Self-Force Reduced Finite Element Poisson Solvers for Monte Carlo Particle Transport Simulators

The purpose of this master's thesis is to implement a Finite Element Poisson solver for a Monte Carlo particle transport simulator without the influence of self-forces. Self-forces are unphysical forces that come into existence when symmetries are not taken into account in a particle-mesh coupling. These self-forces are handled using Kalna's self-force reduction method. A central subject for particle transport simulators are that they need a particle-mesh coupling scheme, this is done using a Dirac delta function in the nearest-element center scheme. The particles' locations in the triangulation are needed for the particle-mesh coupling, and they are found using Guiba's and Stolfi's Point location algorithm. A linear basis is used for the Finite Element method, and the contacts are dealt with using conditions of thermal equilibrium and charge neutrality. To solve the linear system in the discretization, preconditioned Conjugate Gradient method is implemented together with the preconditioners ILUT and ILU0. The usage of these methods and their parameters are discussed, and simulations of a PN-junction is performed to verify that the implementation is working. Improvements to the self-force reduction and the particle location algorithm are made, and a relationship between background charge, particle charge, and element size is found. This relationship is used for the characteristic step length to generate a near-optimal mesh. It is found that the implementation is successful and can be used in the Monte Carlo particle transport simulator to simulate semiconductor devices