Effects of the parameters of each layer on the performance of back-illuminated separate absorption and multiplication hetero-junction AlGaN avalanche photodiodes (APDs) with the polarization effect are investigated numerically, and the detailed physical mechanisms are explained. The results show that the breakdown voltage for the APDs can lower significantly and the gain increases pronouncedly with the optimization of these parameters. The maximum gain for AlGaN APDs with p-GaN layer has been improved more than 300%. This is because the polarization induced charge at the GaN/Al0.4Ga0.6N hetero-interface controls the distribution of the electric field of multiplication, inserting and absorption layer, and enhances the efficiency of injection and multiplication of carriers. Meanwhile, the optimization of the parameters can decrease the dark current of APDs at breakdown voltage.