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I have trouble understanding conductivity of a n-doped semiconductor in the band theory.

I know that donator atoms carry one excess electron that can enter the conduction band easily. If this happens, a fixed positive charge remains.

Assume that due to an applied voltage, the excess electrons in the conduction band are all removed from the semiconductor. How can the current continue to flow, how can new electrons enter the semiconductor or the conduction band?

Are the doping atoms "close enough" to each other so that excess electrons can move from doping atom to another?

I have less trouble understandung conductivity in a p-doped SC: an electron "fills up the missing bond", creating a fixed negative charge. Conduction occurs in the valence band by "passing the hole" from one Si atom to the next.

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  • $\begingroup$ There are two ways of looking at it. One: it's identical to the process you describe for SC. Why do you think it would be different? The other is that the extra electrons join the conduction band, and propagate (nearly) freely through the semiconductor in the same way current flow in a metal. $\endgroup$ – garyp Nov 14 '15 at 14:55
  • $\begingroup$ "it's identical to the process you describe for SC" do you mean p-doped SC? I don't think it's identical, because the Si-Atoms passing "holes" are "next to each other", as opposed to the donator atoms that are only ~1ppm. $\endgroup$ – Jasper Nov 14 '15 at 15:08
  • $\begingroup$ I'm not clear on the distinction. Anyway, a "hole" that starts on a dopant atom can be filled by and "electron" from a neighboring Si atom. Now the dopant has four bonds and and Si has three. $\endgroup$ – garyp Nov 14 '15 at 15:14
  • $\begingroup$ OK, but the common representation puts the dopant atom's electrons close to the conduction band. "How do the Si electrons from the valence band get enough energy to reach the hole at the dopant?" Is there a difference between a hole due to a missing charge or due to an incomplete bond? $\endgroup$ – Jasper Nov 14 '15 at 15:43
  • $\begingroup$ Electric forces are very large. It would take a huge voltage to remove an electron from 1 atom in a million. $\endgroup$ – mmesser314 Nov 14 '15 at 16:40
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If all the dopant electrons were removed from an n-doped material then the material would have a net positive charge. If an applied voltage removes some of the electrons from the material either new electrons will be attracted to the positive dopant ions from elsewhere in the circuit or, if there is not "rest of the circuit", you will have made a capacitor (the same as with any other conducting material).

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  • $\begingroup$ I see that the SC will become more and more positively charged if the dopant's electrons flow away. But to fill the holes, we need electrons with energy close to the conduction band, right? Where do we get electrons with this energy from? $\endgroup$ – Jasper Nov 14 '15 at 21:07
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    $\begingroup$ If the material starts to become significantly charged that will modify its band structure. In particular if the material is positively charged that will reduce the potential of the electrons, lowering the band structure until it is favourable for electrons to flow in. In practice this effect is not noticeable, because the strength of electrostatic forces means that (in the bulk) the SC is never significantly depleted. $\endgroup$ – By Symmetry Nov 14 '15 at 21:31

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