TABLE OF CONTENTS In essentially all semiconductors it is found that the top of the valence band is made from primarily p-type states. As a result unless spin effects are included in bandstructure calculations, the description of the valence band is inaccurate. The spin provides the electron with a means to interact with the magnetic field produced through its orbital motion. An electron in the p-state has an orbital angular momentum of h. Thus there is a strong interaction of the spin with the orbital motion of the electron. As noted above, the top of the valence bandedge states are primarily p-type. Thus the spin-orbit coupling has a strong effect there. While it is possible to calculate spin-orbit coupling in isolated atoms, it is difficult to do so in crystals. Thus, a general form of the interaction is assumed with a fitting parameter which is adjusted to experimentally observed effects. In most materials, the spin-orbit interaction is quite small and one adds its effect in a perturbative approach.
If we add the spin-orbit interaction energy to the previously discussed tight binding Hamiltonian, we have
| (2.42) |  |
The matrix elements arising from the spin-orbit component of the Hamiltonian can couple states of different spin. To calculate these terms, the spin-orbit interaction is written as
| (2.43) |  |
Here, L represents the operator for orbital angular momentum, S is the operator for spin angular momentum, and we can treat ? as a constant. The addition of the spin...
