Efficient algorithm for the determination of the one electron eigenspectrum of a double quantum well semiconductor heterostructure

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Abstract

An efficient algorithm is presented for the numerical solution of the single band effective mass equation for a double well GaAs/InGaAs heterostructure. Sample results are presented showing the efficiency of the bracketting algorithm and differential equation solver. An extrapolation technique is applied, and the superiority of rational function over polynomial extrapolation is demonstrated. The advantages of a particular Runge-Kutta scheme over the extrapolation technique in this context are illustrated. Sample results are presented which show the efficiency of the bracketting algorithm. It is applied to the self-consistent determination of Stark shifts in a In0.3Ga0.7As/GaAs quantum wells located in a p-i-n structure. The effect of coupling on the Stark shifts of optical transition energies is considered, and coupling is found to give a significant enhancement of the Stark shift of the absorbtion edge. The electron-light hole transitions are shown to exhibit blue Stark shifts under certain conditions, as has been observed experimentally. Finally the technique is discussed and suggestions made for possible improvement. © 1992.

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Wilson, S. P., & Allsopp, D. W. E. (1992). Efficient algorithm for the determination of the one electron eigenspectrum of a double quantum well semiconductor heterostructure. Superlattices and Microstructures, 11(4), 363–374. https://doi.org/10.1016/0749-6036(92)90191-7

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