The number of occupied conduction band levels in intrinsic semiconductor is

(A) N_c exp \(\rm\left(−\frac{E_C−E_F}{k T}\right)\)

(B) \(\rm\displaystyle\int_{E_C}^{E_{\text {top }}}\) N(E)F(E)dE

(C) N_c exp \(\rm\left(\frac{E_F−E_C}{kT}\right)\)

(D) \(\rm\displaystyle\int_{E_F}^{E_{\text {top }}}\) exp (N(E))dE

Choose the correct answer from the options given below:

The given expression:

\(\mathop \smallint \limits_{{E_c}}^\infty N\left( E \right)f\left( E \right)dE\)

N(E) gives the distribution of allowed states for electrons over energy.

f(E) gives the fraction of the total allowed states being occupied by an electron.

\(∴ \mathop \smallint \limits_{{E_c}}^{E_T} N\left( E \right)f\left( E \right)dE\) gives the concentration of electrons from energy Ec to ET.

Where Ec denotes the bottom of the conduction band and ET denotes the top of the conduction band.

For simplicity, we can replace ET with infinity.

The number of electrons in the conduction band is \({n_o} = {N_C}.\exp \left( { - \frac{{{E_C} - {E_F}}}{{KT}}} \right)\)