The effect of in-doping on the quantum information entropy of hydrogenic impurity states in the In_xGa_1-xN semiconductor quantum dot

ABSTRACT

The effect of In-doping on the quantum information entropy of the hydrogenic impurity states in the In_xGa_1-xN quantum dot has been studied for the first time. By exploring the Shannon entropy in the position space (S_r), in the momentum-space (S_p) and the Shannon entropy sum S_t, we find some novel and interesting phenomenon. First, although S_r increases and S_p decreases monotonically with the radius of In_xGa_1-xN quantum dot, the Shannon entropy sum S_t exhibits a series of peaks and valleys with the confinement radius. The physical origin of the minimum and maximum values in the Shannon entropy sum S_t is analysed in great detail. Second, the BBM entropy uncertainty principle ($S_t\ge 3[1+\ln (\pi )]$) holds for the hydrogenic impurity state in the semiconductor quantum dot, which can be used to replace the Heisenberg uncertainty principle in the quantum mechanics. Third, the content of the doping In element in the In_xGa_1-xN quantum dot has a great influence on the Shannon entropy of the hydrogenic impurity state. Since the Shannon entropy sum S_t is usually used to measure the position-momentum correlation, therefore, we can explore the uncertainty of position and momentum of the hydrogenic impurity states by changing the content of the doping element in the semiconductor quantum dots. This study has some practical applications in semiconductor material and quantum information measurement, and may guide future experimental researches for the localisation and delocalisation characteristics of hydrogenic impurities states in the semiconductor quantum dots.

KEYWORDS:

• Quantum information entropy
• hydrogenic impurity states
• In_xGa_1-xN quantum dot

Acknowledgement

We also thank the referees for their valuable suggestions.

Disclosure statement

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

Additional information

Funding

This work was supported by the Natural Science Foundation of Shandong Province, China [grant numbers ZR2019MA066 and ZR2020MF103], the Taishan Scholar Project of Shandong Province [grant number tsqn201812098], and the National Natural Science Foundation of China [grant number 62275115].