We have developed a space distribution method for intense sub-nanosecond or even picosecond positron burst detection using a detector array. In this method, piled signals will be generated when more than one photon of the burst is captured by the same detector cell. The way of setting energy threshold of 511 keV could eliminate most of piled signals, but the counts of piled signals that have lower energy than the threshold are not affected. In this paper, a Geant4 model is built to investigate the dependence of these low-energy piled signals counts on scintillator materials, as well as the size of the detector. The results can provide theoretical support for designing suitable array detectors in practice.