In the fabrication of MgB₂ superconducting tapes, doping with nano-sized SiC is effective for enhancing the critical current density (J_c) under magnetic fields. It has been reported that the J_c enhancement is due to the formation of nano-sized silicides such as Mg₂Si and the substitution of C atoms for B atoms in the MgB₂ crystals. In this work, we report more effects of SiC doping on the microstructure formation in MgB₂ tapes. MgB₂/Fe tapes were fabricated using an in-situ powder-in-tube method with MgH₂ as the precursor powder. Analytical transmission electron microscopy combined with a focused ion-beam microsampling technique was used for microstructural characterization. Overall microstructures in the tapes were characterized as densely crystallized MgB₂ areas with 10-200 nm grain size, partially crystallized MgB₂ areas mainly containing MgO and amorphous B-rich phases, and a number of holes and cracks. It was found that SiC doping leads to forming equiaxial granular structures of MgB₂. A significant difference in the distribution of O atoms was observed between the SiC-doped and non-doped MgB₂ tapes. Based on these results, mechanisms of the microstructural formation and J_c enhancement as the results of SiC doping are discussed.