Computational and analytical methods for the simulation of electronic states and transport in semiconductor systems.

摘要

The work in this thesis is focussed on obtaining fast, e cient solutions toudthe Schroedinger-Poisson model of electron states in microelectronic devices.udThe self-consistent solution of the coupled system of Schroedinger-Poissonudequations poses many challenges. In particular, the three-dimensional solutionudis computationally intensive resulting in long simulation time, prohibitiveudmemory requirements and considerable computer resources such asudparallel processing and multi-core machines.udConsequently, an approximate analytical solution for the coupled systemudof Schroedinger-Poisson equations is investigated. Details of the analyticaludtechniques for the approximate solution are developed and the originaludapproach is outlined. By introducing the hyperbolic secant and tangentudfunctions with complex arguments, the coupled system of equations is transformedudinto one for which an approximate solution is much simpler to obtain.udThe method solves Schroedinger's equation rst by approximating the electrostaticudpotential in Poisson's equation and subsequently uses this solutionudto solve Poisson's equation. The complete iterative solution for the coupledudsystem is obtained through implementation into Matlab.udThe semi-analytical method is robust and is applicable to one, two andudthree dimensional device architectures. It has been validated against alternativeudmethods and experimental results reported in the literature and itudshows improved simulation times for the class of coupled partial di erentialudequations and devices for which it was developed.