An Al0.5Ga0.5As/GaAs heterojunction field-effect transistor which consists of InAs nanodots in the barrier layer and a GaAs quantum well channel is grown by molecular beam epitaxy, and the device performance and the electron transport from the quantum well to the nanodots are studied. These InAs nanodots are grown by self-assembling in a vertically stacked form, and their optical and electrical properties are characterized by photoluminescence and capacitance-voltage measurements. The electrical injection of electrons confined at the nanodots produces a persistent electron trapping which yields a memory function in the device performance, showing a potential application for roomtemperature operation.