How Do Band Gaps Arise in Periodic Lattices According to Bloch Theory?

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Band gaps arise in periodic lattices due to the arrangement of atoms, which creates a band structure that includes gaps for semiconductors and insulators. According to Bloch theory, for a specific wave vector (K value), an electron within a band possesses a precise energy determined by the band’s shape. This phenomenon is akin to electrons confined in a potential well, but in a lattice, there are infinitely many potential wells. The presence of band gaps is not a direct result of Bloch theory itself, but rather a consequence of the periodic nature of the lattice. Understanding these concepts is crucial for exploring electronic properties in materials.
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why band gaps occur according to bloch theory?
 
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Band Gaps do not occur according to a theory. It is the band structure (that has a gap only for semiconductors and insulators) that appears any time atoms are arranged in a periodic fashion to form a lattice. Bloch theory only says that for a definite K value, an electron that is in a band, has to have a precise energy depending on the "shape" of the band. This is similar to what happens when an electron is confined to a potential well, but in the case of a lattice, you have a (infinite) number of wells.

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