Suppose you have an injection of holes into a semiconductor such that at some time you have this linear hole profile:
Because the diffusion current at any point is proportional to the slope of P at that point, the diffusion current is equal everywhere from 0 to L. I think this suggests that P(x) should not change over time, as long as this linear profile remains. But it seems to me that this completely linear profile can only exist for an instant since at x=L the charges need to end up somewhere, and if this is some block of P-type silicon of length L then the charges will start to stack up so that P(x) will increase from x=L back toward X=0. So then P(x) will gradually become flat, at which point there will be no more diffusion current. Is this correct?
I'm also wondering about the typical exponential carrier profile, as seen here for example:
Here since the slope of P(x) decreases as x increases, the current (pointing towards the right) decreases as x increases. So for some point x, \$ P(x) > P(x+ \Delta) \$, so at some instant in time more charge is entering some point from the left than is leaving it towards the right. This is generally explained by saying that the diffusing carriers are recombining as they go toward the right. However, like in the linear case, this particular form of P(x) is only valid at some instant, and as time goes on (toward the steady state), P(x) is becoming more flat, i.e. the holes are becoming evenly distributed and so will stop diffusing due to lack of gradient. Doesn't this mean that an alternative explanation of the decrease in current as you go to the right is that some holes are simply starting to build up in certain spots and so stop diffusing, thus leading to less current towards the right?