In an intrinsic semiconductor, the energy gap Eg is 1.2eV. Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at 600K and that at 300K? Assume that the temperature dependence of intrinsic carrier concentration ni is given by

where n₀ is a constant.

Question

In an intrinsic semiconductor, the energy gap Eg is 1.2eV. Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at 600K and that at 300K? Assume that the temperature dependence of intrinsic carrier concentration ni is given by

where n₀ is a constant.

Philoid · Accepted Answer

Given,

Energy gap (E_g) = 1.2eV

The temperature dependence of intrinsic carrier concentration is given as

Where T is the temperature

E_g is the forbidden energy gap

K_B is the Boltzmann’s constant (8.62 × 10^-5 eV/K)

n_o is a constant.

At temperature T₁ = 600K,

……….(1)

At temperature T₂ = 300K,

…..(2)

Dividing eqn. (1) by eqn. (2), we get

⇒

So,

Hence, the ratio of conductivity at 600K to that at 300K is 1.09 × 10⁵.

NOTE: 1. E_g is the forbidden energy gap which is the energy gap between the valence band and conduction bands.

2. Intrinsic semiconductors are pure semiconductors with fewer conductivities. Trivalent and pentavalent impurities are added to intrinsic semiconductors to form p-type and n-type semiconductors respectively. This process is called doping.