The dielectric photonic band gap materials have received broad attention due to their distinguished performance in optical devices, microwave generation and laser acceleration. We have theoretically studied photonic band structure parameters and defected structures of ZnX (X = S, Se, Te). The cavity was formed by a periodic sequence of holes in a dielectric waveguide, with a defect formed by a larger spacing between one pair of holes. The band structures of TE modes were obtained and the frequency/transmission calculations for different geometric structures were implemented. Then, the quality factor of resonance frequency for ZnX structures were examined. High levels of the quality factor values for these structures were obtained. It is proved that these structures carry the characteristics of photonic crystals.