SEMICONDUCTOR PHYSICS

Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field

Yun Kang, Sheng Wang and Xianli Li

+ Author Affiliations

 Corresponding author: Sheng Wang, E-mail: wangsheng10@126.com

PDF

Abstract: Using the finite element method, we investigate the lowest and first few excited state energies in a two-dimensional GaAs quantum ring (QR) with a hydrogenic donor impurity and effective mass approximation under a uniform magnetic field perpendicular to the ring plane. We study in detail the dependence of the energy spectrum with different angular momentum on the inner radius, the outer radius and width of the QR, the magnetic field and impurity position. The results reveal that the electron energies increase with the inner radius while decrease with the outer radius and width of the QR; for a fixed ring, the magnetic field induces the increase of the electron energies. Moreover, the existence of impurity reduces energy levels, and the energy levels depend highly on the impurity position, which decreases as the impurity is far away from the center of the QR. Also, the dependence of the angular momentum on the energy spectrum is analyzed in detail.

Key words: quantum ringhydrogenic donor impuritymagnetic fieldelectron energy states



[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
Fig. 1.  A schematic representation of a two-dimensional QR with a hydrogenic donor impurity under a magnetic field.

Fig. 2.  The energy levels $E_{1}$ (a), $E_{2}$ (b), $E_{3}$ (c) and $E_{4}$ (d) with different angular momentum $l$ $=$ 0, 1 and 2 as functions of inner radius $R_1$ for outer radius $R_{2}=5a^*$ and $\gamma =1$ in the absence of the impurity.

Fig. 3.  The energy levels $E_{1}$ (a), $E_{2}$ (b), $E_{3}$ (c) and $E_{4}$ (d) with $l$ $=$ 0, 1and 2 are depicted as functions of inner radius $R_{1}$ with a donor impurity located at the center of the QR for outer radius $R_{2}=5a^*$ and magnetic field $\gamma =1$.

Fig. 4.  The energy levels $E_{1}$ (a), $E_{2}$ (b), $E_{3}$ (c) and $E_{4}$ (d) with $l$ $=$ 0, 1and 2 are described as functions of outer radius $R_{2}$ with a donor impurity placed on the center of the QR for inner $R_{1}=a^*$ and magnetic field $\gamma =1$.

Fig. 5.  The energy levels $E_{1}$ (a), $E_{2}$ (b), $E_{3}$ (c) and $E_{4}$ (d) with $l$ $=$ 0, 1 and 2 as functions of the width $d$ of the QR (the average radius $\bar {R}=3a^\ast )$ with the on-center impurity and magnetic field $\gamma =1$.

Fig. 6.  The energy levels $E_{1}$ (a), $E_{2}$ (b), $E_{3}$ (c) and $E_{4}$ (d) with $l$ $=$ 0, 1 and 2 as functions of the magnetic field $\gamma$ for inner radius $R_{1}=a^*$ and outer radius $R_{2}=5a^*$ in the presence of donor impurity located at the center of the QR.

Fig. 7.  The energy levels $E_{1}$ (a), $E_{2}$ (b), $E_{3}$ (c) and $E_{4}$ (d) with $l$ $=$ 0, 1 and 2 are shown as functions of impurity position $r_{\rm i}$ varying from 0 to $R_{1}$ with the magnetic field $\gamma =1$ for inner radius $R_{1}=a^*$ and outer radius $R_{2}=5a^*$ of the QR.

DownLoad: CSV
DownLoad: CSV
DownLoad: CSV
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
  • Search

    Advanced Search >>

    GET CITATION

    shu

    Export: BibTex EndNote

    Article Metrics

    Article views: 2830 Times PDF downloads: 40 Times Cited by: 0 Times

    History

    Received: 06 August 2014 Revised: Online: Published: 01 March 2015

    Catalog

      Email This Article

      User name:
      Email:*请输入正确邮箱
      Code:*验证码错误
      Yun Kang, Sheng Wang, Xianli Li. Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field[J]. Journal of Semiconductors, 2015, 36(3): 032003. doi: 10.1088/1674-4926/36/3/032003 Y Kang, S Wang, X L Li. Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field[J]. J. Semicond., 2015, 36(3): 032003. doi: 10.1088/1674-4926/36/3/032003.Export: BibTex EndNote
      Citation:
      Yun Kang, Sheng Wang, Xianli Li. Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field[J]. Journal of Semiconductors, 2015, 36(3): 032003. doi: 10.1088/1674-4926/36/3/032003

      Y Kang, S Wang, X L Li. Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field[J]. J. Semicond., 2015, 36(3): 032003. doi: 10.1088/1674-4926/36/3/032003.
      Export: BibTex EndNote

      Electron energy states in a two-dimensional GaAs quantum ring with hydrogenic donor impurity in the presence of magnetic field

      doi: 10.1088/1674-4926/36/3/032003
      Funds:

      Project supported by the National Natural Science Foundation of China (No. 41202146), the Science and Technology Project of Education Department of Heilongjiang Province of China (Nos. 12541070, 12541064), the Natural Science Foundation of Heilongjiang Province of China (No. A201402), and the Northeastern Petroleum University Youth Science Foundation of China (No. 2012QN128).

      More Information
      • Corresponding author: E-mail: wangsheng10@126.com
      • Received Date: 2014-08-06
      • Accepted Date: 2014-10-11
      • Published Date: 2015-01-25

      Catalog

        /

        DownLoad:  Full-Size Img  PowerPoint
        Return
        Return