Numerical Solution of the Hydrodynamic Model for a One‐dimensional Semiconductor Device

Rudan, Massimo; Odeh, F.; White, J.

doi:10.1108/eb010032

Cited by 65 publications

(23 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This represents that the new model can be applied to devices with larger size, i.e., where the QM effects are negligible. These results agree also very well with that previously reported in the literature [2,14,17,31].…”

Section: Numerical Examplessupporting

confidence: 95%

A quantum corrected energy-transport model for nanoscale semiconductor devices

Chen¹,

Liu²

2005

Journal of Computational Physics

View full text Add to dashboard Cite

Section: Numerical Examplessupporting

confidence: 95%

A quantum corrected energy-transport model for nanoscale semiconductor devices

Chen¹,

Liu²

2005

Journal of Computational Physics

View full text Add to dashboard Cite

“…In the following, a number of simplifications will be illustrated which lead to the hydrodynamic model [1, 10,[12][13][14][15][16]. To begin with, it is possible to simplify the diffusive terms in (2.3.6) and (2.3.8); remembering the definition (2.2.6) of the random velocity Cn and observing that en = 0, one finds in fact UiU = CniCn +UiU and, similarly, EUiU = EUiCn +EUi U.…”

Section: The Convective Terms and Time Derivativesmentioning

confidence: 99%

Hydrodynamic simulation of semiconductor devices

Rudan

Lorenzini

Brunetti

1998

Theory of Transport Properties of Semiconductor Nanostructures

View full text Add to dashboard Cite

INTRODUCTIONRecently the hydrodynamic model has become popular in the field of analysis and simulation of semiconductor devices*. The model has the merit of providing, along with the concentration and current density of the carriers, also their average energy and average energy flux. At the same time, its equations basically retain the same structure of the simpler drift-diffusion model; because of this, it has been possible to incorporate the hydrodynamic equations into existing deviceanalysis codes, thus exploiting a number of robust solution schemes already available there.The hydrodynamic model is derived by applying the moment technique to the Boltzmann transport equation (BTE) and truncating the series of moments at a suitable order. This yields a number of partial differential equations in the r, t space, specifically, the continuity equations for the carrier number, momentum, average energy and average energy flux. In this procedure, due to the integration over the wave vector space and to the series truncation, some of the information originally carried by the distribution function is lost. However, the information provided by the continuity equations indicated above is in most cases sufficient to describe the electrical behaviour of realistic semiconductor devices.It is worth noting that the term hydrodynamic model is not always given exactly the same meaning in the existing literature. What is meant here by this term is a model derived through the following steps: * Part of this work was carried out within ADEQUAT (JESSI BTl I, ESPRIT 8002) and DESSIS (ESPRIT 6075). E. Schöll (ed.), Theory of Transport Properties of Semiconductor Nanostructures

show abstract

“…The solution n t+l is used to update the quai-Fermi potential \|/", which is given by [25] ^+ 1^v i +1 -^ln(^). (5.43) e n a Then we put this quasi-Fermi potential into the Poisson equation to obtain the new potential and the new electron density at time level (t+1).…”

Section: The Numerical Methods For the Transient Problemmentioning

confidence: 99%

“…The Lei-Ting balance equations have been successfully applied to many types of semiconductor microstructures, including studies of nonequilibrium phonon, nonstationary and high frequency transport [22,23]. Unlike other hydrodynamic equation based approaches to device modeling, where the various relaxation rates are imported from Monte Carlo calculations or simply assumed to be constant [24,25,26], the Lei-Ting hydrodynamic balance equations approach includes scattering in the form of frictional force functions due to electron-impurity and electron-phonon interaction and an energy loss function due to electron-phonon interaction. These quantities are calculated within the simulation process itself, as functions of the electron drift velocity, electron temperature, as well as the electron density, without an outside, separate Monte Carlo procedure [21,27,28].…”

Section: Introductionmentioning

confidence: 99%

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation

Cui¹

1997

View full text Add to dashboard Cite

Public reporting burden for this collection of information * estimated to average 1 hour per response, including the time for reviewing «utructtoni, searching existing data sources, gathering and maintaining the data needed, and compleung and reviewing the collection of information. Send comment regarding «is burden estsnates or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for information Operations Hong-Liang Cui Department of Physics and Engineering PhysicsPerformance Period:October 1,1994 -September 30,1997Contract Number: DAAH04-94-G-0413 a 2 December 1997 IntroductionIt is becoming increasingly important to use computer-aided device simulators in the design and fabrication processes of semiconductor devices designing as semiconductor devices continue to decrease in size toward the deep submicron regime. The development of devices involves several iterations of trial and error in fabrication until a specified goal in terms of design conditions is reached. The application of device modeling can provide an inexpensive way to analyze and design the semiconductor devices before expensive device processing. Since traditional equivalent circuit models and close-form analytical models cannot always provide consistently accurate results for all modes of operation of today's small devices. This has meant that there has been a greater demand for models capable of increasing our understanding of how these devices operate and capable of predicting accurate quantitative results.To simulate a device, we solve a transport equation coupled with Poisson equation The accuracy of a simulation is usually determined by how accurately carrier transport is described. Generally, the more sophisticated the approach, the heavier the computational burden, so it is important to choose an adequate approach for the device under study. In the past, the study of electric behavior in a semiconductor device has been based on the drift-diffusion equation. The drift-diffusion model is a low-order approximation of the Boltzmann transport equation, it implies that mobility of the carrier is only a function of the local electrical field and it does not take account of the non-stationary characteristics such as carrier heating and velocity overshoot [1,2]. The application of this model is limited to devices where the spatial variation of the electric field is not very large. However, in modern devices, whose size is in the deep submicron region, the nonstationary phenomena are becoming more important. As a result, the drift-diffusion model is no longer applicable [3][4][5][6].Monte Carlo simulation has been widely used for analyzing carrier transport in bulk semiconductors [7,8,9]. This method tracks the momentum and position of an ensemble of carriers as they move through a device under the influence of an electric field and random scattering forces. Random numbers are chosen to determine the time between collisions, the type of scattering ev...

show abstract

Numerical Solution of the Hydrodynamic Model for a One‐dimensional Semiconductor Device

Cited by 65 publications

References 10 publications

A quantum corrected energy-transport model for nanoscale semiconductor devices

A quantum corrected energy-transport model for nanoscale semiconductor devices

Hydrodynamic simulation of semiconductor devices

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation

Contact Info

Product

Resources

About