The number density of electrons and holes in pure silicon at 27 °C are equal and its value is 2.0 × 1016 m-3. On doping with indium the hole density increases to 4.5 × 1022 m-3, the electron density in doped silicon is

Question

The number density of electrons and holes in pure silicon at 27 °C are equal and its value is 2.0 × 1016 m-3. On doping with indium the hole density increases to 4.5 × 1022 m-3, the electron density in doped silicon is (A) 10 × 109 m-3 (B) 8 .89 × 109 m-3 (C) 11 × 109 m-3 (D) 16.78 × 109 m-3

Tardigrade Admin · Accepted Answer

Using, ne = ni2 Here, ni = 2× 1016 m-3, ρ = 4.5 × 1022 m-3 ∴ n = (ni2/ρ) = ((2× 1016)2/4.5 × 1022) = 8.89 × 109 m-3

Q. The number density of electrons and holes in pure silicon at $2 7^{\circ} C$ are equal and its value is $2.0 \times 1 0^{16} m^{- 3}$ . On doping with indium the hole density increases to $4.5 \times 1 0^{22} m^{- 3}$ , the electron density in doped silicon is

$10 \times 1 0^{9} m^{- 3}$

$8.89 \times 1 0^{9} m^{- 3}$

$11 \times 1 0^{9} m^{- 3}$

$16.78 \times 1 0^{9} m^{- 3}$

Using, $n_{e} = n_{i}^{2}$
Here, $n_{i} = 2 \times 1 0^{16} m^{- 3}$ ,
$ρ = 4.5 \times 1 0^{22} m^{- 3}$
$∴ n = \frac{n _{i}^{2}}{ρ}$
$= \frac{( 2 \times 1 0 ^{16} ) ^{2}}{4.5 \times 1 0 ^{22}}$
$= 8.89 \times 1 0^{9} m^{- 3}$

Q. The number density of electrons and holes in pure silicon at 27∘C are equal and its value is 2.0×1016m−3. On doping with indium the hole density increases to 4.5×1022m−3, the electron density in doped silicon is

10×109m−3

8.89×109m−3

11×109m−3

16.78×109m−3