Modeling the current-voltage (I-V) characteristics of the MOSFET device with quantum mechanical effects due to thin oxide near silicon/silicon dioxide interface using asymptotic methods

A 1-dimensional physical model for the current-voltage (I–V) characteristics of the MOSFET device is developed. The significant contribution of this model is that it includes for quantum mechanical (QM) effects near the Si/SiO₂ interface of the transistor associated with very thin dielectrics. The model is derived directly from the density gradient (DG) theory using matched asymptotic expansion techniques.; The primary theoretical framework for this research is the asymptotic analysis work done by M. J. Ward on the semiconductor classical drift-diffusion (DD) equations (Ward, [3]) based on the matched asymptotic method that was first introduced by Prandtl in 1904. M. G. Ancona, [9], introduced the DG theory to model the quantum effect in the electron and hole transport equations. Since the numerical solution of the DG equation indicates a boundary layer behavior on the inversion charge density near the Si/ SiO₂ interface, matched asymptotic methods are used to solve the DG equation.; The final analytical solution is very suitable for application in SPICE circuit simulator. Furthermore, this model will be very useful for simulation of quantum effects in deep sub-micron CMOS devices and for future generations of smaller scale MOSFET.