Surface states dangling hybrid

Let us return to a further description of the electronic structure at the surface of the crystal. Imagine constructing the electron states in a crystal with a surface, just as bulk states were constructed in Chapter. 1. Bond orbitals are formed for all the bond.s, but those hybrid orbitals directed out of the surface remain unbonded. These orbitals are allied dangling hybrids. Each retains the energy C, seen in Fig. 3-.3 to be greater than the bond energy by V. (We are interested in total... 

We will now consider the open infinite chain, simulating surface formation. If the ideal hybridization condition Eq.(2.128) is satisfied, dangling orbitals with orbital energies a = as = ap appear at the end of the chain. These are the Shockley surface states, because they are strictly localized on atoms 1 and N, The solution for the general case is found by solving the secular equations for the open chain. Equations (2.123) have to be solved with bonding conditions ... 

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