Electromagnetically induced transparency has attracted much attention because of its basic characteristics and its potential applications. With the help of the pump field, the detection field can be transmitted transparently in the medium. When the standing wave field is used as the pump field, the electromagnetically induced transparent medium becomes an electromagnetically induced grating. The electromagnetically induced grating effect is widely used in opticalpath switch, optical storage, quantum Talbot effect, atomic wave interferometry, etc. Its scheme based on electromagnetically induced transparency mainly uses enhanced dispersion to enhance spatial phase modulation, so as to enhance diffraction efficiency. In this paper, spontaneously generated coherence inducing electromagnetically induced phase gratings are studied and compared in different three-level atomic systems: Lamda-type, Ladder-type and V-type. Spontaneously generated coherence refers to the interference between spontaneous emission channels. In Lamda-type and V-type systems, spontaneous emission from a single excited state to two lower near degenerate energy levels or from two near degenerate higher energy levels to the atomic ground state will interfere with each other. Spontaneously generated coherence also probably appears in the Ladder type system in the case of equidistant atomic energy levels. The existence of this coherence depends on whether the two transition dipole moments are orthogonal. The results show that, spontaneously generated coherence can significantly enhance the first-order diffraction efficiency. However the degree of enhancement is different in different systems, and the dependence on the degree of atomic coherence is also different. For Lamda and Ladder type systems, the first-order diffraction efficiency increases with the enhancement of spontaneous emission coherence, especially for the Ladder-type system. In contrast, for the V-type system, the first-order diffraction efficiency increases in the region where the coherence of spontaneous emission is relatively weak. This research has potential applications in the field of quantum optical devices.