ETRI Journal

Electronics and Telecommunications Research Institute (한국전자통신연구원)
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Improved Multi-band Transfer Matrix Method for Calculating Eigenvalues and Eigenfunctions of Quantum Well and Superlattice Structures

  • Published : 1998.12.15
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Abstract

We present an improved transfer matrix algorithm which can be used in solving general n-band effective-mass $Schr{\ddot{o}}dinger$ equation for quantum well structures with arbitrary shaped potential profiles(where n specifies the number of bands explicitly included in the effective-mass equation). In the proposed algorithm, specific formulas are presented for the three-band (the conduction band and the two heavy- and light-hole bands) and two-band (the heavy- and light-hole bands) effective-mass eigensystems. Advantages of the present method can be taken in its simple and unified treatment for general $n{\times}n$ matrix envelope-function equations, which requires relatively smaller computation efforts as compared with existing methods of similar kind. As an illustration of application of the method, numerical computations are performed for a single GaAs/AlGaAs quantum well using both the two-band and three-band formulas. The results are compared with those obtained by the conventional variational procedure to assess the validity of the method.

Keywords

References

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