The emission of secondary electrons from any material is governed by electron excitation in the bulk, their transport to the surface, and their escape through the surface into the vacuum. Here, we address the question of the transport of electrons in polycrystalline diamond and amorphous carbon membranes and discuss the factors that limit it. The results of the measurements of the escape depth of the secondary electrons from the membranes of submicron polycrystalline diamond and amorphous carbon films induced by the hydrogen ion impact are reported here. It is found that the escape depth for the secondary electrons emitted from diamond scales with the grain size of the crystallites in the polycrystalline diamond films and it can be very large. In contrast, for the case of the amorphous carbon membranes, we find this depth to be much shorter. The extremely high electron emission yield, which have been measured following the slowing down of the electrons or ions in diamond, can be explained by the fact that secondary electrons can move rather freely in diamond, hence, can reach the surface from large distances inside the diamond sample.