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Carrier concentration decreasing with increase in temperature in a semiconductor

Electrical Engineering Asked on November 6, 2021

I have come across this equation in my semiconductor study $$
n_{0}=n_{i} exp left(frac{E_{F}-E_{i}}{K{T}}right)
$$
where$$n_i$$ is the intrinsic electron concentration . This equation gives us the electron concentration as a function of temperature.
But this equation suggests that as we increase the temperature, the conduction electron density decreases which is contrary to the fact that as we increase the temperature more and more electrons jump into the conduction band and hence increase in carrier concentration.
Where am I going wrong,please help.
Thank you in advance.

One Answer

you are forgetting that n_i depends on T as well, you can find it's formula by googling it easly, also remember that this equation is approximation for when E_f close enough to E_i (and then you can drop the 1 at the denominator of the fermi functionn)

Answered by Ran Greidi on November 6, 2021

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