A diffusion model for hydrogen (H) in crystalline silicon was established which takes into account the charged state conversion, junction field, mobile traps, and complex formation and dissociation at dopant and trap sites. Carrier exchange among the various charged species is a "fast" process compared to the diffusion process. A numerical method was developed to solve the densities of various charged species from the Poisson's equation that involves shallow-level dopants and one "negative U" impurity, e.g., H. Time domain implicit method was adopted in finite difference scheme to solve the fully coupled equations.

Limiting versions of the model were applied to the problems that are of interest to photovoltaics. Simplified trap-limited model was used to describe the low temperature diffusion profiles, assuming process-induced traps, a constant bulk trap level, and trapping / detrapping mechanisms. The results of the simulation agreed with those obtained from experiments. The best fit yielded a low surface free H concentration, C_s (~ 10¹⁴ cm ^-3) from high temperature extrapolated diffusivity value. In the case of ion beam hydrogenation, mobile traps needed to be considered. PAS analysis showed the existence of vacancy-type defects in implanted Si substrates. Simulation of hydrogen diffusion in pn junction was first attempted in this work. The order of magnitude of C_s (~10¹⁴ cm ^-3) was confirmed. Simulation results showed that the preferred charged state of H is H^- (H⁺) in n^- (p^-) side of the junction. The accumulation of H^- (H⁺) species on n⁺ (p) side of the n⁺-p (P⁺ -n) junction was observed, which could retard the diffusion in junction. The diffusion of hydrogen through heavily doped region in a junction is traplimited. Several popular hydrogenation techniques were evaluated by means of modeling and experimental observations. In particular, PECVD followed by RTP hydrogenation was found to be two-step process: PECVD deposition serves as a predeposition step of H and during RTP anneal step, H is released from the surface traps and redistributed into the bulk.