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The k∙p Method

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

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The k∙p Method

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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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