The tight-binding approach to the problem ofthe electronic energy levels in solids is intuitively very charming.
Atight-binding method using a few interaction parameters describes precise resultsfor the valence bands of the diamond and zincblende crystals. The tight-bindingmethod is equivalent to that of Slater and Koster. These consist phononfrequencies at high-symmetry points, bulk point defects such as vacancies andinterstitials, and surface reconstructions. The TB parametrization rehabilitatesexperimental measurements and ab initio calculations well, indicating that it defindedfaithfully the underlying physics of bonding in silicon.
We used this model tothe investigate of finite temperature vibrational properties of crystallinesilicon and the electronic structure of amorphous systems that are too large tobe practically simulated with ab initio methods. To address the topic ofimproving the diamond lattice band structure we can present an electronicstructure calculation using the sp3d5 parametrization. Wedevelop our analysis of the sp3 parameters to include phonon spectraat several high-symmetry points. All of the structures have higher energy thanthe diamond structure, including some low-energy, rarely examined theoreticalphases such as hexagonal diamond and the clathrate structures. we calculated amodel that accurately reproduces both the valence and conduction bands ofsilicon in the diamond structure, at the price of deterioration in the accuracyof the energetics.The diamond structure has the same as the zinc-blendestructure except that the two atoms in the primitive unit cell are identical.
Foreach tight-binding basis function centered on these atoms, two Bloch functionscan be created. However, for a tight-binding basis function b(r) that the twoBloch functions exist. In the diamond structure crystals we can set bo(r)=b1(r),but in the zincblende crystals the two functions are different. We describedthis statement with an example drawn from the vibrational modes of zinc-blendeand diamond crystals.
By using the matrix-element theorem, very generalselection rules for optical transitions calculated in zinc-blende-type anddiamond-type crystals. The symmetry of the wave functions in the diamondstructure along the 001 directions have quite different from those ofzinc-blende. These are in good agreement with other calculations when allnearest- and one second-nearest-neighbor interactions are included which theeffects of the various interactions on the density of states exsit.