Key moments in the life of a MOSFET

Key moments for a MOSFET tend to occur as a function of z, distance from the oxide (in the semicondoctor), or V (applied gate voltage). They generally involve the relationship of the bands to $\mu$. Focusing on the phenomenology of the space-charge:
1) one obvious "key moment" is when the valence band has moved a few kT away from $\mu$ indicating the onset of depletion,
2) a second, less obvious "key moment", which generally occurs at a smaller value of z, is when the the electron concentration in the conduction band, n(z), becomes greater than $N_a$. At that point one is leaving the depletion regime, in which the space charge can be approximated as a constant ($-e N_a$), and entering a realm in which the space charge will be strongly (exponentially) dependent on z.

(Actually, n(x) always depends exponentially in $E_c (z)$, but that is "hidden" until the rubicon of "2)" is crossed as I understand it. )

(Comments welcome.)

PS. a third key moment might be when $E_c(z)$ crosses $\mu$, but we should probably focus on understand the first 2 before delving into that.