Thesis

# MODELLING OF SEMICONDUCTOR DEVICES FOR ICS AND VLSI

Thesis for: M.Sc, Advisor: M. Elbanna, T. Namoor

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Sameh Ahmed Yousry Elnaggar, Aug 18, 2015 Available from: Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.

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**ABSTRACT:**A model hierarchy for semiconductor devices is presented, in particular kinetic models (Boltzmann and quantum Boltzmann equations) and fluid dynamical models (hydrodynamic, energy-transport and drift-diffusion equations). Fluid dynamical models including quantum correction terms are also discussed. The links between the various models are given. - [Show abstract] [Hide abstract]

**ABSTRACT:**We present a modification to the divide-and-conquer algorithm of Guibas & Stolfi [GS] for computing the Delaunay triangulation of n sites in the plane. The change reduces its &THgr;(n log n) expected running time to &Ogr;(n log n) for a large class of distributions which includes the uniform distribution in the unit square. The modified algorithm is significantly easier to implement than the optimal linear-expected-time algorithm of Bentley, Weide & Yao [BWY]. Unlike the incremental methods of Ohya, Iri & Murota [OIM] and Maus [M] it has optimal &Ogr;(n log log n) worst-case performance. The improvement extends to the composition of the Delaunay triangulation in the Lp metric for 1 < p ≤ ∞. Experimental evidence presented demonstrates that in the Euclidean case the modified algorithm performs very well for n ≤ 216, the range of the experiments. We conjecture that its average running time is no more than twice optimal for n less than seven trillion. - [Show abstract] [Hide abstract]

**ABSTRACT:**Given the anisotropic Poisson equation ¡r ¢ Krp = f, one can convert it into a system of two first order PDEs: the Darcy law for the flux u = ¡Krp and conservation of mass r ¢ u = f. A very natural mixed finite volume method for this system is to seek the pressure in the nonconforming P1 space and the Darcy velocity in the lowest order Raviart-Thomas space. The equations for these variables are obtained by integrating the two first order systems over the triangular volumes. In this paper we show that such a method is really a standard finite element method with local recovery of the flux in disguise. As a consequence, we compare two approaches in analyzing finite volume methods (FVM) and shed light on the proper way of analyzing non co-volume type of FVM. Numerical results for Dirichlet and Neumann problems are included.