A Polynomial Approximation to Self Consistent Solution for Schrödinger–Poisson Equations in Superlattice Structures

Mariusz Mączka and Stanisław Pawłowski
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Mariusz Mączka: Department of Electronics Fundamentals, Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzeszow, Poland
Stanisław Pawłowski: Department of Electrodynamics and Electrical Machine Systems, Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, 35-959 Rzeszow, Poland

Energies, 2022, vol. 15, issue 3, 1-17

Abstract: The paper deals with a new approach to iterative solving the Schrödinger and Poisson equations in the first type of semiconductor superlattice. Assumptions of the transfer matrix method are incorporated into the approach, which allows to take into account the potential varying within each single layer of bias voltage superlattice. The key process of the method is to approximate the charge density and wave functions with polynomials. It allows to obtain semi-analytical solutions for the Schrödinger and Poisson equations, which in turn have significant impact on the accuracy and speed of superlattice simulations. The presented procedure is also suifihue for finding eigenstates extended over relatively large superlattice area, and it can be used as an effective pro-gram module for a superlattice finite model. The obtained quantum states are very similar to the Wannier-Stark functions, and they can serve as the base under non-equilibrium Green’s function formalism (NEGF). Exemplary results for Schrödinger and Poisson solutions for superlattices based on the GaAs/AlGaAs heterostructure are presented to prove all the above.

Keywords: Schrödinger–Poisson equations; semiconductor superlattices; polynomials approximation; transfer matrix method (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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