Impedance Characterization of Substrate Leakage in Wafer Bonded CMUTs

This work investigates substrate leakage in Capacitive Micromachined Ultrasonic Transducers, (CMUTs) having thin backings. CMUTs produced with solid or rigid substrates have a high Q resonance with flat baseline. However, if the operating wavelength of CMUT becomes larger than the thickness of substrate the real part of cell impedance shows elevated baselines with more leakage at DC than at higher frequencies. When a clamped CMUT membrane is excited harmonically the vibrations produced are counterbalanced by the backing medium. Hence some of the energy is coupled to substrate as loss resulting in a lower mechanical Q of resonance. We first derive this energy coupled to the backing medium using FEA analysis considering the velocity field and associated tensile stresses in a thin backing. Substrate impedance is found numerically from isotropic damping of dispersive elastic waves in the backing. This backing impedance is introduced as a shunt mechanical loss across the transduction force in equivalent circuit model. We characterize the measured impedance of CMUT cells with both FEMs and linear circuit models. Simulations results closely agree with the measured impedance levels, frequency and bandwidth of resonance.