Empty lattice approximation: Difference between revisions

Revision as of 16:46, 25 December 2010

Revision as of 16:56, 25 December 2010

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In theory the lattice is infinitely large, so a weak periodic scattering potential will eventually be strong enough to reflect the wave. The scattering process results in the well known [[Bragg's law|Bragg reflections]] of electrons inby the periodic potential of the [[crystal structure]]. The periodicity and the division of [[Reciprocal lattice|k-space]] in Brillouin zones is the result of this scattering process. The periodic energy dispersion relation is

:<math>E_n(\bold{k}) = \frac{\hbar^2 (\bold{k} + \bold{G_n})^2}{2m}</math>

and consists of a increasing number of free electron bands <math>E_n(\bold{k})</math> when the energy rises. <math>\bold{G}_n</math> is the [[reciprocal lattice]] vector to which the band <math>E_n(\bold{k})</math> belongs. Electrons with larger wave vectors outside the first [[Brillouin zone]] are mapped back into the first Brillouin zone by a so called [[Umklapp scattering|Umklapp process]].