Authors: H. Abebe and E. Cumberbatch
Affilation: MOSIS, United States
Pages: 218 - 221
Keywords: mathematical modeling
A 1-dimensional analytic quantum mechanical effects correction formula for the MOSFET inversion charge and I-V characteristics are derived from the density gradient (DG) model 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 based on the boundary layer theory that was first introduced by Prandtl in 1904. The general technique is called the method of matched asymptotic expansions, the techniques has been refined and improved over many years of use. The asymptotic analysis presented in  was improved to achieve explicit formula in . M.G. Ancona, , introduced the DG theory to model quantum effects in electron and hole transport equations. The numerical simulation results of the I-V and the Capacitance-Voltage (C-V) characteristics using the DG model showed good comparison with data, see [5,6]. This numerical approach has been useful at the device simulation level. However, for circuit analysis application a simple analytic model is preferable. This work presents a physically based analytical solution for the DG model and there is a good agreement of the I-V model compared with the numerical data, see Figure 1. We believe that these models are very useful to improve the SPICE circuit simulation in advanced VLSI since the quantum tunneling and confinement effects are very significant in nanoscale MOSFET devices.