A MEMS ultrasonic transducer, MUT, device, comprising a semiconductor body of semiconductor material which defines a support structure, has a first and a second main face opposite to each other along a first axis and integrates at least one MUT element including: - a modulation cavity which extends into the semiconductor body from the second main face towards the first main face; - a membrane body of the semiconductor body, which extends along the first axis between the modulation cavity and the first main face and which is fixed to the support structure so as to be suspended on the modulation cavity, the membrane body comprising a central portion and one or more extremal portions (67") which are interposed, orthogonally to the first axis, between the central portion and the support structure and which mutually couple the central portion and the support structure, the central portion defining at least one transduction membrane body and the one or more extremal portions (67") defining a modulation membrane body; - a piezoelectric modulation structure which extends on the modulation membrane body, on the first main face, and forms, with the modulation membrane body, a modulation membrane of the MUT element, suspended on the modulation cavity; - at least one transduction cavity which extends into the central portion of the membrane body, the transduction membrane body extending along the first axis between the transduction cavity and the first main face; and - a piezoelectric transduction structure which extends on the transduction membrane body, on the first main face, and forms, with the transduction membrane body, a transduction membrane of the MUT element, suspended on the transduction cavity, wherein the modulation membrane body has a first thickness (S 1) along the first axis, and the transduction membrane body has, along the first axis, a second thickness (S 2) smaller than the first thickness (S 1), wherein the piezoelectric modulation structure is electrically controllable to vibrate the modulation membrane at a first vibration frequency and the piezoelectric transduction structure is configured to generate and/or detect the vibration of the transduction membrane at a second vibration frequency higher than the first vibration frequency, in order to emit and/or receive, by the transduction membrane, acoustic waves at a frequency (f o) which depends on the first vibration frequency and on the second vibration frequency. - a modulation cavity which extends into the semiconductor body from the second main face towards the first main face; - a membrane body of the semiconductor body, which extends along the first axis between the modulation cavity and the first main face and which is fixed to the support structure so as to be suspended on the modulation cavity, the membrane body comprising a central portion and one or more extremal portions (67") which are interposed, orthogonally to the first axis, between the central portion and the support structure and which mutually couple the central portion and the support structure, the central portion defining at least one transduction membrane body and the one or more extremal portions (67") defining a modulation membrane body; - a piezoelectric modulation structure which extends on the modulation membrane body, on the first main face, and forms, with the modulation membrane body, a modulation membrane of the MUT element, suspended on the modulation cavity; - at least one transduction cavity which extends into the central portion of the membrane body, the transduction membrane body extending along the first axis between the transduction cavity and the first main face; and - a piezoelectric transduction structure which extends on the transduction membrane body, on the first main face, and forms, with the transduction membrane body, a transduction membrane of the MUT element, suspended on the transduction cavity, wherein the modulation membrane body has a first thickness (S 1) along the first axis, and the transduction membrane body has, along the first axis, a second thickness (S 2) smaller than the first thickness (S 1), wherein the piezoelectric modulation structure is electrically controllable to vibrate the modulation membrane at a first vibration frequency and the piezoelectric transduction structure is configured to generate and/or detect the vibration of the transduction membrane at a second vibration frequency higher than the first vibration frequency, in order to emit and/or receive, by the transduction membrane, acoustic waves at a frequency (f o) which depends on the first vibration frequency and on the second vibration frequency. wherein the modulation membrane body has a first thickness (S 1) along the first axis, and the transduction membrane body has, along the first axis, a second thickness (S 2) smaller than the first thickness (S 1), wherein the piezoelectric modulation structure is electrically controllable to vibrate the modulation membrane at a first vibration frequency and the piezoelectric transduction structure is configured to generate and/or detect the vibration of the transduction membrane at a second vibration frequency higher than the first vibration frequency, in order to emit and/or receive, by the transduction membrane, acoustic waves at a frequency (f o) which depends on the first vibration frequency and on the second vibration frequency.