Velocity - Electric Field Relations and Mobility of Charge Carriers

VELOCITY - ELECTRIC FIELD RELATIONS AND MOBILITY OF CHARGE CARRIERS

We know that in conductors the mobility is due to average velocity acquired by the electrons whereas in semiconductor the velocity it is due to the following reasons, viz.

• The rapid random motion of both electrons and holes due to thermal energy.         

• Additional velocity acquired by the charge carriers due to external electric field.

(i.e) v_d  ∞ E

V_d = μ_e E

Where μ_e is the mobility of the charge carriers.

In a perfect crystal the drift velocity continuously increases, whereas in a crystal with imperfections [such as missing atoms, vacancies, dislocations, interstitial atoms, substitutional atoms etc,] charge carriers are scattered, which in turn affects the drift velocity and hence the mobility of the charge carriers.

The two important causes for scattering in semiconductors are

(i) Lattice vibrations (phonons)

(ii) Ionised impurity atoms

If μ_L is the mobility due to scattering by lattice vibrations and μ_I is the mobility due to ionised impurities.

Then, Actual mobility (μ) is given by

 ......(1)

As mobility due to lattice vibrations, depends on temperature. We can write the relation between mobility and temperature as

.....(2)

Similarly the relation between mobility due to ionised impurities and temperature can be written as

1/ μ_I ∞ T^3/2

(or) 1/ μ_I = bT^3/2  .....(3)

Where 'a' and 'b' proportional constants.

Substituting eqns (2) and (3) in eqn (1) we can write the actual mobility as

Note: On Calculating the mobilites of a imperfect crystal, it is better to take relaxation time into consideration over the entire energy distribution.