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ssp_16 - 5 Continued 5-40 Tight binding approximation k n...

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5-40 5 Continued
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5-41 Tight - binding approximation ψ k n a n ϕ i ( r - r n ) (5.56) linear combination of atomic eigenfunctions ϕ i ψ k Bloch wave a n = e i k r n (cf. eq. 5.44) Fig. 5.19 Band formation by overlap of atomic wave functions (see Chapter 1.1). N = 1, 2, 4, 8 Large overlap of atomic orbitals large splitting Classification of bands according to orbitals of free atoms: s, p, d, ....
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5-42 Fig.5.20. Broardening of the energy levels as a large number of identical atoms from the first row of the periodic table approach one another (schematic). The separation r 0 correspponds to the approximate equilibrium separation of chemically bound atoms. Due to the overlap of the 2 s and 2 p bands, elements such as Be with two outer electrons also become metallic. Deep- lying atomic levels are only slightly broadened and thus, to a large extent, they retain their atomic character Band gaps also form in amorphous materials!
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5-43 Metals, Semiconductors and Insulators Fig. 5.21 Location of the Fermi level in the band structure for metals and insulators. The shaded areas represent the energy range occupied by electrons (schematic). Metal : partly occupied band or overlap of bands Electrons can gradually be accelerated into empty higher energy states in electric field.
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