In a semiconductor, $\frac{2}{3} \mathrm{rd}$ of the total current is carried by electrons and remai

Question

In a semiconductor, $\frac{2}{3} \mathrm{rd}$ of the total current is carried by electrons and remaining $\frac{1}{3} \mathrm{rd}$ by the holes. If at this temperature, the drift velocity of electrons is 3 times that of holes, the ratio of number density of electrons to that of holes is

Professor PC Thomas Classes · Answer

(b) : If $I$ is the total current, then\ Current carried by electrons is $I_e=\frac{2}{3} I$ \ and that carried by holes is $I_h=\frac{1}{3} I$\ But $I_e=n_e e A v_e$ and $I_h=n_h e A v_h$ \ $ 	herefore \quad \frac{I_e}{I_h}=\frac{n_e e A v_e}{n_h e A v_h}=\frac{n_e v_e}{n_h v_h} \quad 	ext { or } \quad \frac{n_e}{n_h}=\frac{I_e}{I_h} \frac{v_h}{v_e} $ \  Here, $I_e=\frac{2}{3} I, I_h=\frac{1}{3} I, v_e=3 v_h$\ $ 	herefore \quad \frac{n_e}{n_h}=\frac{\left(\frac{2}{3} Iight)}{\left(\frac{1}{3} Iight)}\left(\frac{v_h}{3 v_h}ight)=\left(\frac{2}{1}ight)\left(\frac{1}{3}ight)=\frac{2}{3} $