The conductivity of an intrinsic semiconductor depends on temperature as σ = σ 0 e –ΔE/2kT , where σ 0 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.

Question

Philoid · Accepted Answer

Let T₁=300K and T₂=temperature at which the conductivity will be double of its value at T₁.

And let the conductivities at temperatures T₁ and T₂ be σ₁ and σ₂ respectively.

We are given,

Band gap, ΔE= 0.650 eV

2σ₁=σ₂

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Taking natural log both sides,

-11.874525

On solving, we get T₂=317.512K.