JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Semiconductors

In a semiconductor, the number density of intrinsic charge carriers at

2 7^{\circ} C

1.5 \times 1 0^{16} / m^{3}

. If the semiconductor is doped with impurity atom, the hole density increases to

4.5 \times 1 0^{22} / m^{3}

. The electron density in the doped semiconductor is _____

\times 1 0^{9} / m^{3}

Answer: 5

Solution

At a fixed temperature the carrier densities obey the law of mass action,

n_{e} n_{h} = n_{i}^{2}

. Doping changes the individual densities but leaves this product untouched, so

n_{e} = \frac{n _{i}^{2}}{n _{h}} = \frac{( 1.5 \times 1 0 ^{16} ) ^{2}}{4.5 \times 1 0 ^{22}} = \frac{2.25 \times 1 0 ^{32}}{4.5 \times 1 0 ^{22}} = 5 \times 1 0^{9} m^{- 3}

The electron density in the doped semiconductor is

5 \times 1 0^{9}

per cubic metre.

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Integer answer