Question

For a semiconductor on increasing the temprature the resistivity of semiconductor
1. Increase
2. Decrease
3. Remain same
4. May increase or decrease

Answer 1

Correct Answer - Option 2 : Decrease

CONCEPT:

Temperature dependency of Resistivity:

• The resistivity of semiconductor within a limited range of temperature is given by the following equation:

\(⇒ρ (T) = ρ _{0} e^{\frac{E_{g}}{K_{B}T}}\)

Here, ρ(T) = resistivity at a temperature T, ρ₀ = resistivity at a reference temperature T₀, E_g = energy gap between conduction and valence band, K_B = Boltzmann constant

• The energy gap between the conduction band and valence band is more therefore at very low temperatures the conduction band of semiconductors is almost empty, i.e it has no charge carriers and hence resistivity is high, but as the temperature increases more and more electrons jump to the conduction band and the resistivity decreases on account of a high number of charge carriers.

EXPLAINATION:

• As we discussed the dependency of Resistivity in semiconductors was due to the energy gap between the conduction band and valence band.
• Also from the above equation, it can be easily said that on increasing the temperature the resistivity of semiconductor decreases, and vice versa is true.
• Hence, the correct option is (2).