Direct electron beam irradiation without static bias has been used to produce stable structures of ferroelectric domain inversion in LiNbO$_3$ and Nd$^{3+}$ doped LiNbO$_3$ single crystals. Large size cylinder-shaped domain-inverted regions, around 40 μm diametre and 500 μm thick, have been achieved in both types of crystals under the same experimental conditions. Raman spectroscopy has been used to analyze the effect of electron irradiation on the domain-inverted regions in the pure and Nd$^{3+}$ doped LiNbO$_3$ single crystals. The results evidence the structural equivalence of the reversed structures and thus, the suitability of this electron bombardment as a poling technique for high quality photonic devices.