Variation of Fermi Energy Level and Carrier Concentration with Temperature in an Intrinsic Semiconductor

VARIATION OF FERMI ENERGY LEVEL AND CARRIER CONCENTRATION WITH TEMPERATURE IN AN INTRINSIC SEMICONDUCTOR

For an intrinsic semiconductor number of electrons (i.e,) electron density will be the same as that of number of holes (i.e.,) hole density.

(i.e.,) n_e=n_h

Equating equations (7) and (12), we can write

Taking log on both sides we have

 ……..(13)

Equation (13) becomes

 ……..(14)

i.e., the Fermi energy level lies in the midway between E_c and E_v as shown

in Fig. 2.9 (since at 0 K, T=0).

But in actual case m*_h >m *_e and the Fermi energy level slightly increases with the increase in temperature as shown in Fig. 2.9.

Density of electrons and holes interms of E_g

In terms of energy gap (E_g) where E_g = E_c-E_v, we can get the expression of n_c and n_h by substituting the value of E_F in terms of E_c and E_v.

Substituting equation (13) in (7) we get

Since E_g = E_c-E_v, we can write

 ………(15)

Similarly by substituting equation (13) in (12) we get

 ………(16)

Thus, it is found that n_e = n_h = n_i where n_i is the intrinsic carrier concentration.

Results

• In an intrinsic semiconductor the density of electrons in conduction band is equal to the density of holes in valence band. (i.e.,) n_e = n_h

• n_e and n_h increases exponentially as the temperature increases.

Intrinsic Carrier Concentration

We know that, n_i = n_e = n_h  where n_i² =  n_e . n_h  

Substituting from equations (15) and (16), we have

 ………(17)