Statistical analysis of quantized inversion layer in MOS devices with ultra-thin gate oxide and high substrate doping levels

The degree of degeneracy of a quantized inversion layer in an MOS structure is investigated by a fully quantum mechanical approach via self-consistent solution of Schrodinger and Poisson equations. The relative error of carrier sheet density induced by Boltzmann statistics is used as a measurement of the degeneracy. It is shown that the degree of degeneracy of the inversion layer is much weaker due to the quantization of carrier energy compared with the semi-classical case.