A piezoelectric micro-machined ultrasonic transducer (PMUT) comprising: a semiconductor body having a first cavity and a membrane, which is suspended over the first cavity and faces a front side of the semiconductor body; and a piezoelectric transducer assembly extending at least in part on the membrane, which may be actuated for generating a deflection of the membrane. A second cavity extends buried in a peripheral region of the membrane and delimits a central region of the membrane. Moreover, the peripheral portion has a stiffness lower than the stiffness of the central portion.