Question

A pure silicon sample has intrinsic carrier concentration $n_i=1.5\times {10}^{10}c{m}^{-3}$ at room temperature (T = 300 K). The effective density of states in conduction band and in valence band i.e., $N_C=N_V=2.5\times {10}^{14}c{m}^{-3}$ Then the energy gap $\left(E_g\right)$ in the silicon sample is ___ev.
(Assume kT = 0.026eV)

• A. 0.505

Answer 1

The correct option is A 0.505
We know that, For pure silicon sample Intrinsic carrier concentration,
$n_i=\sqrt{N_C{N}_V}\times e^{-\frac{E_g}{2kT}}$

Given,
$n_i=1.5\times {10}^{10}c{m}^{-3}$
$N_C=N_V=2.5\times {10}^{10}c{m}^{-3}$
kT = 0.026 eV
$\therefore 1.5\times {10}^{10}=\sqrt{[2.5\times {10}^{14}{]}^2}\times e^{-\frac{Eg}{2\left(0.026\right)}}$
$\therefore E_g=0.505eV$.