# Diffusion current and carrier concentration equilibrium (unbiased)

## Summary:

Confused about the equilibrium conditions for carrier concentrations in semiconductors depending on how the semiconductor is doped, if at all
Suppose you have a non-uniformly doped piece of semiconductor (without an applied bias) such that the acceptor dopant concentration Na(x) decreases from left to right (as x increases). In this case, the equilibrium hole distribution p(x) will not be uniform since then there would be a net drift current due to the exposed space charge from the dopants. So instead equilibrium p(x) will vary such that diffusion is balanced by drift.

Now suppose you have an intrinsic piece of silicon without an applied bias. If you inject a lot of electrons at one end of it (without also injecting holes), at a time immediately after injection you have n(x=0) large and n(x) decreases as x increases. Say that it decreases exponentially as x increases, becoming zero at the opposite end of the semiconductor (x=L). In this case, what is the shape of the equilibrium carrier concentration? Does it become essentially uniform so that there is no diffusion current and very little drift, since there isn't a lot of recombination due to being intrinsic silicon?

Related to this, if this were a p-type material, then I think this would be similar to what happens at a p-n junction. I'm not sure it's necessarily identical because I'm not assuming that the electrons are being injected due to the presence of an n-type material adjacent to the p-type and so the holes in the p-type won't also be diffusing toward the left. So if this were an isolated (no adjacent n-type block) uniformly doped p-type block and somehow you had a bunch of electrons instantaneously injected at the x=0 end, for example at a concentration comparable to the acceptor doping level, is the equilibrium carrier distribution uniform, or do you still get a space charge region near x=0 due to recombination, so that you approximately have a depletion region around x=0 and then constant p(x) and n(x) to the right of it?

I hope these questions are clear. These aren't homework questions so I don't have given diagrams to accompany them, but if you need them I can make some to try to show what I'm asking. Thank you very much.