Semiconductor diffusion current over time
Illuminating a surface of a piece of semiconductor creates both electrons and holes. Left as they are, these excessive charge carriers will recombine in the bulk of semiconductor. In this scenario, the excessive charge carrier distribution is obeyed to diffusion-type PDE with recombination terms.
To separate holes from electrons, you need to extract light-generated electrons from the bulk by external electric field. Or, alternatively, even without light, with external electric field you can extract heat-generated mobile electrons and have excessive holes that will not only diffuse into the bulk, but also drift into the same direction as they also feel the external electric field. Evidently, the scenario with external electric field is not what you are considering in your question.
You can also inject holes into your piece of semiconductor through a contact with another piece of a semiconductor highly doped with electron acceptors (p-type extrinsic semiconductor). This asymmetric doping configuration results in a p+n junction with depletion region extending mostly in a lightly doped side, that is, into your piece of an admittedly lightly doped n-type semiconductor. In this case, the charge carrier distribution starts with low concentration of holes in the depletion region. Outside a space charge region (depletion zone) and into a quasi neutral region of your lightly doped n-type semiconductor, a hole concentration exponentially approaches the equilibrium hole concentration of a semiconductor under consideration.
Depletion region width in your piece of semiconductor
$$
x_{n0} = \sqrt{2\epsilon_s{\phi_B}\over{qN_d}}
$$
ϵs is the permetivity of semiconductor, q is the elementary charge, ϕB is the built-in potential, Nd is the donor concentration.
Injected hole concentration at x &gt; xn0
$$
{\delta}p_n(x) = p_{n0}*(exp({qV\over{kT}}) - 1)*exp({-(x-x_{n0})\over{L_p}})
$$
Lp is the diffusion length.
This is also unlike any of your graphs.
In all the considered scenarios, even in transient processes, there are no holes that &quot;build up in certain spots and stop diffusing&quot;. The hole's fate is either to tend to equilibrium concentration or to recombine. I suppose you are overthinking the situation.