An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method

Abstract

Capacitive micromachined ultrasonic transducer (CMUT) multilayer membrane plays an important role in the performance metrics including the transmitting efficiency and the receiving sensitivity. However, there are few studies of the multilayer membranes. Some analytical models simplify the multilayer membrane as monolayer, which results in inaccuracies. This paper presents a new analytical model for CMUTs with multilayer membranes, which can rapidly and accurately predict static deflection and response frequency of the multilayer membrane under external pressures. The derivation is based on the Ritz method and Hamilton’s principle. The mathematical relationships between the external pressure, static deflection, and response frequency are obtained. Relevant residual stress compensation method is derived. The model has been verified for three-layer and double-layer CMUT membranes by comparing its results with finite element method (FEM) simulations, experimental data, and other monolayer models that treat CMUTs as monolayer plates/membranes. For three-layer CMUT membranes, the relative errors are ranging from 0.71%–3.51% for the static deflection profiles, and 0.35%–4.96% for the response frequencies, respectively. For the double-layer CMUT membrane, the relative error with residual stress compensation is 4.14% for the central deflection, and −1.17% for the response frequencies, respectively. This proposed analytical model can serve as a reliable reference and an accurate tool for CMUT design and optimization.

Selective Ultrasonic Gravimetric Sensors Based on Capacitive Micromachined Ultrasound Transducer Structure—A Review

“…This model is ideal in situations where a quick solution is needed for general characteristics of CMUT sensor such as collapse voltage, membrane displacement, and electrodynamics [ 50 , 51 ]. Furthermore, the principles of parallel plate capacitor theory are utilized in finite element modeling of CMUTs, where it is segmented into many parallel plate capacitors, which allows an approximation of the electrostatic force that is applied to each element [ 49 , 52 , 53 , 54 ].…”

“…where is the mass constant, is the damping constant, is the spring constant, is the electric loading force, is the acoustic loading force, and is the force due to atmospheric pressure [1]. This model is ideal in situations where a quick solution is needed for general characteristics of CMUT sensor such as collapse voltage, membrane displacement, and electrodynamics [50,51]. Furthermore, the principles of parallel plate capacitor theory are utilized in finite element modeling The top electrode is attracted to the bottom electrode under direct current (DC) bias, oscillations can be excited by the alternating current (AC), whereas at equilibrium, the mechanical spring force of the membrane counters the electrostatic force.…”

“…where m p is the mass constant, r p is the damping constant, k p is the spring constant, f el is the electric loading force, f ac is the acoustic loading force, and f p 0 is the force due to atmospheric pressure p 0 [1]. This model is ideal in situations where a quick solution is needed for general characteristics of CMUT sensor such as collapse voltage, membrane displacement, and electrodynamics [50,51]. Furthermore, the principles of parallel plate capacitor theory are utilized in finite element modeling of CMUTs, where it is segmented into many parallel plate capacitors, which allows an approximation of the electrostatic force that is applied to each element [49,[52][53][54].…”

Fabrication and Characterization of Capacitive Micromachined Ultrasonic Transducers with Low-Temperature Wafer Direct Bonding

“…Ultrasonic transducers are widely used in medical imaging, gas-flow metering, industrial cleaning and non-destructive testing. In many areas of application, capacitive micromachined ultrasonic transducers (CMUTs) have been considered an attractive alternative to conventional piezoelectric transducers [ 1 , 2 , 3 ]. CMUTs can be batch produced with photolithography and other mature techniques in semiconductor industries, which is difficult with piezoelectric transducers [ 4 ].…”