Confusion about why pn junction discussion insensitive to doping variations faster than Debye length

Question

Sze (Physics of Semiconductor Devices, 3e) gives the following discussion which relates to how equilibrium electric fields/equilibrium potential build-up at thermal equilibrium are related to doping variations.

I am particularly puzzled by his claims below, which I have numbered:

(1) This implies that if the doping profile changes abruptly in a scale less than the Debye length, this variation has no effect and cannot be resolved, and (2) that if the depletion width is smaller than the Debye length, the analysis using the Poisson equation is no longer valid.

Why are (1) and (2) true? I've followed this standard derivation of a Poisson-Boltzmann equation, but why does it imply (1) and (2)? Is the point that in (29)'s penultimate step we've neglected \$\Delta N_D /N_D\$ for some reason related to differential equations provided \$\Delta N_D \neq 0\$ only over some short distance? This would seem to be relevant for (1). I'm not sure how it bears on (2) at all however.

Answer 1

"... When doping profiles exceed the Debye length, majority carriers no longer behave according to the distribution of the dopants. Instead, a measure of the profile of the doping gradients provides an "effective" profile that better matches the profile of the majority carrier density. "

https://en.wikipedia.org/wiki/Debye_length