Microchannel plates based on amorphous silicon have the inherent capability to overcome the existing spatial and temporal resolution limitations of single photon detectors. A Monte Carlo model-based study is presented here that serves to exploit their full potential. The dynamics of electron multiplication throughout the microchannels in the presence of an electric field is modelled based on electron emission models and experimental measurements. The geometrical limits for suitable amplification and the expected time resolution of amorphous silicon based microchannel plates are presented. Furthermore, the model is implemented in a finite element method simulator to estimate electron multiplication gain and time response for channels with various geometries. With gains above 1000 and timing jitters below 3 ps that are shown for selected geometries, AMCPs enable ultrafast measurements for medical applications and single photon detection.