For erasing four-terminal semiconductor Non-Volatile Memory (NVM) devices, we apply a high positive voltage bias to the control gate with source, substrate and drain electrodes tied to the ground voltage for moving out stored charges in the charge storage material to the control gate. For improving erasing efficiency and NVM device endurance life by lowering applied voltage biases and reducing the applied voltage time durations, we engineer the lateral impurity profile of the control gate near dielectric interface such that tunneling occurs on the small lateral region of the control gate near the dielectric interface. We also apply the non-uniform thickness of coupling dielectric between the control gate and the storage material for the NVM device such that the tunneling for the erase operation occurs within the small thin dielectric areas, where the electrical field in thin dielectric is the strongest for tunneling erase operation.