Existence and uniqueness of steady states to semiconductor bipolar full quantum hydrodynamic model

Abstract

In this paper, we are concerned with the existence and uniqueness of subsonic steady states to the one-dimensional bipolar full quantum hydrodynamic model for semiconductors in a bounded interval. The main result is proved by perturbation arguments combined with Banach's Fixed Point Theorem. Moreover, we also obtain the uniform estimates of steady states with respect to the physical parameters appear in the model, which comes in useful for discussing the relaxation time limit and semi-classical limit in future study.

Keywords:

• Full quantum hydrodynamic model
• quantum energy-transport model
• non-constant doping profile
• steady states

AMS Subject Classifications:

• 35A01
• 35G60
• 35Q40
• 35Q81

Acknowledgments

This research was completed when the author was visiting the Department of Mathematics and Statistics of McGill University in 2021; the kind hospitality is gratefully acknowledged.

Disclosure statement

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

Additional information

Funding

The author's research was partially supported by the National Natural Science Foundation of China [grant number 11801039], China Scholarship Council [file number 202007535001] and Programme of Scientific Research of Changchun University [grant number ZKP202013].