In MOSFET at strong inversion electrons confined to triangular quantum well, electrons occupy only 1 or 2 lowest subbands.
And the Van Dort model gives the quantum mechanical intrinsic carrier density in inversion channel via increased energy band-gap(ΔE).
N_QM = N_CL× Exp^(-ΔE/2kt) this carrier amount is very high.
But density of states for inversion charges in subbads reduced from the higher 3-D density to the lower 2-D density.

Then still HOW the above Van Dort's formula giving that high amount of charge..