An improved hydrodynamic transport model for silicon

Tang, Ting-Wei; Ramaswamy, S.; Nam, Joonwoo

doi:10.1109/16.223707

Cited by 81 publications

(53 citation statements)

References 10 publications

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“…The electron temperature also behaves as expected. All of our results are in general agreement with other available results, including details of velocity overshoot, obtained with Monte Carlo simulations [40,41]. We also note that the spurious overshoot peak, which usually exists in other hydrodynamic models when electric field drastically decreases, is absent in our result.…”

Section: Steady State Simulationsupporting

confidence: 82%

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation

Cui¹

1997

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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...

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Section: Steady State Simulationsupporting

confidence: 82%

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation

Cui¹

1997

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“…The basic hypothesis underlying this procedure is that, although some approximations are involved in the calculation, the tables are applicable in a realistic range of device operation. In general, the tables are calculated for bulk materials, whence a possible effect of the gradients of the unknowns on the coefficients is lost [20]; in contrast, the surface-scattering effect, which is paramount in MOS devices, has recently been incorporated in the full solution of the BTE based on the spherical-harmonics expansion [21]. In the following, results of relaxation-time calculations are shown, obtained by means of a Monte Carlo simulator for electron transport in Si accounting for the full three-dimensional electron dynamics in the k space for a homogeneous system and including six ellipsoidal, nonparabolic valleys associated to the minima of the conduction band [22,23].…”

Section: )mentioning

confidence: 99%

Hydrodynamic simulation of semiconductor devices

Rudan

Lorenzini

Brunetti

1998

Theory of Transport Properties of Semiconductor Nanostructures

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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

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“…Since these models are not always available, a simplified model with the energy flux mobility being proportional or equal to the carrier mobility has been proposed [23,43]. This assumption introduces an error into the energy flux even for homogeneous conditions but does not influence the current density.…”

Section: From Drift-diffusion To Higher Moments Equationsmentioning

confidence: 99%