Avalanche multiplication effect is to amplify small signal by operating the pn-junction at breakdown voltage. In this thesis, we analyze the physics of avalanche breakdown, and try to get mean gain and noise factor by simulation. With simulated mean gain and noise factor, we can extract the ionization ratio, dark current, sensitivity, and gain-bandwidth product for a certain structure. Base on theory and simulation, we will analyze both silicon-germanium and germanium based avalanche photodetector, and give a summary for these avalanche photodetector. The result shows that, germanium based avalanche photodetector owns large dark current when we operate at breakdown voltage, which gives bad sensitivity. In contrast, silicon-germanium avalanche photodetector can be improved by changing injection type and splitting absorption and multiplication region.