Semiconductor full quantum hydrodynamic model with non-flat doping profile: (II) semi-classical limit

ABSTRACT

This is the other part of our series of studies concerning the full quantum hydrodynamic (FQHD) model for semiconductors with non-flat doping profile. In this paper, as a sequel to Hu H, Zhang K (Semiconductor full quantum hydrodynamic model with non-flat doping profile: (I) stability. 2021, submitted), we proceed to rigorously justify the semi-classical limit of both steady states and global-in-time solutions as Planck's constant ε tends to zero; the strong convergence rates are also obtained. Our main results are proved by using the elaborated energy estimates and compactness analysis.

KEYWORDS:

• Full quantum hydrodynamic model
• dispersive velocity term
• non-flat doping profile
• semi-classical limit
• semiconductor

AMS SUBJECT CLASSIFICATIONS:

• 35A01
• 35B40
• 35M33
• 76Y05

Acknowledgments

This research was initiated when the first author was a postdoc in the Center for Partial Differential Equations of ECNU; then it is now finally completed when the first author is visiting the Department of Mathematics and Statistics of McGill University; the financial support and kind hospitality from both institutes are gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author's and second author's research work was partially supported by National Natural Science Foundation of China [grant number11771071, [grant number11801039]. The first author's research work was partially supported by China Scholarship Council (File No.202007535001) and Programme of Scientific Research of Changchun University [grant number ZKP202013].