Question

The conductivity of an intrinsic semiconductor depends on temperature as σ = σ0 e−ΔE/2kT, where σ0 is a constant. Find the temperature at which the conductivity of an intrinsic germanium semiconductor will be double of its value at T = 300 K. Assume that the gap for germanium is 0.650 eV and remains constant as the temperature is increased.

Answer 1

Explanation:

At temperature T1, let the conductivity be σ1 and at temperature T, let the conductivity be σ2.

In the question, it is given that:

Gap, E = 0.650 eV and T1 = 300 KB

Now, as per the question,

σ = σ0e - ΔE2KT

σ2 = 2σ1

$\Rightarrow \sigma 0 e-\Delta E 2 \mathrm{kT}=2 \times \sigma 0 \mathrm{e}-\Delta E 2 \times \mathrm{k} \times \mathrm{T} 1$

$\Rightarrow \mathrm{e}-0.6502 \times 10-5 \times 8.62 \times \mathrm{T}=6.96561 \times 10-6$

On both the sides, taking natural log, we obtain

$-0.6502 \times 8.62 \times 10-5 \times \mathrm{T}=-11.874525$

⇒T = 317.51178, which is approximately 318K.