A new discretization strategy of the semiconductor equations comprising momentum and energy balance

Forghieri, A.; Guerrieri, R.; Ciampolini, P.; Gnudi, A.; Rudan, Massimo; Baccarani, G.

doi:10.1109/43.3153

Cited by 154 publications

(42 citation statements)

References 21 publications

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“…The basic equations for the nonisothermal device simulation in steady-state, consisting of the Poisson equation (1), current continuity equations for electrons (2) and holes (3), the energy transport equation for electrons (4), and the heat flow equation (5), are given as follows:…”

Section: Basic Equationsmentioning

confidence: 99%

Thermal breakdown simulation of Si MOSFET taking account of thermal interdependence

Kawashima

Dang

1999

Electron. Comm. Jpn. Pt. II

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Section: Basic Equationsmentioning

confidence: 99%

Thermal breakdown simulation of Si MOSFET taking account of thermal interdependence

Kawashima

Dang

1999

Electron. Comm. Jpn. Pt. II

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“…The discretization of momentum and energy balance equations is carried out by a generalization of the Scharfetter-Gummel discretization scheme [33,34]. The balance equations are projected onto the side Ly and the projections are assumed to be constant over the side.…”

Section: Momentum Balance Equationmentioning

confidence: 99%

“…In order to implement the integration, we make an approximation that electron temperature, electric potential and total resistive force density are piecewise linear between two adjacent nodes. With the help of the Scharfetter-Gummel method, the current density along the mesh line between two adjacent nodes i and j can be expressed as [21,26] where n, and rij are the electron concentrations at node i and j. Thus, the expectation value of the electron concentration is given by 1 r*i n,-n,…”

Section: Momentum Balance Equationmentioning

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].…”

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confidence: 99%

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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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“…Not only the above-mentioned Drude model but also most of the hydrodynamic transport models that are widely used in semiconductor simulation environments with various degrees of sophistication [16][17][18][19][20] emerge from the Boltzmann equation. Starting from the latter, one may obtain in particular a set of hydrodynamic momentum and energy balance Eq.…”

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confidence: 99%

Quantum mechanical momentum and energy balance equations for transport of charge carriers

Magnus¹

2003

Physica Status Solidi (b)

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In this paper some basic features of electrical transport are discussed in terms of quantum mechanical energy and momentum balance equations. The latter are presented as an appropriate tool for the investigation of carrier transport in electric circuits containing mesoscopic active areas in the presence of inhomogeneous electromagnetic fields.1 Investigating electrical transport It goes without saying that transport of electrical charges through conducting media has been a topic of utmost importance ever since the discovery of electricity and magnetism. However, realistic models and theories predicting both microscopic and macroscopic transport features have to cope with a fundamental complication: not only do they have to comply with Maxwell's equations governing the electromagnetic fields that are compatible with a given charge and current distribution, they also need to provide the tools to go the opposite way and to find out how charge and current distributions respond to a given electromagnetic field. In other words, all reliable transport theories have to overcome in one way or another a major problem of selfconsistency to arrive at a workable calculation scheme. Macroscopic models relating the electric currents to the voltage drops arising in electric circuits have been established and used long before sound microscopic theories relying merely on first principles were constructed. Ohm's law and Kirchoff's laws addressing the voltage drops in arbitrary network loops and the currents flowing through a network nodes are prominent successful examples of such models. Although practical calculations for complicated circuits can be very cumbersome, they are based on relatively simple recipes emerging from a circuit theory that is partially phenomenological. On one hand, the theory accounts correctly for the basic electric and magnetic induction phenomena by exploiting the integral form of Maxwell's equations and lumping together all microscopic details into global quantities such as capacitance and inductance, characterizing ideally behaving components of the circuit. No phenomenological approach has been invoked at this level, since characteristic quantities like inductance and capacitance can be expressed in a straightforward way in terms of the magnetic permeability, the electric permittivity and a set of geometry dependent form factors [1]. On the other hand, irreversible processes underlying the dissipation of both energy and momentum of the charge carriers due to various microscopic scattering mechanisms, are treated in a purely phenomenological fashion by postulating a frictional force that is

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A new discretization strategy of the semiconductor equations comprising momentum and energy balance

Cited by 154 publications

References 21 publications

Thermal breakdown simulation of Si MOSFET taking account of thermal interdependence

Thermal breakdown simulation of Si MOSFET taking account of thermal interdependence

Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation

Quantum mechanical momentum and energy balance equations for transport of charge carriers

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