Do carriers move across a p-n junction at 0 K?

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SUMMARY

At absolute zero (0 K), carriers in a p-n junction remain confined to their respective energy levels, with no free carriers available for recombination. The band diagram illustrates that electrons from the donor level cannot recombine with holes from the acceptor level due to spatial separation. While typically a depletion zone forms at higher temperatures due to ionization of acceptor and donor carriers, this phenomenon does not occur at 0 K. The discussion emphasizes the theoretical implications of carrier behavior as kinetic energy approaches zero, questioning the existence of a depletion zone under these conditions.

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Wrichik Basu
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Often a band diagram is used to explain what happens when two pieces of the same semiconductor, one p-doped, one n-doped, are put together. I am a little confused about it, so here is my question.

Initially and at ##0\mathrm{K}##, the surplus carriers should be confined to their respective acceptor and donor levels, e.g. the flatband diagram would look like follows:

HGBKU.png


Now, there are no free carriers in the system and thus, the electrons from the donor level should not be able to recombine with the holes from the acceptor levels due to spatial detachment.

Of course, provided some temperature, the acceptor and donor carriers would ionize and free carriers would be at disposal for recombination and thus, a depletion zone would form. But at ##0K## it seems to me that this should not happen. In reality, would a depletion zone be formed anyway somehow (are there other relevant physics taking action)?

Here, I'm considering the ideal case in which ##0K## exists. Let us not go into the discussion whether it practically exists or not.
 

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At 0 K you can't have this electron distribution. Some donor electrons at the border have to fill some of the holes until there is an equilibrium.
 
Ask instead how the behavior changes as the carrier kinetic energy approaches zero: what is the limiting case?
 

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