The Coulomb blockade region was measured directly in an experimental single-electron memory device. The device was constructed with multiple-tunnel junctions (MTJ) formed by making a sidegated constriction in δ-doped GaAs. The Coulomb blockade region is defined by electron transfer rates of less than 10 electrons per second. At low values of sidegate voltages in the MTJ an enhancement of the Coulomb blockade is observed and explained by the formation of a nonuniform electrostatic potential in the semiconductor tunnel junctions.