In this article we concisely present several modern strategies that are applicable to driftdominated
carrier transport in higher-order deterministic models such as the driftdiffusion,
hydrodynamic, and quantum hydrodynamic systems. The approaches include
extensions of “upwind” and artificial dissipation schemes, generalization of the traditional
Scharfetter – Gummel approach, Petrov – Galerkin and streamline-upwind Petrov
Galerkin (SUPG), “entropy” variables, transformations, least-squares mixed methods
and other stabilized Galerkin schemes such as Galerkin least squares and discontinuous
Galerkin schemes. The treatment is representative rather than an exhaustive
review and several schemes are mentioned only briefly with appropriate reference
to the literature. Some of the methods have been applied to the semiconductor device
problem while others are still in the early stages of development for this class of applications.
We have included numerical examples from our recent research tests with
some of the methods. A second aspect of the work deals with algorithms that employ
unstructured grids in conjunction with adaptive refinement strategies. The full benefits
of such approaches have not yet been developed in this application area and we
emphasize the need for further work on analysis, data structures and software to
support adaptivity. Finally, we briefly consider some aspects of software frameworks.
These include dial-an-operator approaches such as that used in the industrial simulator
PROPHET, and object-oriented software support such as those in the SANDIA
National Laboratory framework SIERRA.

Graham F. Carey

A. L. Pardhanani

S. W. Bova

Advanced Numerical Methods and Software Approaches
for Semiconductor Device Simulation

The first completely physical electro-thermal model is presented that is capable of
describing the large signal performance of MESFET- and HEMT-based, high power
microwave and millimeter wave monolithic and hybrid ICs, on timescales suitable for
CAD. The model includes the effects of self-heating and mutual thermal interaction
on active device performance with full treatment of all thermal non linearities. The
electrical description is provided by the rapid quasi-2D Leeds Physical Model and the
steady-state global thermal description is provided by a highly accurate and computationally
inexpensive analytical thermal resistance matrix approach. The order of
the global thermal resistance matrix describing 3-dimensional heat flow in complex
systems, is shown to be determined purely by the number of active device elements, not
the level of internal device structure. Thermal updates in the necessarily iterative, fully
coupled electro-thermal solution, therefore reduce to small matrix multiplications
implying orders of magnitude speed-up compared to the use of full numerical thermal
solutions capable of comparable levels of detail and accuracy.

W. Batty

A. J. Panks

R. G. Johnson

C. M. Snowden

Electro-thermal Modelling of Monolithic and Hybrid
Microwave and Millimeter Wave IC's

A &#8220;smooth&#8221; 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.

Carl L. Gardner

Christian  Ringhofer

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

We present a 3D Ensemble Monte Carlo particle-based simulator with a novel realspace
treatment of the short-range electron – electron and electron-ion interactions. By
using a corrected Coulomb force in conjunction with a proper cutoff range, the shortrange
portion of the force is properly accounted for, and the ‘double counting’ of the
long-range interaction is eliminated. The proposed method naturally incorporates the
multi-ion contributions, local distortions in the scattering potential due to the movement
of the free charges, and carrier-density fluctuations. The doping dependence of the
low-field mobility obtained from 3D resistor simulations closely follows experimental
results, thus supporting the appropriateness of the proposed scheme. Simulations of
ultra-small MOSFETs demonstrate that the short-range electron – electron and electronion
interactions are responsible for the fast thermalization of the carriers at the drain
end of the device, which occurs over distances that are on the order of few nanometers.
The omission of the short-range portions of these two interaction terms leads to significant
overestimation of the distance over which carriers thermalize.

W. J. Gross

D. Vasileska

D. K. Ferry

3D Simulations of Ultra-small MOSFETs
with Real-space Treatment of the Electron – Electron
and Electron-ion Interactions

A new analytical model for carrier mobility in silicon is presented, which is stronglyoriented to CAD and suitable for implementation in device simulators. The effects ofthe electric field, temperature, and doping concentration are accounted for. In particular,the model unifies the descriptions of majority- and minority-carrier mobility andincludes the full temperature dependence. The effects of a high longitudinal field areincluded in the conventional velocity-saturation form; the doping dependence is alsoincorporated in the latter. The model has been worked out starting from a preliminaryinvestigation using a Boltzmann solver, and has been validated by a number of comparisonswith published experiments on silicon.

Susanna  Reggiani

Marina  Valdinoci

Luigi  Colalongo

Massimo  Rudan

Giorgio  Baccarani

An Analytical, Temperature-dependent Modelfor Majority- and Minority-carrier Mobilityin Silicon Devices

Balance equations based on the moment method for the transport of electrons in silicon
semiconductors are presented. The energy band is assumed to be described by the Kane
dispersion relation. The closure relations have been obtained by employing the maximum
entropy principle.The validity of the constitutive equations for fluxes and production terms of the
balance equations has been checked with a comparison to detailed Monte Carlo
simulations in the case of bulk silicon.

A. M. Anile

O. Muscato

V. Romano

Moment Equations with Maximum Entropy Closure
for Carrier Transport in Semiconductor Devices:
Validation in Bulk Silicon

In recent years, substantial advances have been made in understanding hydrodynamic
models, both from the standpoint of analytical infrastructure, as well as the parameters
which play a decisive effect in the behavior of such models. Both classical and quantum
hydrodynamic models have been studied in depth. In this survey paper, we describe
several results of this type. We include, for example, well-posedness for both classical
and quantum reduced models, and the relaxation drift–diffusion limit as examples of
analytical results. As examples of computational results, we include some discussion of
effective algorithms, but most importantly, some information gleaned from extensive
simulation. In particular, we present our findings of the prominent role played by the
mobilities in the classical models, and the role of hysteresis in the quantum models. All
models are self-consistent. Included is discussion of recent analytical results on the use
of Maxwell’s equations. Benchmark devices are utilized: the MESFET transistor and
the n+/n/n+ diode for classical transport, and the resonant tunneling diode for quantum
transport. Some comparison with the linear Boltzmann transport equation is included.

Joseph W. Jerome

Analytical and Computational Advances for Hydrodynamic
Models of Classical and Quantum Charge Transport

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Semiconductor Device Modeling and Simulation

Published Special Issues

VLSI Design

Semiconductor Device Modeling and Simulation

Semiconductor Device Modeling and Simulation

Articles

Advanced Numerical Methods and Software Approaches for Semiconductor Device Simulation

Electro-thermal Modelling of Monolithic and Hybrid Microwave and Millimeter Wave IC's

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

3D Simulations of Ultra-small MOSFETs with Real-space Treatment of the Electron – Electron and Electron-ion Interactions

An Analytical, Temperature-dependent Model for Majority- and Minority-carrier Mobility in Silicon Devices

Moment Equations with Maximum Entropy Closure for Carrier Transport in Semiconductor Devices: Validation in Bulk Silicon

Analytical and Computational Advances for Hydrodynamic Models of Classical and Quantum Charge Transport

Guest Editorial