Band Theory, Kittel chapter 7

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Kronig-Penney model

|α| < 2

⎛

tanka =±⎜

⎜

⎝

2

4−α

α

⎞

⎟

⎠

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Kronig-Penney model |α| < 2 ⎛ tanka =±⎜ ⎜ ⎝ 2 4−α α ⎞ ⎟ ⎠

Kronig-Penney model free electrons (a) The energy-wave number dispersion relation. The dashed line is the Fermi energy. (b) The density of states. (c) The internal energy density (solid line) and Helmholtz free energy density (dashed line). (d) The chemical potential (solid line) and the specific heat (dashed line). All of the plots were drawn for a square wave potential with the parameters: V = 12.5 eV, a =2×10 - 10 m, b =5×10 -11 m, and an electron density of n = 3 electrons/primitive cell.

Page 1 and 2: silicon Institute of Solid State Ph
Page 3 and 4: Kronig-Penney model Solutions can b
Page 5 and 6: Kronig-Penney model at x = a ψ ψ
Page 7: Kronig-Penney model The eigen value
Page 11: from Ashcroft and Mermin Extended,

Band Theory, Kittel chapter 7

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