Calculating modes of quantum wire and dot systems using a finite differencing technique

D. El-Moghraby, R. G. Johnson, P. Harrison

    Research output: Contribution to journalArticlepeer-review

    35 Scopus citations

    Abstract

    In this paper the Schrödinger equation of both a quantum wire and a quantum dot are solved using a finite difference approach. It is demonstrated that the method is valid for the simple case of an infinitely deep quantum wire, where the solutions obtained are within 0.25 meV of the analytical solutions. The method is then used to calculate the eigenenergies of a triangular wire with finite barriers. The eigenenergies of the more complex case of a pyramidal quantum dot were then calculated using this method. The method is compared to an eigenvalue method in terms of memory usage, time requirements and the numerical solutions. It is shown that this method has the advantages of being relatively fast, usable with any wire geometry and any potential profile. In addition, the demand on computer memory varies linearly with the size of the system under investigation.

    Original languageBritish English
    Pages (from-to)235-246
    Number of pages12
    JournalComputer Physics Communications
    Volume150
    Issue number3
    DOIs
    StatePublished - 15 Feb 2003

    Keywords

    • Energy levels
    • Finite difference
    • Pyramidal quantum dot
    • Quantum wire
    • Sparse matrices

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