An analysis is presented on the statistics of deep‐level amphoteric traps in insulators and at interfaces (insulator boundaries) in terms of the occupancy functions for neutral and ionized trapping centers as a function of free carrier injection and spatial distribution of centers. Amphoteric traps are postulated for bulk insulator traps, such as silicon nitride in nonvolatile, erase‐write, semiconductor memory structures. In addition, amphoteric traps may be observed at interfacial boundaries, such as SiO2‐Si3N4, SiO2‐Al2O3, Si‐SiO2, and insulator‐liquid with site bonding. Under free carrier electron injection we find the characteristic trapped‐charge centroid movement decreases for small values ofRn=&sgr;+n/&sgr;0n, the ratio of capture cross sections for ionized to neutral trapping centers. These results reduce to Arnett’s treatment for single‐occupancy trapping centers (Rn≫1). Efficient conversion of positive (unoccupied) to negative (double‐occupancy) charged centers occurs under free carrier electron injection withRn&bartil;1. An analogous situation exists for the reverse operation, namely, conversion of negative to positive charged centers under free carrier hole injection.