This is Fermi-Dirac distribution for semi-conductors and from (a) to (d) represe

Question

This is Fermi-Dirac distribution for semi-conductors and from (a) to (d) represents the involvement of thermal energy.

However I do not understand the difference between (c) and (d) where Ec(conduction energy level) and Ev(valence energy level).

Why suddenly gap energy shows up in (d) and not in (a) to (c).

Please explain in terms of electrons and energy levels of Ef, Ec, and Ev.

Thank you !

p.s.

I wasn't too sure about those red dots in the graphs.

They are electrons, right?

0.5 1 f(E) 0 0.5 1 f(E) 0 0.5 1 f(E) 0 1 f(E) Figure 6.6: The Fermi-Dirac distribution function. (a) For T 0 K, all allowed states bellow the Fermi level are occupied by two electrons. (b, c) At T>0 K not all states below the Fermi level are occupied and there are some states above the Fermi level that are occupied. (d) In an energy gap between bands no electrons are present.

Explanation / Answer

Yes , the red balls are electrons. and the place where there is vacancy of electron in valance band is called as hole.

In d , we can see that electrons have reached the conduction already and Ec is the minimum energy that required to go the conduction band.

one must supply the energy diffrece of Ec-Ev to make the electons to move into the conduction band.

If the energy of electrons whose energy is greater than Ev but less than Ec will be immoble and again fall into valance band after some time.

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