We see that the current due to the majority carrier decreases near the junction as shown above, which means the majority carrier concentration should also decrease since the diffusion current is given by the derivative of the carrier concentration with respect to x.
But when we look at the carrier distribution, the majority carrier distribution increases instead of decreasing. What am I understanding wrong?
For Figure-1，it is an ideal diode assumption.
Simon M. Sze : Semiconductor Devices Physics and Technology 3rd Edition, Page-99 and P-100, the book says that
(a) the depletion region has abrupt boundaries and, outside the boundaries, the semiconductor is assumed to be neutral;
(b) the carrier densities at the boundaries are related by the electrostatic potential difference across the junction;
(c) the low-injection condition, that is, the injected minority carrier densities are small compared with the majority carrier densities (in other words, the majority carrier densities are changed negligibly at the boundaries of neutral regions by the applied bias);
(d) neither generation nor recombination current exists in the depletion region and the electron and hole currents are constant throughout the depletion region.
For Figure-2，it is a realistic diode model.
Solid State Electronic Devices,7th Global Edition,Ben G. Streetman and Sanjay K. Banerjee,2016,P-245: 5.6.2 Recombination and Generation in the Transition Region P-246 to P-247: (1)Electron capture,(2)Hole generation,(3)Hole capture,(4)Electron generation
I think this can be understood in 2 ways:
Just using equations:
We’re in stationary condition so we have constant Jid=Jn+Jp, considering the p region we know that Jn is a decreasing exponential, so we can just get Jp by subtracting Jn from Jid (but this really isn’t useful to understand what’s happening).
With a bit of intuition:
As you have probably figured out by now, majority carriers don’t move by diffusion, the concentration profile is incompatible.
We’re then forced to admit that majority carriers move by drift, and thus that a field exists. I’m honestly not quite sure about the origin of this field, I suppose it’s caused by the potential applied to the junction which doesn’t completely drop over the depletion region, but take this with a grain of salt, I’m just a student.
Also, as I understand it, this is what causes the majority carrier build up: we have quasi-neutral regions created by the injection of minority carriers, for example when electrons are injected in the p region some charge is exposed so we have a small field which in turn attracts holes that balance the exposed charge.
