Approximate calculation of electronic energy levels of axially symmetric quantum dot and quantum ring by using energy dependent effective mass
Liu Yu-Min(刘玉敏)†, Yu Zhong-Yuan(俞重远), and Ren Xiao-Min(任晓敏)
Institute of Optical Communication and Optoelectronics, Beijing University of Posts and Telecommunications, Beijing 100876, China;Key Laboratory of Optical Communication and Lightwave Technologies, Ministry of Education (Beijing University of Posts and Telecommunications), Beijing 100876, China
Abstract Calculations of electronic structures about the semiconductor quantum dot and the semiconductor quantum ring are presented in this paper. To reduce the calculation costs, for the quantum dot and the quantum ring, their simplified axially symmetric shapes are utilized in our analysis. The energy dependent effective mass is taken into account in solving the Schrödinger equations in the single band effective mass approximation. The calculated results show that the energy dependent effective mass should be considered only for relatively small volume quantum dots or small quantum rings. For large size quantum materials, both the energy dependent effective mass and the parabolic effective mass can give the same results. The energy states and the effective masses of the quantum dot and the quantum ring as a function of geometric parameters are also discussed in detail.
Received: 10 December 2007
Revised: 25 August 2008
Accepted manuscript online:
(Fermi surface: calculations and measurements; effective mass, g factor)
Fund: Project supported by the National
Basic Research Program of China (Grant No 2003CB314901), the
National Natural Science Foundation of China (Grant No 60644004),
and the High School Innovation and Introducing Talent Project of
China (B07005).
Cite this article:
Liu Yu-Min(刘玉敏), Yu Zhong-Yuan(俞重远), and Ren Xiao-Min(任晓敏) Approximate calculation of electronic energy levels of axially symmetric quantum dot and quantum ring by using energy dependent effective mass 2009 Chin. Phys. B 18 9
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