High accuracy numerical solutions for band structures in strained quantum well semiconductor optical amplifiers

doi:10.1007/s12200-011-0220-3

Front Optoelec Chin

2011, Vol. 4

Issue (3) : 330-337 https://doi.org/10.1007/s12200-011-0220-3

RESEARCH ARTICLE

High accuracy numerical solutions for band structures in strained quantum well semiconductor optical amplifiers

Xi HUANG, Cui QIN, Xinliang ZHANG(

)

Wuhan National Laboratory for Optoelectronics, College of Optoelectonic Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

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Abstract

In this paper, we have calculated the band structure of strained quantum well (QW) semiconductor optical amplifiers (SOAs) by using plane wave expansion method (PWEM) and finite difference method (FDM), respectively. The difference between these two numerical methods is presented. First, the solution of Schr?dinger’s equation in a conduction band for parabolic potential well is used to check the validity and accuracy of these two numerical methods. For the PWEM, its stability and computational speed are investigated as a function of the number of plane waves and the period of QW. For FDM, effects of mesh size and QW width on its accuracy and calculation time are discussed. Finally, we find that the computational speed of FDM generally is faster than that of PWEM. However, the PWEM is more efficient than the FDM when wider SOAs are needed to be calculated. Therefore, to obtain high accuracy and efficient numerical solutions for band structures, numerical methods should be selected depending on required accuracy, device structure and further applications.

Keywords semiconductor optical amplifier quantum well devices plane wave expansion method finite difference method

Corresponding Author(s): ZHANG Xinliang,Email:xlzhang@mail.hust.edu.cn

Issue Date: 05 September 2011

Cite this article:

Xi HUANG,Cui QIN,Xinliang ZHANG. High accuracy numerical solutions for band structures in strained quantum well semiconductor optical amplifiers[J]. Front Optoelec Chin, 2011, 4(3): 330-337.

URL:

https://academic.hep.com.cn/foe/EN/10.1007/s12200-011-0220-3
https://academic.hep.com.cn/foe/EN/Y2011/V4/I3/330

Fig.1 The lowest four confined eigenenergies of a finite parabolic quantum well, black lines from bottom to top: the lowest four confined eigenenergies, blue line: parabolic potential

Tab.1 Convergence test of two numerical methods at г point

Fig.2 Percentage error in the first ten eigenenergies solved by two numerical methods

Fig.3 CPU time with two different numerical methods as a function of parabolic quantum well period

Fig.4 Rectangular potential well and the first two wavefunctions in conduction band. (a) FDM method; (b) PWEM method (solid line: the first sub-band in the conduction, dotted line: the second sub-band)

Fig.5 Envelope wavefunction for HH1 sub-band of rectangular potential well with different numerical methods. HH is heavy hole sub-band, LH is light hole sub-band, SO is spin-orbit sub-band. (a) FDM method; (b) PWEM method

Fig.6 Energy dispersions in conduction band (a) and valence band (b) solved by two different numerical methods, inset (a1): the detail of conduction band

Fig.7 Percentage error in the first eigenenergy (compared with analytic solution) as a function of quantum well period (a), the number of plane waves (b) and mesh size (c), respectively

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