Energy Levels of Confined Electrons

Most semiconductors used in electronic and photonic devices are group IV elements or compoimds formed by III-V or II-VI elements. They are characterized by an sp hybrid bond in which an s-electron is promoted to a p-state in order to form a tetrahedral directed diamond-like bond. The four valence electrons occupy the bonding states from which the antibonding states, which form the conduction band, are separated by the energy gap Eg. 

The width of the energy gap decreases as the lattice parameter increases, or as the atoms become larger and farther apart. Thus, diamond has the highest bandgap energy and the bandgap decreases with Si, Ge, and disappears with Sn and Pb, which are metals. The compound systems follow the same trend. 

Even though the valence electrons are tied up in covalent bonds, they are not completely localized and have similar band structure and dispersion relationships (E vs. k) as nearly free electrons. Thus the band structure becomes a powerful tool for understanding the properties and behavior of semiconductors. 

When an electron is promoted to the conduction band, it leaves a hole in the valence band, which frees up states in the valence band so that the valence electrons can also respond to an electrical field. The hole in the valence band can be treated as a particle with positive mass and positive charge, while the electron in the conduction band behaves as a particle with positive mass and negative charge. Thus in response to an applied electrical field, electrons carry the charge in one direction while holes carry the opposite charge in the opposite direction and both contribute to the conduction of current. 

In direct bandgap materials, electrons may go directly from the conduction band to the valence band with a photon emission, which makes them suitable as LEDs or solid-state lasers. Indirect transitions from the conduction to the valence band must be accompanied by the emission of a phonon and are nonradiative transitions, which results in heating the material. 

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