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The dopant atoms are part of the same system, and they are contributing electrons which are fermions. Thus it is obvious that these electrons should follow the Pauli's exclusion principle. However it turns out that all the electrons provided by the dopant atoms are present at a discrete energy level. According to me(Just a speculation), there should have been a separate band corresponding to the dopant atoms formed somewhere between the band gap of the crystal.

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  • $\begingroup$ You can combine two fermions to form a boson. Bosons can exists in single state. $\endgroup$ – Yashas Aug 10 '16 at 9:06
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The dopants form localised states just above the valence band or just below the conduction band depending on the dopant type. These are separate localised states with at most very limited interaction with each other. They are too widely separated to form anything resembling a band. There is no problem with the exclusion principle because the electrons from the dopants are not trying to populate the same state.

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    $\begingroup$ And when you add enough dopants, they form a degenerate band with some width. $\endgroup$ – Jon Custer Aug 10 '16 at 14:47
  • $\begingroup$ when we plot the energy band diagram, the diagram represents all the electrons within the crystal. Now the electrons corresponding to the dopants are part of the same entire system, i.e. the crystal. So, it only makes sense that the electrons corresponding to the dopant atoms, each have an unique and quantized energy state. Thus if I plot the band diagram at 0K, I should get almost continuous energy levels present somewhere around that discrete level of dopant electrons. So Pauli's principle, according to me, is not being followed. I'll be grateful if you can clear this doubt. $\endgroup$ – Ekdeep Singh Lubana Aug 10 '16 at 19:54
  • $\begingroup$ @EkdeepSinghLubana: at low levels of dopant the dopant states don't overlap and don't form a band. At high levels the dopant states will start to overlap at some point, and they will form a band just like the valence band only narrower. Since you're presumably happy that the valence band doesn't contradict Pauli's principle I don't understand why you think a dopant band would contradict the Pauli principle. $\endgroup$ – John Rennie Aug 11 '16 at 4:48

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