A simplified quantum energy-transport model for semiconductors

Jüngel, Ansgar; Milišić, Josipa-Pina

doi:10.1016/j.nonrwa.2010.08.026

Cited by 6 publications

(5 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another way to derive quantum-corrected energy-transport models is to perform a relaxation-time limit in the quantum hydrodynamic equations. Indeed, in the diffusive time and small velocity scaling, the following (simplifying) set of equations has been formally derived in [76]:…”

Section: Quantum Energy-transport Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Energy transport in semiconductor devices

Jüngel

2010

Mathematical and Computer Modelling of Dynamical Systems

Self Cite

View full text Add to dashboard Cite

The modelling, analysis and numerical approximation of energy-transport models for semiconductor devices are reviewed. The derivation of the partial differential equations from the semiconductor Boltzmann equation is sketched. Furthermore, the main ideas for the analytical treatment of the equations, employing thermodynamic principles, are given. A new result is the proof of the weak sequential stability of approximate solutions to some time-dependent energy-transport equations with physical transport coefficients. The discretization of the stationary model using mixed finite elements is explained, and some numerical results in two and three space dimensions are presented. Finally, energytransport models with lattice heating or quantum corrections are reviewed.

show abstract

Section: Quantum Energy-transport Modelsmentioning

confidence: 99%

“…The second equation follows from the last equations in ( 8) and ( 41) in the small-velocity limit. An analysis of the above model has been performed in [76] for the case κðn; T Þ ¼ n.…”

Section: Quantum Energy-transport Modelsmentioning

confidence: 99%

Energy transport in semiconductor devices

Jüngel

2010

Mathematical and Computer Modelling of Dynamical Systems

Self Cite

View full text Add to dashboard Cite

show abstract

“…K. Wang and S. Wang [12] studied the limit of vanishing Debye length in a bipolar drift-diffusion model for semiconductors with physical contactinsulating boundary conditions in one-dimensional case. The existence of global-in-time weak solution to a quantum energy-transport model for semiconductors is proved in [13]. J.W.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors

Liu¹

2016

JPDE

View full text Add to dashboard Cite

Abstract. The well-posedness of smooth solution to a 3-D simplified Energy-Transport model is discussed in this paper. We prove the local existence, uniqueness, and asymptotic behavior of solution to the equations with hybrid cross-diffusion. The smooth solution convergences to a stationary solution with an exponential rate as time tends to infinity when the initial date is a small perturbation of the stationary solution.

show abstract

“…Based on this experience it is natural to also exploit the hierarchy of macroscopic semiconductor quantum models. Here, one uses the quantum drift diffusion model [1,2,25,24] as well as the quantum energy transport model [18,7,19]. First analytical and numerical results concerning corresponding optimization problems can be found [38,31,26,29].…”

Section: Introductionmentioning

confidence: 99%

The Semi-Classical Limit of an Optimal Design Problem for the Stationary Quantum Drift-Diffusion Model

Pinnau,

Rau,

Schneider

et al. 2014

Preprint

View full text Add to dashboard Cite

We consider an optimal semiconductor design problem for the quantum drift diffusion (QDD) model in the semiclassical limit. The design question is formulated as a PDE constrained optimal control problem, where the doping profile acts as control variable. The existence of minimizers for any scaled Planck constant allows for the investigation of the corresponding sequence. Using the concepts of Gamma-convergence and equi-coercivity we can show the convergence of minima and minimizers. Due to the lack of uniqueness for the state system and optimization problem, it was necessary to establish a new result for the QDD model ensuring the existence of a sequence of quantum solutions converging to an isolated classical solution. As a byproduct, we obtain new insights into the regularizing property of the quantum Bohm potential. Finally, we present the numerical optimization of a MESFET device underlining our analytical results.

show abstract

A simplified quantum energy-transport model for semiconductors

Cited by 6 publications

References 26 publications

Energy transport in semiconductor devices

Energy transport in semiconductor devices

Asymptotic Behavior of the Solution to a 3-D Simplified Energy-Transport Model for Semiconductors

The Semi-Classical Limit of an Optimal Design Problem for the Stationary Quantum Drift-Diffusion Model

Contact Info

Product

Resources

About