Steady hydrodynamic model of semiconductors with sonic boundary and transonic doping profile

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function. Furthermore, we prove uniqueness of subsonic solutions for sufficiently small currents.

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“…with φ x given by (11), and φ 1 related to j by (14). Equation ( 18) is supplemented with boundary conditions…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…We also refer to [10] for a non-isentropic case. More recently, the existence of supersonic solutions was proven in [11], and the existence of solutions for sonic boundary conditions was studied in a series of papers [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility

et al. 2021

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“…The hydrodynamic model of semiconductors, first introduced by Bløtekjaer [7], usually characterizes the motion of the charged fluid particles such as electrons and holes in semiconductor devices [24]. This paper is a follow-up of our series of study [8,19,20] on the Euler-Poisson equations of semiconductor models subjected to sonic boundary. Different from [8,19,20] on 1-D equations with sonic boundary, here we are mainly interested in the multiple-dimensional Euler-Poisson system [4,10] as follows:…”

Section: Introductionmentioning

confidence: 98%

“…This paper is a follow-up of our series of study [8,19,20] on the Euler-Poisson equations of semiconductor models subjected to sonic boundary. Different from [8,19,20] on 1-D equations with sonic boundary, here we are mainly interested in the multiple-dimensional Euler-Poisson system [4,10] as follows:…”

Section: Introductionmentioning

confidence: 99%

“…For the one-dimensional case, if system (1.2) is with sonic boundary, the structures of all types of solutions for (1.2) have been intensively studied when the doping profile is subsonic [19], supersonic [20] or transonic [8]. In the case of the subsonic [19] and subsonic-dominated [8] doping profile, there exist a unique interior subsonic, at least one interior supersonic solution, infinitely many transonic shock solutions (the sufficiently large relaxation time, i.e. τ ≫ 1), and infinitely many C 1 -smooth transonic solutions (the sufficiently small relaxation time, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Radial solutions of the hydrodynamic model of semiconductors with sonic boundary

Chen

Mei

Zhang

et al. 2020

Preprint

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The purpose of this paper is to study radial solutions for steady hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary. The existence and uniqueness of radial subsonic solution, and the existence of radial supersonic solutions are derived by using the energy method and the compactness method, but under a general condition of the doping profile. In particular, for radial supersonic solutions, it is more difficult to get the related estimates by the effect of high dimensional space and the sonic boundary, so we apply a special iteration to complete the proofs. The results obtained essentially improve and develop the previous studies in the one-dimensional case.

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The subsonic or sonic–subsonic solution of the electric potential driven problem to the HD model for semiconductors

Li,

Zhang,

Zhang

2024

Applied Mathematics Letters

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Steady hydrodynamic model of semiconductors with sonic boundary and transonic doping profile

Cited by 19 publications

References 18 publications

On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility

On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility

Radial solutions of the hydrodynamic model of semiconductors with sonic boundary

The subsonic or sonic–subsonic solution of the electric potential driven problem to the HD model for semiconductors

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