Inversion charge density of MOS transistor with generalized logistic functions

In this paper, the expression for the charge density in inversion layer at the surface of semiconductor has been improved. The improvement is related to the replacement of an empirical smoothing factor by new one which has generalized logistic (GL) functional form. The introduction of the GL function of the second type in the original interpolating expression leads to continual and smooth transition of the inversion charge density (ICD) between different regions of metal-oxide-semiconductor (MOS) operation. Moreover, in this way any empirical determinations are avoided. The simulated values of the ICD match closely with the numerical results of implicit charge sheet model for a wide range of dopant concentration and oxide thickness. In addition, the proposed GL fitting procedure has been also extended in the case where quantum mechanical effects play important role in inversion mode of scaled MOS devices.