The application of photonic crystal,density states of triangle lattice photonic crystal with three generation of semiconducting material were calculated by plane wave expansion method (PWM).We gained maximum photonic band gap with f=0.25 in the background material′s Si,and f=0.24 in the background material′s AlP,and f=0.3 in the background material′s GaN.Maximum photonic crystal band gap of three generation of semiconductor constitution photonic crystal increases gradually compared to the first generation and the second generation.This result provides theoretic basis theoretic basis for the photonic crystal devices.