Dear Amit,

The inversion layer is not abrupt, but you can however estimate its thickness (t) by different methods. For instance: if you've an NMOSFET, with substrate concentration (Nb) and qn inversion layer with surface density (Ns), use the relation: t = Ns/Nb at the onset of inversion (where the volume density of electrons in the inversion layer is equal to the background p-type substrate). For deep inversion, you'd use a correcting factor (about 1/2). Needless to say, this is easy to write in a plot (Tony plot) command.

Dear Amit Das ,Adding to the colleagues above the inversion charge is distributed across the inversion layer with its highest concentration at the surface. Assuming the bulk is p-type with a a hole concentration p0 and minority electron concentration n0. So because of the inversion as a consequence of the influence of the electric field resulting form the applied voltage at the gate the surface region becomes an n-type at sufficient gate voltage. Then the type of the material conduction will become n-type. Between the two types there will be an intrinsic type material with p=n=ni. This is the boundary between the p-type and n-type material and therefore it bounds the inversion layer from the side of the substrate. The other boundary is the surface of the substrate which is interfaced to above oxide layer.

You can the get the thickness of the inversion layer by plotting the electron concentration vertically from the surface of the substrate the point at which n=ni determines the boundary of the inversion layer.

You can also plot the energy level diagram including the Fermi level and the intrinsic Fermi level. The point at which both levels intercept will be the intrinsic

point.

Best wishes

Thank you Abdelhalim abdelnaby Zekry , Muhammad Hamza El-Saba and Aparna Sathya Murthy

Muhammad Hamza El-Saba sir, can you please tell me how to calculate NS or throw some light over calculating NS?