Question

Explain the mobility of a charge carrier and obtain the formula for the conductivity of a semiconductor.

Answer 1

Explanation:

hope this helps you child

Answer 2

Mobility of a charge carrier:

The charge carrier defines the particle which carries charge. In most of the metals, the charge carrier is electrons.

The mobility is defined as the drift velocity of the particle per unit electric field. The mobility defines the speed of the charge carrier which depends on the conductivity of the conductor.

Formula for conductivity of a semiconductor:

Length of the semiconductor = l

Number of electrons = $\bold{n_e}$

Number of holes = $\bold{n_h}$

Drift velocity of electrons = $\bold{v_e}$

Drift velocity of holes = $\bold{v_h}$

Current carried by electrons = $\bold{i_e}$

Current carried by holes = $\bold{i_h}$

Now, the current passing through the conductor is:

$\bold{i=i_e+i_h}$

The current is given by the formula:

$\bold{I=nAV_d}$

Now,

$\bold{i=n_eeAV_e+n_heAV_h}$

$\bold{i=eA[n_eV_e+n_hV_h]}$

$\bold{\frac{i}{A}=e[n_eV_e+n_hV_h]\longrightarrow(1)}$

The resistivity of the conductor is given as:

$\bold{R=\frac{\rho I}{A}}$

$\bold{\rho=\frac{RA}{I}}$

We know, that V=IR, now,

$\bold{\frac{E}{\rho}=\frac{V/i}{\rho}}$

$\bold{\frac{E}{\rho}=\frac{(V/i)i}{\rho}}$

$\bold{\frac{E}{\rho}=\frac{V}{RA}}$

Where, I=V/R

$\bold{\frac{E}{\rho}=\frac{i}{A}\longrightarrow(2)}$

On equation equation (1) and (2), we get,

$\bold{\frac{E}{\rho}=e[n_eV_e+n_hV_h]}}$

$\bold{\frac{1}{\rho}=\frac{e}{E}[n_eV_e+n_hV_h]}}$

The conductivity is reciprocal of resistivity.

$\bold{\sigma =\frac{e}{E}[n_eV_e+n_hV_h]}}$

Where σ is conductivity.