Modeling the effect of dislocations on the minority carrier diffusion length of a semiconductor

An analysis is given of the minority carrier diffusion and collection in a semiconductor with a surface junction, in the presence of a periodic array of straight dislocations perpendicular to the surface. A dislocation is characterized by its line recombination velocity and is attributed a finite cross section. An approximate solution is obtained for the three-dimensional charge collection probability φ(r) in the unit cell of the array. The integral of φ over the unit cell is used to introduce a new definition of effective diffusion length and to give its analytical expression. It is shown that the relative reduction of diffusion length produced by the dislocation array coincides with the fractional decrease of the total number of junction-injected carriers. This result establishes a connection between the efficiency of charge collection and luminescence of a sample containing dislocations. The analysis is extended to the case of a thin sample, and is compared to previous discussions of the same problem. The consequences of the theory are illustrated by numerical examples and applications to published experimental data.