20. Electrical conduction of solids - band theory of solids, explanation of bands and band-gap. Difference between metals and semi-metals. Fermi level. (5p.)

Question 1

Band theory of solids

Answer 1

In a single isolated atom, the electrons in each orbit have definite energy associated with it. But in case of solids all the atoms are close to each other, so the neighboring atoms affect the energy levels of outermost orbit electrons. When two single or isolated atoms are brought close to each other, then the outermost orbit electrons of two atoms interact and are shared with each other. Due to this phenomenon, the energies of the electrons will not be in the same level, the energy levels change to a value, which is higher or lower than that of the original energy level of the electron.

The electrons in the same orbit exhibit different energy levels. The grouping of these different energy levels is called the energy band. However, the energy levels of inner orbit electrons are not affected by the presence of neighboring atoms.

Question 2

Bands/band-gap

Answer 2

There are three energy bands, which are the most important when it comes to understanding the behavior of solids: valence band, the conduction band and the energy gap/forbidden band. For electrical properties of solids, the most important is a degree of occupation of their conduction bands, and, if unoccupied, their energy distance from their valence bands.

Question 3

Difference between metals and semi-metals. Fermi level.

Answer 3

In conductors, i.e. in metals and semimetals, the conduction band is only partially filled (a metal) or it overlaps the valence band (semi-metal) so that the energy gap practically disappears. The electrons do not fall to the bottom of the valence band, because they are prevented from doing so by the exclusion principle. Instead, they fill the available levels up to some maximum level called the Fermi level 𝐸 ! , which is 3-8 eV above the bottom of the band. The electrons in this partially filled conduction band can respond to an electric field because there are many nearby occupied levels available.