Multiple Steady-State Solutions in a Multijunction Semiconductor Device

Multiple steady-state solutions are constructed for a multijunction semiconductor device using a combination of asymptotic and numerical techniques. The multijunction device is modeled by the drift-diffusion equations of semiconductor physics. In the drift-diffusion model three sign alterations of the doping are assumed, and a Shockley-Read-Hall recombination is allowed for. In the parameter range for which the current-voltage relation is monotonic, the quasi-neutral approximation to the drift-diffusion model is found to be valid and solutions are constructed asymptotically in the limit of large doping densities. In contrast, in the parameter range for which the current-voltage relation is S-shaped, the quasi-neutral approximation is found to poorly approximate solutions to the full model on the middle and lower branches. A suitable modification to the quasi-neutral approximation is then introduced to describe the middle and lower branches of the current-voltage relation under the assumption of no recombination. The asymptotic results are compared to numerical solutions of the drift-diffusion model.