The conductivity of a pure semiconductor is roughly proportional to T^3/2 e^–ΔE/2kT where ΔE is the band gap. The band gap for germanium is 0.74 eV at 4 K and 0.67 eV at 300 K. By what factor does the conductivity of pure germanium increase as the temperature is raised from 4 K to 300 K.

Question

Philoid · Accepted Answer

Given:

At temperature 4K, E₁= 0.74

At temperature 300K, E₂=0.67

The conductivity is proportional to T^3/2 e^–ΔE/2kT,

Let conductivity at 4K be =σ₁

and at 300k be = σ₂

∴

∴ conductivity increases by the factor of

The conductivity of a pure semiconductor is roughly proportional to T3/2 e–ΔE/2kT where ΔE is the band gap. The band gap for germanium is 0.74 eV at 4 K and 0.67 eV at 300 K. By what factor does the conductivity of pure germanium increase as the temperature is raised from 4 K to 300 K.