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

AbstractThe work in this thesis is focussed on obtaining fast, efficient solutions to the Schroedinger-Poisson model of electron states in microelectronic devices. The self-consistent solution of the coupled system of Schroedinger-Poissonequations poses many challenges. In particular, the three-dimensional solution is computationally intensive resulting in long simulation time, prohibitive memory requirements and considerable computer resources such as parallel processing and multi-core machines. Consequently, an approximate analytical solution for the coupled system of Schroedinger-Poisson equations is investigated. Details of the analytical techniques for the approximate solution are developed and the original approach is outlined. By introducing the hyperbolic secant and tangent functions with complex arguments, the coupled system of equations is transformed into one for which an approximate solution is much simpler to obtain. The method solves Schroedinger’s equation first by approximating the electrostatic potential in Poisson’s equation and subsequently uses this solution to solve Poisson’s equation. The complete iterative solution for the coupled system is obtained through implementation into Matlab. The semi-analytical method is robust and is applicable to one, two and three dimensional device architectures. It has been validated against alternative methods and experimental results reported in the literature and it shows improved simulation times for the class of coupled partial differential equations and devices for which it was developed.