Nanotech 2005 Vol. 3
Nanotech 2005 Vol. 3
Technical Proceedings of the 2005 NSTI Nanotechnology Conference and Trade Show, Volume 3

Computational Methods, Numerics and Software Tools Chapter 10

A Wavelet Method for the Density-Gradient Equation

Authors: H. Morris and A. Limon

Affilation: San Jose State University, United States

Pages: 700 - 703

Keywords: quantum tunneling, density-gradient equation, unstructured grids, wavelets, boundary layer.

As MOSFET device lengths have shrunk to submicron level, so too has the oxide thickness steadily reduced. At around 4-5nm thicknesses quantum effects start to become noticeable as electrons are able to tunnel through the oxide layer. The Density-Gradient equation is a means of calculating approximate quantum corrections to existing formulae without solving the full Poisson-Schodinger system. The problem of solvingdensity gradient equationsthe gate region of a MOSFET is considered. These equations comprise a singularly perturbed system of ordinary differential equations with boundary layer type solutions. In order to treat the solution in the boundary layer correctly, special numerical techniques are needed. Several methods have been proposed in literature and include nonlinear discretization schemes which appear to be sensitive to boundary conditions. We therefore propose a new way to solve the equations using a wavelet method similar to methods used in chemical physics. This wavelet method allows us to combine the best features of each of the exiting approaches.

A Wavelet Method for the Density-Gradient Equation

ISBN: 0-9767985-2-2
Pages: 786
Hardcopy: $109.95