Extended Hydrodynamical Model of Carrier Transport in Semiconductors

Anile, A. M.; Russo, Giovanni; Romano, Vittorio

doi:10.1137/s003613999833294x

Cited by 82 publications

(68 citation statements)

References 48 publications

(94 reference statements)

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“…In [5,6] a suitable extension for one-dimensional balance laws with (possibly stiff ) source terms has been developed on the basis of the Nessyahu and Tadmor scheme [3] for homogeneous hyperbolic system. It has been applied in [22,23] to parabolic band hydrodynamical models of semiconductors. Here we extend the scheme to the bidimensional case starting from the bidimensional version of the Jiang and Tadmor scheme [4].…”

Section: Methodsmentioning

confidence: 99%

“…However, it was found in [7] that the first-order model is sufficiently accurate for numerical applications and avoids some irregularities due to nonlinearities, as in the parabolic band case [23]. A similar approach was followed in [24,25], where the smallness of the anisotropy was used to justify the truncation of the expansion of the distribution function in spherical harmonics up to the harmonics of order zero and one.…”

Section: The Modelmentioning

confidence: 99%

“…A numerical scheme for problems of this kind based on central differencing has been developed in [5,6,22] for the one-dimensional case and applied in [7,9] to bulk silicon and to an n + -n-n + silicon diode (for the parabolic band case see [23]). The obtained results are rather encouraging regarding the accuracy of the model and the performance of the numerical scheme.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

Romano¹

2002

Journal of Computational Physics

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Section: Methodsmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

Romano¹

2002

Journal of Computational Physics

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“…In fact, Dirichlet conditions for T n and T p may lead to artificial boundary layers [11]. Moreover, in [5] it was argued that the use of homogeneous Neumann conditions for T n and T p can be justified in highly doped regions close to the contacts. For the lattice temperature, we employ Robin boundary conditions in order to model the temperature exchange between the semiconductor device and the connected thermal and circuit elements.…”

Section: 3mentioning

confidence: 99%

Self-heating in a coupled thermo-electric circuit-device model

Brunk

Jüngel

2010

J Comput Electron

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Abstract. The self-heating of a coupled thermo-electric circuit-semiconductor system is modeled and numerically simulated. The system consists of semiconductor devices, an electric network with resistors, capacitors, inductors, and voltage sources, and a thermal network. The flow of the charge carriers is described by the energy-transport equations coupled to a heat equation for the lattice temperature. The electric circuit is modeled by the network equations from modified nodal analysis coupled to a thermal network describing the evolution of the temperatures in the lumped and distributed circuit elements. The three subsystems are coupled through thermo-electric, electric circuit-device, and thermal network-device interface conditions. The resulting system of nonlinear partial differential-algebraic equations is discretized in time by the 2-stage backward difference formula and in space by a mixed finite-element method. Numerical simulations of a one-dimensional ballistic diode and a frequency multiplier circuit containing a pn-junction diode illustrate the heating of the semiconductor device and circuit resistors.Key words. Energy-transport equations, lattice heating, thermal network, circuit equations, mixed finite-element method, partial differential-algebraic equations.AMS subject classifications. 65L80, 65M60, 82D37.1. Introduction. Due to growing package densities, self-heating becomes more and more important in modern integrated circuits and power devices. Thermal effects may strongly influence the device behavior and even reduce its performance. In order to understand the influence of self-heating, power dissipation and temperature evolution have to be taken into account in the electric network models.In industrially used circuit simulators, complex semiconductor device models are usually substituted by circuits of basic network elements, resulting in simpler so-called compact models, and thermal effects are described heuristically by correction factors or simple heat models. In order to achieve accurate simulations of modern circuits, however, a very large number of circuit elements and a careful adjustment of a large number of parameters is needed. Therefore, it is preferable to model those devices which are critical for the parasitic effects by semiconductor transport equations and to include physical heat flow models.Beacuse of missing structural informations about the coupled device-circuit equations, first approaches to couple circuits and devices were based on a combination of device and circuit simulators as "black box" solvers [16] or on simple extensions of device simulators by more complex boundary conditions [26]. More recently, electric network models were coupled to semiconductor transport equations, such as driftdiffusion [34] or energy-transport models [11], leading to a coupled system of partial differential-algebraic equations. The work [11] includes temperature models for the

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“…On the insulating parts of the boundary Γ N , it is assumed that the normal components of the current densities and of the electric field vanish. For the temperature, homogenous Neumann boundary conditions are assumed as in [1]. We have shown in [5] that boundary layers for the particle densities can be avoided if Robin-type boundary conditions similar as in [14] are employed on the remaining boundary parts,…”

Section: Modelingmentioning

confidence: 99%

Numerical Simulation of Thermal Effects in Coupled Optoelectronic Device-circuit Systems

Brunk

Jüngel

Mathematics – Key Technology for the Future

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Extended Hydrodynamical Model of Carrier Transport in Semiconductors

Cited by 82 publications

References 48 publications

2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

2D Simulation of a Silicon MESFET with a Nonparabolic Hydrodynamical Model Based on the Maximum Entropy Principle

Self-heating in a coupled thermo-electric circuit-device model

Numerical Simulation of Thermal Effects in Coupled Optoelectronic Device-circuit Systems

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