Variation of Carrier Concentration with Temperature

VARIATION OF CARRIER CONCENTRATION WITH TEMPERATURE

The carrier concentration (n_e and n_h) in n-type semiconductor varies with the increase in the temperature.

Electron concentration

At very low temperature (i.e.,) at  0 K, 1/T is high, the Fermi level will lie exactly in the middle between E and Ea and the carrier concentration is at the most zero in the conduction band and hence point A is obtained in the graph. Fig. 2.21.

Now when the temperature is slowly increased, the donor atom gets ionised and the electrons move towards conduction band. Hence the carrier concentration increases slowly in the conduction band for electrons Fig. 2.21. Since this range is obtained due to impurity atoms, it is called impurity range shown by curve AB in Fig. 2.21.

When the temperature is further increased to reach upto say room temperature, all the donor atoms are ionised and hence the carrier concentration (n_e) increases in the conduction band and reaches to a steady state. Since this range is obtained due to exhaustion of donar atoms it is called exhaustion range, shown by curve BC in Fig. 2.21.

When the temperature is still further increased, due to thermal ionisation, the electrons from the valence band  is lifted up to go to the conduction band and hence there is an increase in the carrier concentration (n_e).

In this case since the number of available electrons in donor energy level, is almost exhausted, many number of electrons are shifted from valence band to conduction band and thus the carrier concentration increases rapidly, tracing the curve CD (Fig. 2.21). Since the material practically becomes intrinsic in this range, this range is known as intrinsic range.

Note: In practical devices the material will be operated on impurity or exhaustion range so that the properties of the impurity atoms can be utilised completely.

Hole Concentration

At 0 K electrons concentration is zero in conduction band. Now, when temperature is increased slowly the electrons will move from the donor energy level to conduction band. Now, when temperature is very high the electrons are transferred from valence band to conduction band and holes are created in valence band. The electron concentration in conduction band equalises the hole concentration in valence band. Therefore electron concentration curve and hole concentration curve overlaps only in the intrinsic region.

Conductivity of Extrinsic Semiconductor

The variation in the conductivity of an extrinsic semiconductor, with the increase in temperature is as shown in Fig. 2.22.

When the temperature is slowly increased from 0 K impurity atoms are slowly ionised and goes to conduction band and hence conductivity increases.

When all the impurities are ionised the mobility of charge carriers decreases slightly and therefore log σ becomes constant (or) may slightly decreases.

At high temperature the carrier density increases enormously due to thermal agitation and hence conductivity increases enormously.