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Calculation of Bulk Material Electronic Band Structure Using Matrix Mechanics: A Pedagogical Approach

  • Author / Creator
    Pavelich, Robert L
  • We present a method, intended primarily for pedagogical purposes, to extend the one-dimensional Kronig-Penney model (the standard starting point for solid-state physics) to the case of arbitrary potential shapes and to higher dimensions using matrix mechanics. We generate, either analytically or numerically, the matrix elements for a unit cell of some potential which can then be diagonalized to give the energies and eigenstates. Bloch’s theorem can be introduced as purely additive non-potential-dependent terms on the main diagonal which allows us to “sweep out” the band structure at virtually no additional cost. In one-dimension our results correspond exactly with the known analytical solutions to the Kronig-Penney model, and in higher dimensions our results match the usual shallow and deep well limits, namely the nearly free electron model and the tight binding model respectively. Our method has the advantage of using only concepts familiar to a senior quantum mechanics student, lending it conceptual simplicity and clarity. This provides a tool for senior undergraduates and beginning graduate students to generate their own band structures, allowing for a tight coupling between computational exploration and intuition formation.

  • Subjects / Keywords
  • Graduation date
    2016-06:Fall 2016
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3377656G
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Physics
  • Supervisor / co-supervisor and their department(s)
    • Marsiglio, Frank (Physics)
  • Examining committee members and their departments
    • Vaidyanathan, Mani (Electrical and Computer Engineering)
    • Sydora, Richard (Physics)
    • LeBlanc, Lyndsay (Physics)