Dangling hybrid

Crystalline dcfcci.s, such as vacancies, also produce dangling hybrids, and the. same kind of Jahn-Tcllcr distortion is known to occur this always tends to sweep states from the gap. The extreme case is the amorphous covalent solid, which, even though disordered, retains an open covalent structure and is semiconducting. 

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... 

Now let us allow for the addition of an electron to (or the removal of an electron from) the dangling hybrid. We must now add (or subtract) the energy of that electron. It now becomes very important whether or not we rotate the liybrids, since rotation changes the sp mixture and the energy of the hybrid. The calculation requires a little trigonometry. In Fig. 10-3, a dangling hybrid with three back bonds is shown. We construct hybrids +... 

This remarkably simple result applies for -doubly occupied dangling hybrid and subtracted for an empty dangling hybrid. The result is shown for silicon in Fig. 10-4. 

Notice that a surface atom with a doubly occupied level is predicted to be displaced almost until the dangling hybrid is completely. s-like. The predicted inward displacement of the empty hybrid is not so great the minimum occurs at... 

CalcLilaicd energy as a function of the outward displacement w of a (111) surface atom in silicon when the dangling hybrid is doubly occupied or empty. The constitution of the dangling hybrid is indicated at the bottom of the figure. Arrows indicate displacements predicted by Chadi (1978). 

Reconstructed surfiices in a hoinopolar semiconductor. The geometry of the crystal before reconstruction was the same as in Fig. lO-l, but here the surface atoms have been allowed to relax. The positions for the corner atoms are not necessarily meaningful. Doubly occupied dangling hybrids are represented by double lines. The reconstruction on a real (OOT) surface is more likely a variation on the reconstruction shown here. One possibility is illicstrated in Fig. 10-8. 

The essential elTect of reconstruction is to split the dangling hybrid to the energies and Cj, both very far from the gap. Again, corrections can be made in the simplified theory, but we would not expect them to modify this result reconstruction should eliminate all dangling hybrid states from the gap by displacing them deep into the conduction and valence bands. 

We turn finally to added atoms from column 4, with the addition of a silicon atom to silicon being the most important case, since it will occur naturally from difl usion across the surface. We can expect the most stable position for an added atom outside (he surface to be above three surface atoms, ju.st as for columns 3 and 5. The additional atom bonds with three dangling hybrids, leaving a single dangling hybrid surrounded by an alternate in-out reconstruction. It would be reasonable to expect that such an added atom would have higher energy than those in the undisturbed iii-out reconstruction, and that thc.se added atoms would... 

Conslruci an energy-level diagram for ihc GaA.s surface, in analogy with iluu in Fig. 10-9 for silicon, indicating the cnergie.s of dangling hybrids before and after full reconstruction. 

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