We report on a first-principles band structure calculation of twin boundaries in 3C-SiC, Si, and diamond, based on the density functional theory in the local density approximation. It is found that the electron wave functions belonging to the conduction and valence band edge states in 3C-SiC tend to be localized almost exclusively on different sides of the boundaries, while there is no such feature in Si and diamond. We have interpreted these localization and segregation phenomena as a consequence of the electrostatic field caused by the spontaneous polarization due to the hexagonal symmetry around twin boundaries. A mechanism for the creation of twin boundaries, i.e., propagation of partial dislocations in neighboring basal planes, has been investigated using total energy calculations, and it has been realized that the double-intrinsic-stacking-fault structure in 3C-SiC, coinciding with the extrinsic stacking faults, is much energetically favored.