6.18: Bandstructure of Bulk Semiconductors

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As stated above, most of the common semiconductors are constructed from \(sp^{3}\)-hybridized atoms assembled in the diamond crystal structure.

Unfortunately, \(sp^{3}\)-hybridization makes the bandstructure calculation much harder. In our earlier \(sp^{2}\)-hybridized examples, we were able to ignore all of the atomic orbitals involved in \(\sigma\) bonds, and we considered only the \(\pi\)-bonding electrons from the unhybridized p atomic orbital. Since \(sp^{3}\)-hybridized materials only contain \(\sigma\) bonds, we can no longer employ this approximation and our calculation must include all four \(sp^{3}\)-hybridized atomic orbitals. In fact, to obtain reasonable accuracy, bandstructure calculations usually include the next highest unfilled orbital also.

For a diamond structure, with a two atom unit cell, this means that we must consider 10 atomic orbitals per unit cell (one set of five per atom in the unit cell).

The calculation itself follows the procedures we described for graphene. But now we must solve a 10x10 matrix. We will draw the line here in this class.