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250 4 Semiconductors
Figure 4.13. Electronic states in the nearly free electron model for a 1-D chain with unit cell length, a.
The energy states in (a) represent solutions to the Schrodinger equation (via the Bloch theorem) with an
infinitesimal potential. In contrast, solution (b) represents a finite lattice potential, which results in the
formation of gaps between the parabolas at the BZ boundary. That is, there is no longer a continuum of
states from the lowest to infinity, but regions where no allowed states may exist. Reproduced with
permission from Hofmann, P. Solid State Physics: An Introduction, Wiley: New York, 2008. Copyright
2008 Wiley-VCH Verlag GmbH & Co.
