Three-dimensional simulation is used to study the electron beam induced current collected by a nano-contact forming a nano-junction. For the calculation the surface recombination velocity is supposed to be either infinite or zero. The influence of the bulk diffusion length, energy of the incident electron beam, shape and size of the depletion zone beneath the nano-contact on the induced current collected by the nano-junction is studied. From the fit of the simulated data, the minority carrier effective diffusion length is extracted, and its variation with the electron beam energy is compared with experimental measurements obtained with the nano-EBIC (electron beam induced current) technique that we have developed by combining scanning probe microscopy and scanning electron microscopy. The effective diffusion length is an increasing function with electron beam energy up to a certain value beyond which it decreases. The simulation shows that the same behavior also occurs in the case of the conventional detection by a semi-infinite Schottky contact perpendicular to the electron beam. This is the first time, to our knowledge, that this behavior is pointed out.