the size of the largest feasible cell pattern and not the size of the library
of patterns as would be the case for library-based approaches. Also, whereas existing cell generator-based
matching techniques combine the tasks of matching (identification) and covering (selection), constructive matching
provides more flexibility by not restricting the covering phase. Empirical results demonstrate the increased quality
of the technology-mapped circuits when larger cells are available.

Martin Lefebvre

Cliff Liem

Cell Generator-Based Technology Mapping
by Constructive Tree-Matching
and Dynamic Covering

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VLSI Design

Table of Contents

Table of Contents: 1995

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

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

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

On the Structure and Closure-Condition of the Hydrodynamic Model

Hydrodynamic Models of Semiconductor Electron Transport at High Fields

Classical and Quantum Hydrodynamic Device Models and Energy Transport

New Methods for the Construction of Test Cases for Partitioning Heuristics

Cell Generator-Based Technology Mapping by Constructive Tree-Matching and Dynamic Covering