While the importance of atomic-scale features in silicon-based device for quantum application has been recognized and even the placement of a single atom is now feasible, the role of a dopant in the substrate has not attracted much attention in the context of quantum technology. In this paper, we report random telegraph signals (RTSs) originated from trapping and detrapping of an electron by a donor in the substrate of a p-type metal–oxide–semiconductor field-effect-transistor. RTSs, not seen when the substrate was grounded, were observed when a positive bias was applied to the substrate. The comprehensive study on the signals observed reveals that the nature of the RTSs is discrete threshold voltage variations due to the change in the depletion layer width depending on the charge state of a single dopant, neutral or positively charged.