Energy Bands

• When the isolated atoms are brought together to form the solid, electron wave functions begin to overlap.
• Many interactions take place, and, at proper interatomic spacing for the crystal, forces of attraction and repulsion find the balance.
• Because of Pauli Exclusion Principle, the discrete energy levels of the individual atoms split into bands belonging to pair instead of individual atoms.
• In a solid, because of the large number of atoms, the split energy levels for essentially continuous bands of energy.

Figure- Splitting  of  the individual  energy  levels  to  the energy  bands  as  atoms  are  brought  closer to each other.

• Imaginary formation of the diamond crystal from isolated carbon atoms 1s²2s²2p².
• Each of the atom has two 1s states, two 2s states, six 2p states, and higher states.
• For the N number of atoms, the states are 2N, 2N, and 6N of type 1s, 2s, and 2p respectively.
• With the reduction in interatomic spacing, these energy levels split into bands, and the 2s and 2p bands merge into the single band having 8N available states.
• Since the interatomic spacing approaches the equilibrium spacing of diamond crystal, this band gets splits into two bands separated by the energy gap E_g, here no allowed energy states for the electrons exist    forbidden gap.

• The upper band (known as conduction band) and the lower band (known as valence band) contain 4N states each.
• The lower 1s band is filled with the 2N electrons, but, the 4N electrons residing in the original n = 2 state will occupy states either in valence band or in conduction band.
• At temperature 0 K, the electrons will occupy lowest energy states available to them    thus, the 4N  states  in  valence  band  will  be  totally  filled,  and  4N  states  in  the conduction band will be completely empty.

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