Energy band:

the energy band picture for

Ii an- type, and

Iii ap - type semiconductor

Indicate the position for, the donor and acceptor levels.

Sol.(a) Fermi level is defined as the energy state which has 50% probability of being filed by an electrons . Fermi level lies is in the centre of forbidden of gap for intrinsic semiconductor. Some important points related to Fermi level are as follows:

(1) Fermi level is a measurement of probability of occupancy of the allow the energy states by electrons.

(2) Fermi level the highest  energy7 level that are electrons can occupy at 0 k >

(3) Fermi level is the energy level at which at chances of electrons is 50%

(4) With increase in temperatures, few colorant bond break and electrons jump to condition band .therefore concentration of electrons in condition band width rise in temperature.

(5) (1) Fermi level n intrinsic semiconductor

(6) For an intrinsic semiconductor

(7) No of elections=no. of holds using equation  equations level shows that b Fermi level lies in centre of forbidden gap for intrinsic semiconductor band .

(8) (ii) in a  n type semiconductor , number of electrons = number of donor electrons , therefore Fermi level lies below conduction band (although it is below donor energy level  acceptor

(iii) For p type semiconductors holes = numbers of acceptor atoms

There for, Fermi level lies above valance band width increase in temperature a large number of electrons holes b pair are generated these thermally generated charges carriers must exceed charge carriers present due to doping. For example consider an n type semiconductor with 1000 do pated electrons and negligible holes Fermi level nib n Type extrinsic semiconductor

Consider donar type impurity is added to a crystal and all donor atoms are ionized at a given temperature. now the first states in conduction band will be filled states it become difficult for the valance band electrons to bridge the energy gap by the number of electrons hole pair thermally generated at the temperature is reduced . We know that Fermi level is a measure of probability of occupancy of the allowed energy states. Hence the Fermi level must move closer to the conduction band to indicate much energy state in a band arte filled by the donar electrons and fewer holes exits in valance band.