It is well known that the gain‐bandwidth product of an avalanche photodiode can be increased by utilizing a thin multiplication region. Previously, measurements of the excess noise factor of InP/InGaAsP/InGaAs avalanche photodiodes with separate absorption and multiplication regions indicated that this approach could also be employed to reduce the multiplication noise. This letter presents a systematic study of the noise characteristics of GaAs homojunction avalanche photodiodes with different multiplication layer thicknesses. It is demonstrated that there is a definite ‘‘size effect’’ for multiplication regions less than approximately 0.5 &mgr;m. A good fit to the experimental data has been achieved using a discrete, nonlocalized model for the impact ionization process. ©1996 American Institute of Physics.