Formation of energy bands in solids

1. The solid crystals are formed when the isolated atoms are brought together. Various interactions occur between the neighboring atoms.
2. At a particular interatomic spacing d, there is a proper balance between forces of attraction to form a crystal. In this process, the changes occur in the electron energy level configurations.
3. In case of a single atom, there is a single energy for an electron orbit.
4. However, when two atoms are brought close to each other, it leads to intermixing of electrons in the valence shell.
5. As a result, the number of permissible energy levels is formed, which is called an energy band.
6. Three bands are important from the conductivity point of view, which are,
7. Valence band
8. Conduction band
9. Forbidden gap or band
10. The simple energy band diagram, showing these bands is shown in the figure

1. In the normal state, the electrons involved in the covalent bonds in the crystal occupy the valence band and the conduction band is empty. Hence the electrons in the outermost shell are called valence electrons and the outermost shell is called valence shell.
2. At higher temperature, these electrons acquire energy and move to the conduction band as electron is not allowed to occupy any energy state in forbidden gap. These electrons are called free electrons.
3. For any given type of material the forbidden energy gap may be large, small or nonexistent. The classification of materials as insulators, conductors and semiconductors is mainly dependent on the widths of the forbidden energy gap.

Classification on the basis of energy theory:

Based on the ability of various materials to conduct current, the materials are classified as conductors, insulators and the semiconductors.

Conductors

• A material having large number of free electrons can conduct very easily. For example, copper has 8.5x1028 free electrons per cubic meter which is a very large number. Hence copper is called good conductor.
• Intact, in the metals like copper, aluminum there is no forbidden gap between valence band and conduction band.
• The two bands overlap. Hence even at room temperature, a large number of electrons are available for conduction.
• So without any additional energy, such metals contain a large number of free electrons and hence called good conductors. An energy band diagram for a conductor is shown in the Figure (a).

Insulators

• An insulator has an energy band diagram as shown in the Figure (b).
• In case of such insulating material, there exists a large forbidden gap in between the conduction band and the valence band.
• Practically it is impossible for an electron to jump from the valence band to the conduction band.
• Hence such materials cannot conduct and called insulators.
• The forbidden gap is very wide, approximately of about 7 eV is present in insulators. For a diamond, which is an insulator, the forbidden gap is about 6 eV.
• Such materials may conduct only at very high temperatures or if they are subjected to high voltage. Such conduction is rare and is called breakdown of an insulator. The other insulating materials are glass, wood, mica, paper etc.

Semiconductors

• Semiconductors are neither insulators nor conductors. The forbidden gap in such materials is very narrow as shown in Figure (c). Such materials are called semiconductors.
• The forbidden gap is about 1 eV. For such materials, the energy provided by the heat at room temperature is sufficient to lift the electrons from the valence band to the conduction band.
• Therefore at room temperature, semiconductors are capable of conduction. But at 0 IC or absolute zero (-273 °C), all the electrons of semiconductor materials find themselves locked in the valence band.

• Hence at 0 IC, the semiconductor materials behave as perfect insulators. In case of semiconductors, forbidden gap energy depends on the temperature. For silicon and germanium, this energy is given by,

  $E_G = 1.21 - 3.6 \times 10^{-4} \times T \hspace{1cm} eV \text{(for Silicon)} $

  $E_G = 0.785 - 2.23 \times 10^{-4} \times T \hspace{1cm} eV \text{(for Germanium)} $

  where T = Absolute temperature in K