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The band structure describes the variation of the energy with the wave-vector . The valence bands contain the last filled energy levels at K, whereas the conduction bands are empty at K. The band gap separates the conduction band from the valence band. The band structure is usually visualized by plotting on symmetry lines, where denotes the band index. In Figure 3.6 the band structure of Si is plotted on the symmetry lines given in (3.27).
The band structure close to the conduction band edge can be approximated by ellipsoidal energy surfaces and a parabolic energy dispersion . In Si the conduction band edge is located near the zone boundary points along the symmetry lines. For the conduction band valley at the energy dispersion reads
Due to the point symmetry of the fcc lattice the six directions , ,, ,, and are equivalent. Consequently, there are six conduction band valleys. The constant energy surfaces of all six equivalent valleys along the principal axes are shown in Figure 3.7. Since electron transport in unstrained Si involves the electrons moving in all of the six valleys, it shows little anisotropy, even though there is strong anisotropy in each valley.
The valence band edge is located at the point, where the heavy hole (HH) and light hole (LH) band are degenerate. The split-off band (SO) is very close, since the split-off energy is only 44 meV in Si. For very small energies constant energy surfaces can be approximated by
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