Mobility and Electrical Conductivity of Intrinsic Semiconductors

MOBILITY AND ELECTRICAL CONDUCTIVITY OF INTRINSIC SEMICONDUCTORS

The electrical conductivity (σ) of an intrinsic semiconductor in terms of mobility of charge carriers is given by

σ_i =n_i e (μ_e+μ_h) ……..(1)

Where, n_i→ intrinsic carrier concentration

e → charge of the electron

μ_e→ mobility of electrons

μ_h → mobility of holes.

Note: Mobility of electrons or holes is defined as the velocity gained by an electron or hole under unit potential gradient.

Substituting the value of n_i from equation (17) in equation (1) we have

Here the electrical conductivity depends on the exponential of forbidden energy gap between valence band and conduction band and on the mobility of charge carriers, both μ_e and μ_h. But the term (μ_e + μ_h.) has a temperature dependence and it will cancel with the T^3/2 term and hence we can write

 ………(2)

where C is a constant.

Taking log on both sides we have

log  σ_i = log C – (E_g/2K_BT)

If a plot is made between log σ_i and 1/T we get a straight line here σ_i increases with temperature. as shown in Fig. 2.10.