Electric Conductivity - Practice Questions & MCQ

 Electrical Conductivity (σ)-

The semiconductor conducts electricity with the help of these two types of electricity or charge carriers (i.e electrons and holes).

These holes and electrons move in the opposite direction. The electrons always tend to move in opposite direction to the applied electric field.

Let the mobility of the hole in the crystal is μ_h and the mobility of electron in the same crystal is μ_e

The current density due to drift of holes is given by,

$
J_h=e n_h v_h=e n_h \mu_h E
$

And The current density due to the drift of electrons is given by,

$
J_e=\mathrm{en}_{\mathrm{e}} \mathrm{v}_e=\mathrm{en}_{\mathrm{e}} \mu_e E
$

hence resultant current density would be

$
\begin{aligned}
& J=J_h+J_e=e n_h v_h+e n_e v_e=e n_h \mu_h E+e n_e \mu_e E=\left(n_h \mu_h+n_e \mu_e\right) e E \\
& \text { and } J=\sigma E
\end{aligned}
$

So, the general equation for conductivity is given as

$
\sigma=e\left(n_e \mu_e+n_h \mu_h\right)
$

where
$n_e=$ electron density
$n_h=$ hole density
$\mu_e=$ mobility of electron
$\mu_h=$ mobility of holes
For intrinsic semiconductors (no impurities)-
As the number of electrons will be equal to the number of holes.
i.e $n_e=n_h=n_i$

$
\sigma=n_i e\left(\mu_e+\mu_h\right)
$