The slab effective index difference between the transverse-electric (TE) and transverse-magnetic (TM) polarizations was utilized to obtain complete photonic bandgap (CPBG) in a silicon nitride (SixNy) photonic crystal slab. For this, coincident frequency range in the TE photonic bandgap (PBG) and TM PBG, which denotes the CPBGs of the slab, must be found with the same structure. Through adjusting the effective index pair of TE and TM polarizations by changing the thickness of the SixNy core layer, and also optimizing the structure parameters within the photonic crystal plane, a large normalized CPBG of 5.62% was theoretically obtained in a slab of SixNy with a refractive index of 2.5. Moreover, based on the obtained CPBG, a microcavity which could support both TE and TM polarization was theoretically demonstrated. The cavity modes for different polarizations were both well confined, which proved the reliability of the CPBG. In addition, using the same method, the lowest refractive index of SixNy on silica slab for a CPBG could be extended to as low as 2. The results indicate that there is potential for development of various high-performance CPBG devices based on SixNy slab technology.