In an atom, the electrons revolve around the nucleus in almost circular orbits (Bohr’s model). Energy of electrons in each subshell is definite. These definite energy values are called energy levels of the atoms. But in crystals, atoms are arranged in a regular and periodic manner. A solid crystal contains about 1023 atoms/cm3. So each atom is in the electrostatic field of neighbouring atoms and due to interaction between the atom, the modification of energy level takes place. The maximum effect of the interaction is on the valence electron and the energy E between E + ∆E. Thus each energy level becomes broad. This broadening of energy level is called energy band. The electrons in the inner shell are strongly bound to the nuclei, so they are slightly affected by the presence of neighbouring atoms. They are called core levels. If an energy bond consists of as much electrons as permitted by Pauli’s Exclusion Principle, then it is said to be completely filled band, and in such a band there will be no free electrons for conduction of electricity, while for a partially filled band conduction is possible.
In order to understand how the modification of energy level takes place, let us consider a single crystal of Si having N atoms. The electronic configuration of Si is 1s2, 2s2, 2p6, 3s2, 3p2. The energy levels of Si atom in isolated state as well as in the crystal form are shown in Fig. Here the interatomic spacing is r and distance ‘a’ corresponds to the crystal lattice spacing. The process of splitting is summarised as follows:
1. When r > c.
The atomic spacing is sufficiently wide, so the interaction between atoms is negligible and practically, here is no modification of 3s and 3p energy sublevels.
2. When r = c.
When atoms are brought further close to each other, their interaction increases and the real splitting of the sublevels starts. The energy difference between 3s and 3p sublevels is denoted by double arrow and is called forbidden gap.
3. When r < c.
The forbidden gap decreases and reduces to zero at r = b2. So at r = b2 the two bands overlap. At a distance between b2 and c instead of single 3s or 3p level, we get a large number of closely packed levels. The number N is very large so this collection of closely spaced levels is called an energy band.
4. When b1 < r < b2.
When the atomic spacing is further reduced, the 3s and 3p levels remain merged into each other and thus there is no restriction on the electrons to move from 3s sublevels to 3p sublevel or vice versa. The energy gap between 3s and 3p disappears, and the two band overlap. In this situation all 8N levels (2 from s and 6 from p) are now continuously distributed. Here we cannot distinguish between the electrons belonging to 3s and 3p sublevels. At such a situation one can only say that 4N sublevels are filled and 4N sublevels are empty.
5. When r = a.
This is known as equilibrium distance because the atoms in crystal lie at this interatomic separation. Here is the band divide and spread widely Here we find that band of filled energy level and empty energy level are separated by an energy gap called forbidden gap or forbidden band. The lower band which is completely filled up is known as valence band and the upper band which is normally (at 0 K) empty, is referred to as the conduction band.
The gap between valence band and conduction band is called fobidden band and it is a measure of energy E. Thus E is the amount of energy that should be given to the electron in valence band, so that it could jump to the conduction band. For insulator it is of the order of 5 to 10 eV, and for semiconductor like Ge is about 0.72 eV and for Si it is about 1 eV.
