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The k·p Method: Analyzing Band Dispersion in Semiconductors

Learn about the k·p method, its history and applications in obtaining band structures and effective masses in semiconductors. Discover the Matrix Element Theorem and its relevance to wave functions and operators. Explore examples like the Wigner-Eckart Theorem and conduction band effective masses.

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The k·p Method: Analyzing Band Dispersion in Semiconductors

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  1. The k∙p Method Brad Malone Group Meeting 4/24/07

  2. First used by Bardeen (1937) and Seitz (1940) • Later extended by Shockley, Dresselhaus, Kittel, and Kane Uses: • Obtaining analytic expressions for band dispersion and effective masses • Can also be used to get the band structure for the whole zone from zone center energy gaps and optical matrix elements

  3. The Matrix Element Theorem- The matrix element between the operator A and the wave functions Ψ1 and Ψ2 is nonzero only if the direct product of the representations of A and Ψ1 contains an irreducible representation of Ψ2 Example: The Wigner-Eckart Theorem

  4. Conduction Band effective mass in III-V and II-VI semiconductors: -Conduction band has Г1 symmetry; p has Г4 symmetry Ge GaAs InP InAs GaSb InSb CdTe Eg (eV) 0.89 1.55 1.34 0.45 0.81 0.24 1.59 m*/m (exp) 0.041 0.067 0.073 0.026 0.047 0.015 0.11 m*/m (theory) 0.04 0.078 0.067 0.023 0.04 0.012 0.08

  5. Splitting of a degenerate extremum by spin-orbit

  6. Löwdin’s perturbation method:

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