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We theoretically analyze the contrast observed at the outcrop of a threadingdislocation at the GaN(0001) surface in cathodoluminescence and electron-beaminduced current maps. We consider exciton diffusion and recombination includingfinite recombination velocities both at the planar surface and at thedislocation. Formulating the reciprocity theorem for this general case enablesus to provide a rigorous analytical solution of this diffusion-recombinationproblem. The results of the calculations are applied to an experimental exampleto determine both the exciton diffusion length and the recombination strengthof threading dislocations in a free-standing GaN layer with a dislocationdensity of $6\times10^{5}$~cm$^{-2}$.

Dislocation contrast in cathodoluminescence and electron-beam induced current maps on GaN(0001)