The contributions in the total current flowing through a semiconductor due to electrons and holes are 4 3 and 4 1 respectively. If the drift velocity of electrons is 2 5 times that of holes at t

Question

The contributions in the total current flowing through a semiconductor due to electrons and holes are 4 3 ​ and 4 1 ​ respectively. If the drift velocity of electrons is 2 5 ​ times that of holes at this temperature, then the ratio of the concentrations of electrons and holes is-

TestHub · Accepted Answer

The relation for current contribution is

$I \propto q n v_{d} .$

The electron and hole contributions to the total current are

$I_{n} = \frac{3}{4}, I_{p} = \frac{1}{4},$

which gives

$\frac{I _{n}}{I _{p}} = \frac{3/4}{1/4} = 3.$

Since the current is proportional to the product of concentration and drift velocity,

$\frac{I _{n}}{I _{p}} = \frac{n v _{n}}{p v _{p}} .$

The drift velocities are related by

$v_{n} = \frac{5}{2} v_{p} .$

Using this relation in the current ratio,

$3 = \frac{n ( \frac{5}{2} v _{p} )}{p v _{p}} .$

After canceling

$3 = \frac{5}{2} \cdot \frac{n}{p} .$

Thus,

$\frac{n}{p} = 3 \cdot \frac{2}{5} = \frac{6}{5} .$

$\frac{n}{p} = \frac{6}{5}$

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