Piezoelectric ultrasonic transducer and system

A system comprising a piezoelectric ultrasonic transducer comprising:

• a cavity comprising walls and a membrane supported between the walls of the cavity for communications of ultrasonic waves, wherein the membrane comprises
• a structural layer on a side of the membrane inwards to the cavity, and
• a piezoelectric layer attached to the structural layer on an opposite side of the membrane with respect to the cavity,
• wherein a temperature coefficient of Young's modulus of the structural layer and a temperature coefficient of Young's modulus of the piezoelectric layer have opposite signs for passive temperature compensation of operating frequency of the piezoelectric ultrasonic transducer, wherein the membrane has at least one gap through the piezoelectric layer up to the structural layer;
• and
• one or more processors connected electromechanically to the piezoelectric layer for transmitting and/or receiving ultrasonic waves.