Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors

Sungjin Ra; Hakho Hong

Applications of Mathematics (2024)

  • Volume: 69, Issue: 1, page 113-137
  • ISSN: 0862-7940

Abstract

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This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in ℝ 3 , we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into that of the simplified quantum energy-transport model and the quantum drift-diffusion model for the moment relaxation limit, and the moment and energy relaxation limit, respectively.

How to cite

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Ra, Sungjin, and Hong, Hakho. "Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors." Applications of Mathematics 69.1 (2024): 113-137. <http://eudml.org/doc/299206>.

@article{Ra2024,
abstract = {This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in $\mathbb \{R\}^3$, we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into that of the simplified quantum energy-transport model and the quantum drift-diffusion model for the moment relaxation limit, and the moment and energy relaxation limit, respectively.},
author = {Ra, Sungjin, Hong, Hakho},
journal = {Applications of Mathematics},
keywords = {quantum hydrodynamic equation; quantum Euler-Poisson system; bipolar semiconductor model; relaxation-time limit},
language = {eng},
number = {1},
pages = {113-137},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors},
url = {http://eudml.org/doc/299206},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Ra, Sungjin
AU - Hong, Hakho
TI - Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 113
EP - 137
AB - This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in $\mathbb {R}^3$, we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into that of the simplified quantum energy-transport model and the quantum drift-diffusion model for the moment relaxation limit, and the moment and energy relaxation limit, respectively.
LA - eng
KW - quantum hydrodynamic equation; quantum Euler-Poisson system; bipolar semiconductor model; relaxation-time limit
UR - http://eudml.org/doc/299206
ER -

References

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