When learning about the formation of the depletion region when n-type and p-type semiconductors are brought together, I note that many resources state that whilst electrons diffuse from the n-type material to the p-type material, holes also diffuse in the other direction.
The Feynman Lectures section 14-4 says this:
When the electrons in the n-type material arrive at the boundary they will not be reflected back as they would at a free surface, but are able to go right on into the p-type material. Some of the electrons of the n-type material will, therefore, tend to diffuse over into the p-type material where there are fewer electrons. This cannot go on forever because as we lose electrons from the n-side the net positive charge there increases until finally an electric voltage is built up which retards the diffusion of electrons into the p-side. In a similar way, the positive carriers of the p-type material can diffuse across the junction into the n-type material. When they do this they leave behind an excess of negative charge.
, and Wikipedia says this:
Electrons and holes diffuse into regions with lower concentrations of them, much as ink diffuses into water until it is uniformly distributed. By definition, the N-type semiconductor has an excess of free electrons (in the conduction band) compared to the P-type semiconductor, and the P-type has an excess of holes (in the valence band) compared to the N-type. Therefore, when N-doped and P-doped semiconductors are placed together to form a junction, free electrons in the N-side conduction band migrate (diffuse) into the P-side conduction band, and holes in the P-side valence band migrate into the N-side valence band.
This idea of holes and electrons both diffusing across the junction is also shown in this video, and is shown in the following image:
I am struggling to understand the idea of holes being able to move across the junction, however. My understanding is best shown by the HyperPhysics page on the PN junction, which says the following:
When a p-n junction is formed, some of the free electrons in the n-region diffuse across the junction and combine with holes to form negative ions. In so doing they leave behind positive ions at the donor impurity sites.
In my mind, the diffusion of electrons causes holes in the p-type region near the junction to be filled. Additionally, the departure of these electrons from the n-type region leaves a net positive charge behind - notably, however, despite this positive charge there should be no holes, as the donor atoms would retain a full outer shell. Thus, whilst this movement fills holes, it creates no holes in its place. This seems to put my interpretation (and seemingly HyperPhysics) at odds with the other mentioned resources.
I would like to look at the following quotes from the Feynman Lectures:
This cannot go on forever because as we lose electrons from the n-side the net positive charge there increases until finally an electric voltage is built up which retards the diffusion of electrons into the p-side
In a similar way, the positive carriers of the p-type material can diffuse across the junction into the n-type material
The first quote seems to be referencing the behaviour described by HyperPhysics. The second quote, however, seems to be mentioning the diffusion of holes as independent to the diffusion of electrons.
My initial interpretation of these materials had me considering that the description of "holes" was being applied to the n-type side despite each atom having a full outer shell, simply as a tool for describing the behaviour. This, however, seems incompatible with the following Wikipedia quote:
Following transfer, the diffused electrons come into contact with holes and are eliminated by recombination in the P-side. Likewise, the diffused holes are recombined with free electrons so eliminated in the N-side.
So, what is it? Is the diffusion of electrons causing a net positive charge on the n-type side of the depletion region, or are holes diffusing independently across, or somehow both? If holes are indeed diffusing across, how do they manage to get past the diffusing electrons without being filled?