In an intrinsic semiconductor band gap is $1.2 \mathrm{eV}$ then ratio of number of charge carriers at $600…
In an intrinsic semiconductor band gap is $1.2 \mathrm{eV}$ then ratio of number of charge carriers at $600 \mathrm{~K}$ and $300 \mathrm{~K}$ is
$10^4$
$10^7$
$10^5$
$10^3$
Solution
The energy gap \(E_g=1.2 \mathrm{eV}\)
Now the relation in charge carrier and temperature is \(n_i=n_o \exp \left[-E_g / 2 K_B T\right]\) where \(K_B\) is Boltzmann constant and its value is \(8.62 \times 10^{-5} \mathrm{eV} / \mathrm{K}\)
So at the given temperature of 300 K the relation is
\(n_{i 1}=n_o \exp \left[-E_g / 2 K_B \times 300\right]\)
Similarly at the given temperature of 600 K the relation is
\(n_{i 2}=n_o \exp \left[-E_g / 2 K_B \times 600\right]\)
Now the ratio of the given two is
\(\begin{aligned}
& \frac{n_{i 2}}{n_{i 1}}=\frac{n_o \exp \left[-E_g / 2 K_B \times 600\right]}{n_o \exp \left[-E_g / 2 K_B \times 300\right]} \\
& =\exp \frac{E_g}{2 K_B}\left[\frac{1}{300}-\frac{1}{600}\right] \\
& =\exp [11.6] \\
& =1.09 \times 10^5 \\
& \approx 10^5
\end{aligned}\)