Two-dimensional binary-phase diffraction gratings which can be employed to fabricate two- and three-dimensional periodic structures are designed and analyzed using rigorous coupled-wave analysis. These gratings serve as phase-masks which generate several diffracted waves from a normally incident beam and thus can produce a periodic interference pattern in space via nearfield holography. The properties of the diffracted beams can be controlled by varying the polarization and wavelength of the incident beam, surface-profile, groove depth and duty cycle of the mask. For the two-dimensional structure, optimum results can be obtained when the diffraction efficiency of the zero-order beam is minimized while that of the first-order maximized. On the other hand, when the diffraction efficiency of the zero-order is appreciable or even greater than other orders, we can obtain a variety of three-dimensional interference patterns which may be used to fabricate photonic crystals of tetragonal-body-centered and hexagonal structures in a submicron scale. scale.