A normally-off HEMT transistor includes a heterostructure including a channel layer and a barrier layer on the channel layer; a 2DEG layer in the heterostructure; an insulation layer in contact with a first region of the barrier layer; and a gate electrode through the whole thickness of the insulation layer, terminating in contact with a second region of the barrier layer. The barrier layer and the insulation layer have a mismatch of the lattice constant (“lattice mismatch”), which generates a mechanical stress solely in the first region of the barrier layer, giving rise to a first concentration of electrons in a first portion of the two-dimensional conduction channel which is under the first region of the barrier layer which is greater than a second concentration of electrons in a second portion of the two-dimensional conduction channel which is under the second region of the barrier layer.