A Coupled Schrödinger Drift-Diffusion Model for Quantum Semiconductor Device Simulations

Degond, Pierre; Ayyadi, Asma El

doi:10.1006/jcph.2002.7122

Cited by 32 publications

(63 citation statements)

References 36 publications

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“…Using the asymptotics (2.2) of the scattering states ψ p , one can derive boundary conditions for ψ p at the boundaries x 1 and x 2 , see [6,7,10,1]. Furthermore, note that the transmission and reflection amplitudes are given in terms of ψ p (x i ) and ψ p (x i ), i = 1, 2, see [6,1] for details.…”

Section: The Quantum Regionmentioning

confidence: 99%

“…Another hybrid model, which is more closely related to the model we will treat in this paper, was introduced in [6] and [7]. The Boltzmann equation together with the reflection-transmission conditions of the kinetic-quantum model of [3] was replaced by the drift-diffusion equation and corresponding connection conditions by the use of a diffusion approximation.…”

Section: Introductionmentioning

confidence: 99%

“…The two hybrid models described above, i.e. [3] and [6], assume that the quantum region is ballistic and collisions are only taken into account in the classical regions. But electron-phonon collisions play an important role also in the quantum region.…”

Section: Introductionmentioning

confidence: 99%

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A 1D coupled Schrödinger drift-diffusion model including collisions

Baro

Abdallah

Degond

et al. 2005

Journal of Computational Physics

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We consider a one-dimensional coupled stationary Schrödinger drift-diffusion model for quantum semiconductor device simulations. The device domain is decomposed into a part with large quantum effects (quantum zone) and a part where quantum effects are negligible (classical zone). We give boundary conditions at the classicquantum interface which are current preserving. Collisions within the quantum zone are introduced via a Pauli master equation. To illustrate the validity we apply the model to three resonant tunneling diodes.

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Section: The Quantum Regionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A 1D coupled Schrödinger drift-diffusion model including collisions

Baro

Abdallah

Degond

et al. 2005

Journal of Computational Physics

Self Cite

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show abstract

“…A lot of works are devoted to the numerical simulations of quantum transport models in semiconductors (see e.g. [34], [50], [59], [33], [24]). Yet, most of these authors do not attempt to adapt DriftDiffusion and Energy-Transport theories but rather, start from different models.…”

Section: Introductionmentioning

confidence: 99%

Quantum Energy-Transport and Drift-Diffusion Models

2005

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We show that Quantum Energy-Transport and Quantum Drift-Diffusion models can be derived through diffusion limits of a collisional Wigner equation. The collision operator relaxes to an equilibrium defined through the entropy minimization principle. Both models are shown to be entropic and exhibit fluxes which are related with the state variables through spatially non-local relations. Thanks to an expansion of these models, 2 perturbations of the Classical Energy-Transport and Drift-Diffusion models are found. In the DriftDiffusion case, the quantum correction is the Bohm potential and the model is still entropic. In the Energy-Transport case however, the quantum correction is a rather complex expression and the model cannot be proven entropic.

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“…In RTDs, the electron transport in the vicinity of the double barriers can be expected to be quantum and collisionless while transport in the access zone is mainly classical and collisional. This is why a class of hybrid models was developped [1,13,9,27] but the coupling methodology is far from obvious.…”

Section: Introductionmentioning

confidence: 99%

An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes

Degond

Gallego

Méhats

2007

Journal of Computational Physics

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We present an entropic Quantum Drift Diffusion model (eQDD) and show how it can be derived on a bounded domain as the diffusive approximation of the Quantum Liouville equation with a quantum BGK operator. Some links between this model and other existing models are exhibited, especially with the Density Gradient (DG) model and the Schrödinger-Poisson Drift Diffusion model (SPDD). Then a finite difference scheme is proposed to discretize the eQDD model coupled to the Poisson equation and we show how this scheme can be slightly modified to discretize the other models. Numerical results show that the properties listed for the eQDD model are checked, as well as the model captures important features concerning the modeling of a resonant tunneling diode. To finish, some comparisons between the models stated above are realized.

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A Coupled Schrödinger Drift-Diffusion Model for Quantum Semiconductor Device Simulations

Cited by 32 publications

References 36 publications

A 1D coupled Schrödinger drift-diffusion model including collisions

A 1D coupled Schrödinger drift-diffusion model including collisions

Quantum Energy-Transport and Drift-Diffusion Models

An entropic quantum drift-diffusion model for electron transport in resonant tunneling diodes

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