In MOS theory, the following steps will hapeen , whenever you just turn on it.
Before study about inversion layer, we have to know what is fermi potential:
" The Fermi level of a body is a thermodynamic quantity, and its significance is the thermodynamic work required to add one electron to the body".
Basically , inorder to form an inversion (otherwise in order to make the positive substrate in to negative, is called inversion) the potential which was present at the inteface of oxide and substrate should be the 2*fermipotential.
If that voltage is 1*fermipotential it is called weak inversion.
What causes inversion?
The main and important for inversion are minority electrons present in the P-substrate (in NMOS case). If you apply a small positive potential at the gate the minority electrons present in the substrate will attract to this, at the same time, the holes will repel by leaving negative ions. Because of this immobile negative ions the depletion region will form.
But the minority electrons are can't establish a strong a channel.
Then you try to inrease the gate positive potential, causes the Electron-Hole pairs which were present in the substrate will break and release the electrons, this happened when the surface or interface potentail reaches the 2*fermi potential of silicon. Now we have a plenty of electrons to make the surface make negative or too strong.
I hope the above info may help to you to understand inversion in MOS