Title: Quantum corrections: a multilevel solver for the density-gradient equation

Authors: Hedley Morris, Alfonso Limon

Addresses: Department of Mathematics, San Jose State University, OneWashington Square, San Jose, CA 95192, USA. ' School of Mathematical Sciences, Claremont Graduate University, 710 N. College Avenue, Claremont, CA 91711, USA

Abstract: Miniaturisation of integrated circuits continues to shrink device lengths to such an extent that quantum tunnelling and confinement effects change the behaviour of MOSFET devices. In this paper, we present a methodology by which to model the gate region of an n-Metal Oxide Semiconductor (MOS) device using a simplified version of the density-gradient equations. The resulting singularly perturbed ODEs are solved using an adaptive wavelet collocation method that adapts dynamically to the boundary layer. Our results are shown to be in good agreement with those from a direct numerical solution of the Schrodinger-Poisson system.

Keywords: MOSFETs; quantum tunnelling; density-gradient equations; singular perturbation; adaptive mesh refinement; adaptive wavelet collocation; nanoscale technology; metal oxide semiconductors; MOS; n-MOS; nanotechnology; miniaturisation; integrated circuits.

DOI: 10.1504/IJCSE.2006.012763

International Journal of Computational Science and Engineering, 2006 Vol.2 No.3/4, pp.119 - 128

Available online: 14 Mar 2007 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article