Stanojević, N. orcid.org/0009-0007-5122-2219, Demić, A. orcid.org/0000-0003-1335-6156, Vuković, N. orcid.org/0000-0002-4941-2546 et al. (4 more authors) (2025) Derivative Transfer Matrix Method: Machine precision calculation of electron structure and interface phonon dispersion in semiconductor heterostructures. Computer Physics Communications. 109573. ISSN 0010-4655
Abstract
We develop a machine precision transfer matrix method that can be used for a wide range of ordinary differential equations and eigenvalue problems. One of the major drawbacks of transfer matrix approaches is the requirement to sweep parameters in a shooting-like manner, thus lacking in precision in comparison to finite difference methods. We resolve this by finding the zero of the analytically calculated first derivative of the transfer matrix. This allows us to outperform the finite difference approach and compute eigenvalues with high precision and linear numerical complexity. We test the developed model in the following scenarios in semiconductor quantum heterostructures: standard Schrödinger equation under effective mass approximation with parabolic subbands, with two-band nonparabolicity, a 4th order Schrödigner equation that accounts for nonparabolic subbands using the 14 k⋅p approach and calculation of the interface phonon modes dispersion relations and the mode profiles. We show that the developed derivative transfer matrix method outperforms the finite difference method by being able to handle higher spatial resolution and having better time performance. The numerical implementation of our models is available as an open-source package.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Transfer matrix method; Machine precision; Electron structure; Interface phonon; Terahertz quantum-cascade laser |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Electronic & Electrical Engineering (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Mar 2025 14:41 |
Last Modified: | 06 Mar 2025 14:41 |
Status: | Published online |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.cpc.2025.109573 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:224103 |