GATE 2023 EC – Question 61
In a semiconductor device, the Fermi-energy level is 0.35 eV above the valence band energy. The effective density of states in the valence band is $1\times10^{19}$ cm$^{-3}$. The thermal equilibrium hole concentration in silicon at 400 K is ________ $\times10^{13}$ cm$^{-3}$ (rounded off to two decimal places).
Given $kT$ at 300 K is 0.026 eV.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 63.17 to 63.81
Explanation
$p=N_v\,e^{-(E_F-E_v)/kT}$ with $N_v\propto T^{3/2}$. At 400 K: $kT=0.026\times\frac{400}{300}=0.034667$ eV and $N_v=10^{19}\left(\frac43\right)^{3/2}=1.5396\times10^{19}$ cm$^{-3}$. $p=1.5396\times10^{19}\,e^{-0.35/0.034667}=1.5396\times10^{19}\times4.124\times10^{-5}=6.35\times10^{14}$ cm$^{-3}$ $=63.49\times10^{13}$ cm$^{-3}$ (taking $E_F-E_v$ as fixed).