Question

A pure semiconductor like \[\ce{Ge}\] or \[\ce{Si}\], when doped with a small amount of suitable impurity, becomes an extrinsic semiconductor. In thermal equilibrium, the electron and hole concentration in it are related to the concentration of intrinsic charge carriers. A p-type or n-type semiconductor can be converted into a p-n junction by doping it with suitable impurity. Two processes, diffusion and drift take place during formation of a p-n junction. A semiconductor diode is basically a p-n junction with metallic contacts provided at the ends for the application of an external voltage. A p-n junction diode allows currents to pass only in one direction when it is forward biased. Due to this property, a diode is widely used to rectify alternating voltages, in half-wave or full wave configuration.

At a given temperature, the number of intrinsic charge carriers in a semiconductor is 2.0 × 10¹⁰ cm⁻³. It is doped with pentavalent impurity atoms. As a result, the number of holes in it becomes 8 × 10³ cm⁻³. The number of electrons in the semiconductor is ______.

पर्याय

• 2 × 10²⁴ m⁻³

• 4 × 10²³ m⁻³

• 1 × 10²² m⁻³

• 5 × 10²² m⁻³

Answer 1

At a given temperature, the number of intrinsic charge carriers in a semiconductor is 2.0 × 10¹⁰ cm⁻³. It is doped with pentavalent impurity atoms. As a result, the number of holes in it becomes 8 × 10³ cm⁻³. The number of electrons in the semiconductor is 5 × 10²² m⁻³.

Explanation:

`n_i^2 = n_en_h`

⇒ 4 × 10²⁰ = n_e × 8 × 10³

`n_e = (4 xx 10^20)/(8 xx 10^3) = 0.5 xx 10^17 cm^-3`

= 0.5 × 10¹⁷ × (10⁻² m)⁻³

= 0.5 × 10¹⁷ × 10⁶ m⁻³

= 0.5 × 10²³ m⁻³

= 5 × 10²² m⁻³