Question

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?

Answer 1

As the pure germanium’s conductivity increases, the temperature also increases to 300 K from 4 K.

Explanation:

At temperature, the conductivity is given as T1 = σ1.

At temperature, the conductivity is shown as T2 = σ2.

It is given:

T1= 4 K

T2 = 300 K

The conductivity varies with regard to the band gap and the temperature of the material. This is shown as .

Therefore,$\sigma 2 \sigma 1=-\Delta E 2 / 2 \mathrm{kT} 2 \mathrm{e}+\mathrm{T} 2 \mathrm{T} 13 / 2 \mathrm{e}-\Delta \mathrm{E} 1 / 2 \mathrm{kT} 1$

$\Rightarrow \sigma 2 \sigma 1=10463$.