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Current flow in a PN junction is generally expressed in terms of the excess minority carrier concentrations in a PN junction, i.e. the excess holes on the N side and the excess electrons on the P side. As an aside, for example when discussing high-level injection, some texts will mention that when one applies a forward bias to a PN junction, actually the majority carrier concentration increases as well, and furthermore that excess holes on the P side ($p_p$) follow the same distribution in space as the excess electrons on the P side ($n_p$). The same situation is found on the N side. A diagram of all the excess carrier densities can be seen on page 10 of this lecture.

I haven't been able to find an explanation for why this happens other than an appeal to conservation of charge, that $\Delta p = \Delta n$. This would make sense to me e.g. in a photogeneration process where a new electron-hole pair are simultaneously created, but it's harder for me to understand here since the excess charge profiles are a result of an applied bias alone. That is, the very high equilibrium concentrations of free electrons/holes in the N/P regions respectively are because of doping, not light.

I understand that if the N side contains some total number of excess holes injected from the P side and the P side likewise contains a number of excess electrons from the N side, and that these numbers are not necessarily the same due to different doping on each side, that somehow charge neutrality must be maintained in the majority carrier numbers.

Specifically, why does it make sense that excess majority carriers follow the exact same distribution in space as the minority carriers on each side of the junction, as shown in slide 10 above? The excess minority carriers are injected there due to the barrier lowering of the forward bias, but what's bringing the majority carriers there?

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I'll read into notes and references (if I don't forget to do so) for the last last question and update the answer.

In short, holes are more so a mathematical tool rather than something. They are "the absence of an electron". With this in mind, if an electron migrates, there will be an electron missing, hence a hole. By changing the difference of potential, the excess move or the number changes at the same rate as the concentration. As your slides mention, in the quasi neutral zone, there is a conservation on charges, which is not always true in the depletion zone as charges move around a lot more. I hope it helps a bit in the meanwhile I check boots and my notes. Good question btw. Cheers

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Carrier transport across a PN junction is ambipolar due to the quasi-neutrality assumption. That is, excess electrons and holes are injected together as pairs across the junction to maintain charge neutrality. Obviously, since they are paired up any excess of electrons will result in an equal excess of holes and vice versa.

Inspection of the ambipolar transport coefficients yields that these excess electron-hole pairs under low-level injection diffuse and drift like holes in n-type material and like electrons in p-type material. This arrives at the same well-known derivations assuming individual electrons and holes transport.

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