10 February 2014
M.Sc. (Physics) / A computer program called RAUPV was developed to simulate one-dimensional p-n structures and photo-voltaic cells. In order to simulate multilayer structures, the device is devided into a large number of discrete points with variable spacings. The physical parameters are calculated at each point, subjected to given external boundary conditions at the endpoints of the device. The physical processes are formulated from first principles, in such a way that they can be handled by numerical methods. A Newton-Raphson iteration technique is used to solve the large number of coupled, linear equations. The simulation is formulated in such a way that the equations must be solved for three variables at each point: the electron potential, the quasi-Fermi level for electrons and the quasi-Fermi level for holes. For the case of thermodinamic equilibrium, Poisson's equation is solved. A formulation is developed to handle the equation numericaly for variable intervals. Expressions for the free carrier concentrations are obtained using Fermi-Dirac statistics. Expressions for the charge density in traps are also obtained and several types of boundary conditions are considered. The program is able to calculate the band structure, charge density, internal electric field and free carrier concentrations for any multi-layer device. For the non-equilibrium case, Poisson's equation is solved simultaneously with the two continuity equations for electrons and holes. A special formulation for the current densities was developed, to assure convergence during the iteration process. Recombination is formulated in terms of capture cross-sections of trap states within the gap. Several types of boundary conditions are considered. The program is able to calculate the current densities of electrons and holes within the device and yield as output the net current through the device for a given external applied voltage. A technique was developed for the Newton-Raphson iteration to work only with the diagonals of the matrix containing the partial derivatives. This technique saves much computing time and memory. Various techniques are built into the program to assure convergence and to decrease computing time. The solar spectrum is processed in order to calculate the optical exitations within the device. Multiple reflections are taken into account and an anti-reflection layer is also simulated. The program can thus calculate current-voltage curves for a photo-voltaic cell for any given spectrum. The program runs on a PC and is able to analise p-n structures in detail. It can be used to design photo-voltaic cells using fundamental physical principles as point of departure.
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