Question

In a semiconductor, $2/3rd$ of the total current is carried by electrons and remaining $1/3rd$ 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

• A. $\frac{3}{2}$
• B. $\frac{2}{3}$
• C. $\frac{5}{3}$
• D. $\frac{3}{3}$
• E. $\frac{1}{3}$

Answer 1

The correct option is B $\frac{2}{3}$

Given, $I_e=\frac{2}{3}I$
$I_h=\frac{1}{3}I$ and $v_e=3v_h$
We know that,
Electron current, $I_e=n_{e}eA{v}_e....\left(i\right)$
Hole current, $I_h=n_{h}eA{v}_h....\left(ii\right)$
On dividing Eq. (i) and (ii), we get
$\frac{I_e}{I_h}=\frac{n_e{v}_e}{n_h{v}_h}$
$\Rightarrow \frac{n_e}{n_h}=\frac{I_e}{I_h}\times \frac{v_h}{v_e}=\frac{\frac{2}{3}I}{\frac{1}{3}I}\times \frac{v_h}{3v_h}$
$\Rightarrow \frac{n_e}{n_h}=\frac{2}{3}$.